DEVELOPMENT OF RATIONAL
PAY FACTORS BASED ON
CONCRETE COMPRESSIVE
STRENGTH DATA
Final Report 608
Prepared by:
Busaba Laungrungrong, Ph. D. Student
Barzin Mobasher, CEE, Professor
Douglas Montgomery, IE, Professor
Ira A. Fulton School of Engineering
Arizona State University
Tempe, AZ, 85287- 5306
June 2008
Prepared for:
Arizona Department of Transportation
206 South 17th Avenue
Phoenix, Arizona 85007
in cooperation with
U. S. Department of Transportation
Federal Highway Administration
The contents of the report reflect the views of the authors who are responsible for the facts and the
accuracy of the data presented herein. The contents do not necessarily reflect the official views or
policies of the Arizona Department of Transportation or the Federal Highway Administration. This
report does not constitute a standard, specification, or regulation. Trade or manufacturers’ names that
may appear herein are cited only because they are considered essential to the objectives of the report.
The U. S. Government and The State of Arizona do not endorse products or manufacturers.
Technical Report Documentation Page:
1. Report No.
FHWA- AZ- 08- 608
2. Government Accession No.
3. Recipient's Catalog No.
4. Title and Subtitle
5. Report Date
June 2008
DEVELOPMENT OF RATIONAL PAY FACTORS BASED ON CONCRETE
COMPRESSIVE STRENGTH DATA
6. Performing Organization Code
7. Author
Busaba Laungrungrong, Barzin Mobasher, Douglas Montgomery
8. Performing Organization Report No.
9. Performing Organization Name and Address
10. Work Unit No.
Departments of Civil and Environmental Engineering and Industrial Engineering
Arizona State University
Tempe, Arizona, 85287- 5306
11. Contract or Grant No.
SPR- PL- 1( 69) 608
12. Sponsoring Agency Name and Address
ARIZONA DEPARTMENT OF TRANSPORTATION
206 S. 17TH AVENUE
13. Type of Report & Period Covered
Sept. 2006 – Nov. 2007
Final Report
PHOENIX, ARIZONA 85007
Project Manager:
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared in cooperation with the U. S. Department of Transportation, Federal Highway Administration
16. Abstract
This research project addresses the opportunity to contain the escalating costs of concrete materials in construction projects. Both
statistical process control and rational acceptance criteria show that quality improvement and cost savings can be achieved. The
report presents a comprehensive statistical evaluation of the compressive strength of concrete used in various sectors of the
transportation infrastructure in Arizona. The proposed methodology is applicable to the concrete materials specified at other
industrial sectors such as privately financed construction projects. Several case studies are conducted based on actual field data to
show that performance based specification procedures can be used to improve the quality control process while decreasing the overall
construction costs. Three sets of compressive data from various construction projects were selected. These data were evaluated by
means of statistical process- control tools while state- of- the art procedures were utilized to evaluate the strength as a measure of
quality. Several acceptance criteria based on the percent within limit ( PWL) and operational- characteristic curves ( OC) are proposed
and evaluated. Various pay factor equations are considered and the historical records are evaluated based on hypothetical pay factor
equations.
The report furthermore addresses the strengths and weaknesses associated with the present acceptance criteria in comparison to a
PWL based method. Opportunities in sampling, optimization, operational- characteristics curves, and quality specification are
discussed in detail. It is shown that the cost savings associated with both performance based- specification and quality control,
sufficiently justify the amount of effort needed in order to implement these methodologies in the development of specifications.
17. Key Words
Pay factor, exploratory data analysis, standard deviation,
acceptance quality level, quality control, out of control data,
lower/ upper specification limits, X- bar, S- chart, design
compressive strength, required compressive strength,
concrete quality
18. Distribution Statement
Document is available to the
U. S. public through the
National Technical Information
Service, Springfield, Virginia
22161
23. Registrant's Seal
19. Security Classification
Unclassified
20. Security Classification
Unclassified
21. No. of Pages
22. Price
98
SI* ( MODERN METRIC) CONVERSION FACTORS
APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS
Symbol When You Know Multiply By To Find Symbol Symbol When You Know Multiply By To Find Symbol
LENGTH LENGTH
in inches 25.4 millimeters mm mm millimeters 0.039 inches in
ft feet 0.305 meters m m meters 3.28 feet ft
yd yards 0.914 meters m m meters 1.09 yards yd
mi miles 1.61 kilometers km km kilometers 0.621 miles mi
AREA
AREA
in2 square inches 645.2 square millimeters mm2 mm2 square millimeters 0.0016 square inches in2
ft2 square feet 0.093 square meters m2 m2 square meters 10.764 square feet ft2
yd2 square yards 0.836 square meters m2 m2 square meters 1.195 square yards yd2
ac acres 0.405 hectares ha ha hectares 2.47 acres ac
mi2 square miles 2.59 square kilometers km2 km2 square kilometers 0.386 square miles mi2
VOLUME VOLUME
fl oz fluid ounces 29.57 milliliters mL mL milliliters 0.034 fluid ounces fl oz
gal gallons 3.785 liters L L liters 0.264 gallons gal
ft3 cubic feet 0.028 cubic meters m3 m3 cubic meters 35.315 cubic feet ft3
yd3 cubic yards 0.765 cubic meters m3 m3 cubic meters 1.308 cubic yards yd3
NOTE: Volumes greater than 1000L shall be shown in m3.
MASS MASS
oz ounces 28.35 grams g g grams 0.035 ounces oz
lb pounds 0.454 kilograms kg kg kilograms 2.205 pounds lb
T short tons ( 2000lb) 0.907 megagrams
( or “ metric ton”)
mg
( or “ t”)
mg
( or “ t”)
megagrams
( or “ metric ton”)
1.102 short tons ( 2000lb) T
TEMPERATURE ( exact) TEMPERATURE ( exact)
º F Fahrenheit
temperature
5( F- 32)/ 9
or ( F- 32)/ 1.8
Celsius temperature º C º C Celsius temperature 1.8C + 32 Fahrenheit
temperature
º F
ILLUMINATION ILLUMINATION
fc foot- candles 10.76 lux lx lx lux 0.0929 foot- candles fc
fl foot- Lamberts 3.426 candela/ m2 cd/ m2 cd/ m2 candela/ m2 0.2919 foot- Lamberts fl
FORCE AND PRESSURE OR STRESS FORCE AND PRESSURE OR STRESS
lbf poundforce 4.45 newtons N N newtons 0.225 poundforce lbf
lbf/ in2 poundforce per
square inch
6.89 kilopascals kPa kPa kilopascals 0.145 poundforce per
square inch
lbf/ in2
Table of Contents
I. Executive Summary ..................................................................................................... 1
II. Introduction ................................................................................................................. 5
Objectives .......................................................................................................................... 6
Preliminary Results ............................................................................................................ 6
III. Sample Collection and Analysis Procedures ........................................................... 9
1. Preliminary Data Selection ......................................................................................... 9
1.1. ADOT Supplied Test Cases ( Series 1) ....................................................................... 9
1.2. Randomly Selected Test Cases ( Various supplier, plant, and
mix specification) ( Series 2) ................................................................................ 10
1.3. Members of the ADOT/ ARPA committee Supplied Test Cases ( Series 3) .............. 11
2. Exploratory Data Analysis ........................................................................................ 11
2.1. Exploratory Data Analysis of Series 1 ...................................................................... 12
2.2. Exploratory Data Analysis of Series 2 ...................................................................... 15
2.3. Exploratory Data Analysis of Series 3 ...................................................................... 16
3. Pay Factor Determination ......................................................................................... 16
3.1. FHWA- PWL Method .............................................................................................. 18
3.2. Current ADOT Pay Factor Determination ................................................................ 22
3.3. Proposed ADOT Pay Factor Determination ............................................................. 23
3.4. California Department of Transportation method .................................................... 25
IV. Discussion of Results ............................................................................................... 27
1. Comparing two different methods for PWL based analysis of FHWA method ....... 27
2. Sensitivity analysis of PWL and the Q- value for FHWA method ............................ 30
3. Comparing Current and New ADOT methods ......................................................... 34
4. Exploring the Comparison of Four Different Methods ............................................ 37
V. Conclusions ................................................................................................................ 41
APPENDIX A ( Probability Plots) ................................................................................. 43
APPENDIX B ( X bar- S charts for Series 1) ................................................................ 50
APPENDIX C ( X bar- S charts for Series 2) ................................................................ 59
APPENDIX D ( X bar- S charts for Series 3) ................................................................ 83
APPENDIX E ( Pay Factors) ......................................................................................... 89
APPENDIX F ( Data Information) ................................................................................ 90
REFERENCES ................................................................................................................ 91
LIST OF FIGURES
Figure 1. Correlation of Data from both the Specified Strength and the Actual
Strength of Concrete Delivered to the Job Site from a Single Ready Mix
Producer. ......................................................................................................... 7
Figure 2. Data from a Single Ready Mix Producer During a Two Year Cycle
Representing the Amount of Over- Strength Concrete Delivered. .................. 7
Figure 3. Plot of the Comparison of Strength Data Distribution to Specification ......... 8
Figure 4. Probability Plot for Series 1.......................................................................... 12
Figure 5. X- bar and S Chart for Project 8 in Series1 ................................................... 14
Figure 6. Plot of the Relationship between the Q- Value and the PWL........................ 18
Figure 7. The Defining Table of Type I and Type II Errors from
Mahboub and Hancher.................................................................................. 19
Figure 8. Plot of Relationship between PWL and Pay Factor by Category II ............. 20
Figure 9. OC Curve from Mahboub and Hancher........................................................ 20
Figure 10. The Payment Curve from Mahboub and Hancher ........................................ 21
Figure 11. Plot of the Relationship between PWL and Pay Factor
by Kentucky OC curve.................................................................................. 22
Figure 12. Comparison of the Present ADOT Pay Factor Equation ( Shown in Black)
and the Proposed Method which is Dependant on the Concrete
Strength Class ............................................................................................... 24
Figure 13 Figure 13 Comparison of two methods ( FHWA PWL
and Kentucky DOT) penalties for all series.................................................. 29
Figure 14. Plot of Relationship between Q- Value and PWL ......................................... 30
Figure 15. Plot of Pay Factor ( Penalty) between Q- Value and the PWL
by Category II .............................................................................................. 32
Figure 16. Plot of Pay Factor ( Penalty) between Q- Value and PWL
by the Kentucky OC Curve........................................................................... 32
Figure17. Penalty from both ADOT Methods............................................................... 36
Figure 18. Plot Comparing Four Methods for All Series............................................... 39
Figure A1. Probability Plot for Series 1.......................................................................... 43
Figure A2. Probability Plot for Project A: A11, A13 and A21....................................... 44
Figure A3. Probability Plot of Project B: B11, B12, B13, B21 and B22........................ 45
Figure A4. Probability Plot of Project C: C11, C12, C13, C21, C22 and C23 ............... 46
Figure A5. Probability Plot of Project D: D12, D13, D21 and D23 ............................... 47
Figure A6. Probability Plot of Project E: E11, E12, E13, E21, E22 and E23................. 48
Figure A7. Probability Plot for Series 3.......................................................................... 49
Figure B1 Tracs number: H576801C............................................................................. 50
Figure B2 Tracs number: H552501C............................................................................. 51
Figure B3 Tracs number: H407601C from plant 55041 and
mix specification 14016................................................................................ 52
Figure B4 Tracs number: H407601C from plant 60141 and
mix specification 1332439............................................................................ 53
Figure B5 Tracs number: H416001C from the Lake Havasu plant and
mix specification 2500S................................................................................ 54
Figure B6 Tracs number: H416001C from the Lake Havasu plant and
mix specification 3500S…………............................................................. 55
Figure B7 Tracs number: H319003C from the Tucson plant and
mix specification 0203- 10......................................................................... 56
Figure B8 Tracs number: H319003C from the Tucson plant and
mix specification 0203- 15 ......................................................................... 57
Figure B9 Tracs number: H313401C.......................................................................... 58
Figure C1 Project A11 ................................................................................................ 59
Figure C2 Project A13 ................................................................................................ 60
Figure C3 Project A21 ................................................................................................ 61
Figure C4 Project B11................................................................................................. 62
Figure C5 Project B12................................................................................................. 63
Figure C6 Project B13................................................................................................. 64
Figure C7 Project B21................................................................................................. 65
Figure C8 Project B22................................................................................................. 66
Figure C9 Project C11................................................................................................. 67
Figure C10 Project C12................................................................................................. 68
Figure C11 Project C13................................................................................................. 69
Figure C12 Project C21................................................................................................. 70
Figure C13 Project C22................................................................................................. 71
Figure C14 Project C23................................................................................................. 72
Figure C15 Project D12 ................................................................................................ 73
Figure C16 Project D13 ................................................................................................ 74
Figure C17 Project D21 ................................................................................................ 75
Figure C18 Project D23 ................................................................................................ 76
Figure C19 Project E11................................................................................................. 77
Figure C20 Project E12................................................................................................. 78
Figure C21 Project E13................................................................................................. 79
Figure C22 Project E21................................................................................................. 80
Figure C23 Project E22................................................................................................. 81
Figure C24 Project E23................................................................................................. 82
Figure D1 Wilson Wash.............................................................................................. 83
Figure D2 Sandy Blevens............................................................................................ 84
Figure D3 Quail Springs ............................................................................................. 85
Figure D4 Poison......................................................................................................... 86
Figure D5 Deveore...................................................................................................... 87
Figure D5 Apprentice.................................................................................................. 88
LIST OF TABLES
Table 1: Series 1 Data Set ................................................................................................... 9
Table 2: Series 2 Data Set ................................................................................................. 10
Table 3: Series 3 Data Set ................................................................................................. 11
Table 4: Factors Used for Constructing Variable Control Charts..................................... 13
Table 5: Out- of- Control Data in All Series....................................................................... 17
Table 6: Relationship between PWL and Pay Factor........................................................ 21
Table 7: Adjustment in Contract for ADOT Method........................................................ 22
Table 8: Sensitivity of Adjustment in Contract for ADOT Method ................................. 23
Table 9: Adjustment in Contract for New ADOT Method ............................................... 23
Table 10: The Value of β .................................................................................................... 24
Table 11: Penalty Calculated by the Cost per Cubic Yard.................................................. 25
Table 12: Series 1. The FHWA Penalty for both Kentucky OC Curve and
Category II Pay Factor Methods......................................................................... 27
Table 13: Series 2. The Penalty from both the Kentucky OC
and the Category II Methods............................................................................... 28
Table 14: Pay Factor in the FHWA Method Calculated
Using Different LSL and US .............................................................................. 29
Table 15: Series 3. The Results for both Methods .............................................................. 29
Table 16: Pay Factors in FHWA Category II Method Calculated
Using Different Q’s............................................................................................. 31
Table 17: Pay Factors in the FHWA Kentucky OC Method Calculated
by Using Different Q’s........................................................................................ 33
Table 18: Series 1. Comparison of Pay Factors for Current and New ADOT Methods..... 34
Table 19: Series 2. Comparison of Pay Factors for Current and New ADOT methods ..... 35
Table 20: Series 3. Comparison of Pay Factors for Current and New ADOT Methods..... 36
Table 21: Series 1. Comparison of Pay Factors for the Different Methods........................ 37
Table 22: Series 2. Comparison of Pay Factors for Different Methods.............................. 38
Table 23: Series 3. Comparison of Pay Factors for Different Methods.............................. 38
Table 24: All Series. Comparison of Pay Factors for Different Methods........................... 39
1
I. Executive Summary
Continuous development of civil infrastructure systems in support of population growth
and economic productivity for the State of Arizona is a challenge faced by many decision
makers in the planning, administrative, engineering, and executive branch of government.
The State of Arizona utilizes more than 15 million cubic yards of concrete per year; a
number that has been increasing at an annual rate of 15% during the past several years.
This volume places a tremendous strain on the resources and the supply of cement and
concrete products especially when one considers the increased demand for infrastructure
development. It is therefore natural to expect that competition for resources and material
shortages directly affects the escalating costs of construction projects and result in
construction delays.
The rapid growth of the infrastructure has resulted in an ever increasing demand on the
environment. For each ton of cement produced, a ton of carbon dioxide is emitted.
Therefore, it would be advantageous to reduce the amount of cement, aggregates, and
other natural materials that are used in construction projects without affecting the
performance. Alkali- silica reactions and sulfate attack in concrete are among the major
durability concerns in civil infrastructure systems. The corrosion of reinforcing steel,
leading to the ultimate cracking of the concrete on highway bridges, was estimated to
cost $ 8.29 billion in the U. S. A thorough understanding of the specifications will
improve the decision making process in every stage of construction and maintenance,
thus supporting a sustainable design approach.
This research project addresses areas of opportunity to contain the escalating costs of
concrete materials in construction projects. The main objective for this project is to show
that performance- based specification procedures can be used to improve the quality
control process while decreasing the overall construction costs. Through the use of
statistical process control and rational acceptance criteria, it can be shown that both a
significant improvement in quality and cost savings can be achieved. By addressing the
quality control measures, the incentives for payment based on early age or long term
properties of concrete can be developed. Both sustainable and economical design
methodologies can be addressed through proper specification guidelines.
New guidelines and cost structures for concrete materials are analyzed so that more
economical alternatives can be evaluated and considered during the preliminary design of
a project. As the cost of raw materials changes, many potential alternatives become cost
effective. Examples include performance enhancing admixtures and/ or supplementary
cementitious materials, curing, and finally quality control ( QC) parameters that affect the
cost of a project. These alternatives, which have been addressed in a different report by
the author [ 1], may not be regularly specified for highway structures due to the lack of
available field data. The focus of the present work is based on a need to better understand
the role of quality control and quality assurance in a sustainable design philosophy. The
goal is directed toward generating cross- disciplinary tools to guide us toward more
economical engineering and construction policies. Life cycle cost modeling, combined
2
with statistical quality control measures, could identify potential savings. Enabling
methodologies are proposed to help with statistical process control.
This report presents a comprehensive statistical evaluation of the compressive strength of
concrete used in various sectors of the transportation infrastructure in Arizona. The
proposed methodology is also applicable to the concrete materials specified in other
industrial sectors such as privately financed construction projects. The report
furthermore addresses the strengths and weaknesses associated with the present
acceptance criteria in comparison to the percent- within- limits ( PWL) based methods.
Opportunities in sampling, optimization, operational characteristics curves, and quality
specification are discussed in detail. It can be shown that the cost savings associated with
performance- based specification, together with good quality control, sufficiently justify
the effort needed to implement these methodologies.
Three sets of compressive data from various construction projects were selected. The
data, which were evaluated by means of statistical process control tools and state- of- the
art procedures, were utilized to evaluate the strength as a measure of quality. Several
acceptance criteria based on the percent- within- limits ( PWL) and operational characteris-tic
( OC) curves are proposed and evaluated. Various pay factor equations are considered
and the historical records are evaluated based on hypothetical pay factor equations.
Results indicate that a majority of the samples evaluated meet and far exceed the strength
requirements specified by the Arizona Department of Transportation ( ADOT)
specifications by as much as 30%- 50%. There are excessive variations in the trends of the
data which do not correlate with the specified strength of the concrete and the areas of its
applications. These represent areas of potential opportunity to reduce both the average
and standard deviations of the strength data. Reduction of the mean strength values
delivered at the expense of better quality control will translate into significant raw
materials savings.
Pay factor equations are used as the basis for payment, and they serve as a penalty or
incentive to meet the specifications. The adherence to the pay factor equations often
results in excessive over- strength design of the concrete mixtures. This study indicated
that the total amount of penalties in comparison to the cost of many projects is
insignificant. Out of a total materials cost of $ 13,590,000 for the projects studied, the
total penalties assessed were $ 124,000 ( 0.91% of total) and $ 36,200 ( 0.26% of total) for
the present and proposed ADOT formulas, respectively.
Several methods were employed to better understand the acceptance criteria. The Federal
Highway Administration ( FHWA) approach utilizes a PWL penalty based on many
factors such as the Q- value table and the specification upper and lower limit. The FHWA
approach should be employed carefully because of the sensitivity of the method. Six
bridge cases were studied where each case had rejected lots by the current ADOT, new
proposed ADOT, FHWA, and California Department of Transportation ( Caltrans)
methods. Various penalty factors for these cases were determined.
3
A comparison of two different pay factors- the PWL and the Kentucky OC curve shows
that the two methods are quite similar. The PWL computed by Kentucky OC curve was
generally friendlier to suppliers as compared to the FHWA’s Category II which is based
on an acceptance quality limit ( AQL) of 90% specification. In addition, the Kentucky
OC curve provided an award or bonus to the supplier whereas there was no extra
payment by using Category II. The FHWA method results in a higher penalty than the
other methods ( 1.38% of the total cost of the projects), whereas the Caltrans method
shows a lower penalty ( 0.81%). The huge penalty is attributed to the rejection of several
sublots. The penalties are less than 1% for current ADOT, proposed ADOT, and the
Caltrans methods.
Comparing the current and proposed ADOT methods, the penalties were assessed in all
six bridge cases. The average level of penalty was in the range of 6.9%. This level of
penalty could be reduced to 2.2% upon adoption of the new ADOT cost factor policy.
Average cost comparisons between the current and proposed ADOT equations indicate
that the approximate penalties in the new ADOT method are in the range of 26% of the
present penalty levels. The FHWA method with pay factor Category II, showed only
three cases that were penalized. The penalties given by FHWA, current ADOT, and
Caltrans methods were similar and averaged 6% of the total costs. The penalty from the
new ADOT method was the lowest and resulted in 2.2% penalty.
The proposed ADOT method seems to be friendlier to suppliers while still providing a
stable penalty. The penalty is 0.27% and is slightly lower than the current ADOT method
( 0.92%). Applying methods with quality control criteria would benefit projects by
reducing out- of- spec concrete on jobsites, retaining required strength, and minimizing
materials consumption.
While the proposed modifications to the specifications provide reasonable and justifiable
changes to the current pay factor equations used by ADOT, real materials savings can be
realized when the cost of raw materials used is reduced through the implementation of a
balanced and comprehensive statistical quality control acceptance criteria.
4
5
II. Introduction
Continuous development of civil infrastructure systems in support of the population growth
and economic productivity of the State of Arizona is a challenge faced by many decision
makers in the planning, administra tive, engineering, and executive branches of our state.
Concrete is the most commonly used building material in the world. Its production in the
United States has almost doubled from 220 million cubic yards per year in the early 1990’ s
to more than 430 million cubic yards in 2004. Arizona’s share has been about 15 million
cubic yards of concrete per year; a number that is increasing at an annual rate of 15%
during the past several years. This has placed a tremendous strain on the suppliers when
one considers the increased demand for infrastructure development. Construction delays
and material shortages have resulted in escalating costs.
A significant amount of energy is required to produce cement. For each ton of cement
produced, a ton of carbon dioxide is emitted into the environment. Therefore, it would be
advantageous to reduce the amount of cement and other virgin materials that are used in
cement- based composites. Chemical attack such as corrosion and alkali silica reaction
( ASR) in concrete is among the major durability concerns in civil infrastructure systems.
These mechanisms affect the service life and long term maintenance costs. For example,
the average annual direct cost of corrosion for highway bridges was estimated by Yunovich
to be $ 8.29 billion in the U. S.[ 2] A better understanding of how the environment
influences concrete performance will improve the decision making process in every stage
of construction and maintenance. The initial design of a structure must consider the entire
service life, and any new proposals for modification of the formulations should consider
the materials science aspects of the performance. This report, however, addresses methods
that can be used to better understand the quality control measures and incentives for the
payment based on early age properties of concrete.
One of the reasons for the extensive use of cement- based systems is the design versatility
which can be tailored to each application. Based on the intended use, varying constituent
materials and processing techniques can be used to achieve performance metrics from fresh
state properties to superior mechanical properties and durability. From a technical
perspective, numerous challenges remain in promotion and use of blended cements as
sustainable and cost saving alternatives. It would be beneficial to utilize and recycle waste
by- products such as class C fly ash as value added ingredients for concrete production,
according to Roy.[ 3] One must however appreciate the complexity of integration of
cement chemistry, early age properties, and specifications when using blended cements in
construction projects, per Mobasher and Ferraris.[ 4]
It is imperative that new guidelines and cost structures for concrete materials be analyzed
so that more economical alternatives can be evaluated and considered during the
preliminary design of a project. As the cost of raw materials changes, many potential
alternatives become cost effective, such as the use of performance enhancing admixtures
and/ or supplementary cementitious materials, curing, and finally quality control ( QC).
These alternatives may not be regularly specified for highway structures due to the lack of
avail- able field data. The focus of the present work is based on a need to better understand
6
the role of quality control and quality assurance in a sustainable design philosophy. The
goal is directed toward generating cross- disciplinary tools to guide us toward more
economical engineering and construction policies. Life cycle cost modeling combined with
statistical quality control measures could identify potential savings, claim Burati et al. [ 5]
The interaction of various choices for an appropriate cost reduction strategy is especially
important in hot, arid regions where special attention must be paid to the materials design
with respect to curing, early shrinkage, and cracking. These will ultimately affect the
durability and quality of the concrete. Not all loading cases, applications, and
specifications can be translated into compressive strength values of concrete; hence this
parameter cannot and should not be used as the sole measure of concrete quality and
performance. Knowledge of various alternatives would allow state officials to make cost-effective
decisions when specifying concrete and provide contractors greater flexibility in
meeting design requirements and future needs.
Objectives
The objective of this work is to promote better quality and economy when using concrete
materials by focusing on:
• Evaluation of the acceptance criteria and current pay factor adjustment methods based
on bonus/ penalty factors in order to improve quality control and specification
procedures.
• Use of a mix design formulation that is based on the principles of economy but still
improves the durability of the finished product.
This report addresses recommendations drafted in consideration of the concerns of various
stakeholders, including state and federal transportation officials, local cement suppliers,
concrete ready mix plants, and construction companies. The opportunities developed in
earlier reports addressed both the quality and economy of concrete materials used locally.
Preliminary Results
Results from a preliminary study conducted for a committee consisting of members of
Arizona Rock Products Association and the Arizona Department of Transportation ( herein
referred to as the ARPA/ ADOT committee) are discussed first. Figure 1 presents data from
a single concrete manufacturer that was obtained from ADOT’s Field office Automation
SysTem ( FAST) database. The plot shows specified strength vs. the strength of concrete
delivered to the job- site. Each data point represents a single compressive strength value for
a representative volume of material. Assuming that each cylinder represents a lot of 50
cubic yards on average, the data represents approximately 300,000 cubic yards of concrete.
For a major portion of the materials delivered, the strength value delivered far exceeded
that required for the job. It is clearly shown that quite often, the strength of concrete
delivered is approximately 1100- 1500 psi higher than the specified values. As such, the
amount of cement that could be saved by reducing the total cement content in the mixture is
significant. The worksheet cost analysis model has been developed which shows the
potential cost savings of cement substitution by supplementary cementitious products. By
implementing a quality control process for the acceptance of concrete, it is clear that one
can reduce both the standard deviations and the mean strength values while maintaining the
7
same level of risk. The net result would be realized in the reduction of the average cement
dosage requirements. Figure 2 shows the running average strength value for a 2- year period
of a single supplier for a 3000 psi class of concrete. Note that the over- strength
conservatism is significantly higher with as much as 1500 psi mean over- strength values.
2000 4000 6000
Specified Strength, psi
2000
4000
6000
8000
10000
Delivered Strength, psi
All concrete classes
28 day strength
Figure 1. Correlation of data from both the specified strength and the
actual strength of concrete delivered to the job site from a single ready
mix producer. The solid line represents a 1: 1 correlation.
800 1200 1600 2000
Sample Number
0
2000
4000
6000
8000
Delivered Strength, psi
3000 psi concrete class
28 day strength
08/ 2003 to 09/ 2005
Figure 2. Data from a single ready mix producer during a two year cycle
representing the amount of over- strength concrete delivered.
8
It would also be ideal to evaluate the 7- day strength results and use that information as a
basis to determine if the 28- day strength results are capable of meeting the design
objectives or not. In Figure 3, red dots represent the 7- day strength values whereas the
black dots represent the 28- day strength values. The specified strength of the concrete is
2500 psi at 28 days. It is clear that the 28- day strength is greater than the 7- day strength;
however, no correlation is apparent in the trend of the data. While it is true that the
strength might be improved by the extended curing time, there is no methodology to
correlate the 28- day strength with 7- day strength. Subsequently, there is no way to
determine if the trend and variations in the 28- day strength are too large to be statistically
significant.
12/ 10/ 02 1/ 14/ 04 2/ 17/ 05 3/ 24/ 06
Date
0
1000
2000
3000
4000
Compressive Strength, psi
7- day strength data
28- day strength data
Specified strength( 2500 psi)
Strength Data Distibution
Figure 3. Plot of the Comparison of Strength Data Distribution to Specification
9
II. Sample Collection and Analysis Procedures
1. Preliminary Data Selection
Three types of data sets were used in this survey. These included data provided by
industry in cases of previous dispute which had been resolved using the pay factor
equations. Data was also provided by ADOT resident engineers based on their prior
experience with cases which required additional investigation. The third set of data
involved a random selection of a range of available data within the FAST data base.
Three sets of various data bases were addressed. These data were categorized in the
following case studies.
1.1 ADOT Supplied Test Cases ( Series 1)
Six projects using a total of nine mixes were identified as cases which required further
statistical evaluation. They were identified by ADOT Resident Engineers as test cases
for analysis and in depth evaluation. These cases were identified as problem projects
which had historically required further investigation such as coring and additional testing
( for example, H407601C, H416001C, H552501, and H576801C). The following
Transportation Accounting ( TRACs) numbers are used within the Series 1 category and
further investigated:
Table 1: Series 1 Data Set
Project TRACs
number
Supplier Plant number Product
number
Required
strength
( psi)
Age
( days)
1 H576801C Rinker 33341 1333115 4500 28
2 H552501C Sunshine Concrete Kingman S3000A 3000 28
3A H407601C Rinker 55041 14016 3500 28
3B H407601C Rinker Materials 60141 1332439 4000 28
4A H416001C Campbell Redi- mix Lake Havasu 2500S 2500B 28
4B H416001C Campbell Redi- mix Lake Havasu 2500S 3500S 28
5A H319003C McNeil Const. Co. Tucson 0203- 10 4000 28
5B H319003C McNeil Const. Co. Tucson 0203- 15 4000 28
6 H313401C McNeil Const. Co. Tucson 9710- 3 4000 28
10
1.2 Randomly Selected Test Cases ( Various supplier, plant, and mix specification)
( Series 2)
The data in this test case were randomly selected. Five different suppliers ( Chandler
Ready Mix, Rinker, Arizona Materials, Hanson Aggregates of AZ, and TPAC) are
selected with two plants each, and three mix specifications each as shown in Table 2.
Table 2: Series 2 Data Set
No Supplier Plant Mix
specification
Required
strength
( psi)
Age ( days)
A11 Chandler Ready Mix 03 130624 3000 28
A12 Chandler Ready Mix 03 972502 2900 28
A13 Chandler Ready Mix 03 4425 2500 28
A21 Chandler Ready Mix 01 140204 4000 28
A22 Chandler Ready Mix 01 160604 6000 28
A23 Chandler Ready Mix 01 130224 3000 28
B11 Rinker 11241 14030 3500 28
B12 Rinker 11241 1333066 4000 28
B13 Rinker 11241 14504 4500 28
B21 Rinker 33341 14016 3000 28
B22 Rinker 33341 1333004 3500 28
B23 Rinker 33341 1345459 3000 28
C11 Arizona Materials Val Vista 15030 4500 28
C12 Arizona Materials Val Vista 13008 2500 28
C13 Arizona Materials Val Vista 14030A 4000 28
C21 Arizona Materials Queen Creek 13008 3000 28
C22 Arizona Materials Queen Creek 14030 3000 28
C23 Arizona Materials Queen Creek 13530 3000 28
D11 Hanson Agg. of AZ Valley Plant C35501 3500 28
D12 Hanson Agg. of AZ Valley Plant C40501 4000 28
D13 Hanson Agg. of AZ Valley Plant C35501A 3500 28
D21 Hanson Agg. of AZ 40 D402521 4000 28
D22 Hanson Agg. of AZ 40 1205104 4000 28
D23 Hanson Agg. of AZ 40 840913 4000 28
E11 TPAC Phoenix 447 5000 28
E12 TPAC Phoenix 444 5500 28
E13 TPAC Phoenix 448M 5500 28
E21 TPAC Tucson 2245 4500 28
E22 TPAC Tucson 2248 5000 28
E23 TPAC Tucson 2250 6000 28
11
1.3 Members of the ADOT/ ARPA committee Supplied Test Cases ( Series 3)
The industrial members of the task group identified several test cases which had resulted
in compressive strength disputes. Six bridge projects were recommended for exploration.
These test cases are listed as shown in Table 3.
Table 3: Series 3 Data Set
Case Number Bridge Name Required strength ( Psi)
1 Wilson Wash 4500
2 Sandy Blevens 4500
3 Quail Springs 4500
4 Poison 4500
5 Deveore 4500
6 Apprentice 4500
2. Exploratory Data Analysis
Statistical process control is widely used in various manufacturing sectors. The first step
in the evaluation of the data is to conduct an exploratory data analysis. In this procedure,
the number of samples, distribution of the samples, and basic statistical techniques are
utilized to evaluate if the data meets certain criteria for follow up steps. In the
exploratory data analysis section, the adequacy of the data was tested by scatter plot,
histogram, and probability plots. These plots verify the validity of assumptions. The
assumption in applying the control chart is that the data is normally distributed. In this
case a normal distribution was assumed, due to a sufficient number of data points
representing the symmetrical nature of a bell shaped curve with equal distribution about
the mean. The Anderson- Darling ( AD) test, which can be applied to any assumed
distribution, confirmed a normal distribution. Additionally the AD test also
acknowledged that the test samples came from a much larger population of normally
distributed data. If there is sufficient sample size to form a hypothesis, then the analysis
on the data yields a very good estimation of the entire population. If there is not a
sufficiently large sample size, then the margin of error is rather large. Most probability
plots satisfied this assumption. The test data which did not meet the normal distribution
criteria was not used in the analysis. The cases were rejected primarily because there
were few sample points ( six or seven strength values) in these cases, the reliability of the
analysis is quite low, so larger data sets, which could provide a better representation of
statistical process, were chosen. The basic control chart is also applied to the concrete
strength data. The X- bars are presented for two methods including current ADOT and
modified American Concrete Institute ( ACI) methods. ADOT employs the design
strength ( F’c) as the lower limit. The X- bar and S charts are also employed by using a
modified ACI method which requires specified strength ( F’cr) as the mean of the chart.
The X- bar chart plots the subgroup means, whereas the S chart relates to the subgroup
standard deviation, according to Montgomery.[ 6] The X- bar control chart presents the
mean. S charting measures the process variability and helps monitor the stability of
process. The data is shown in chronological order, so the trends or shifts in the process
can be detected.[ 7]
12
2.1. Exploratory Data Analysis of Series 1
Figure 4 represents the Normal Probability plot for Series 1 data sets ( see Appendix A).
Here N represents the number of samples tested and StDev represents the standard
deviation with a 95% Confidence Indicator ( CI) with respect to the mean, The AD test is
a statistical procedure applied to evaluate if the samples come from a particular
distribution, as explained by the National Institute of Standards and Technology[ 8] and
Hayes et al,[ 9] A small AD value indicates that an assumed distribution ( for example a
normal distribution) fits the data. Projects 5 ( H416001C_ Campbell Redi- mix_ Lake
Havasu_ 2500S_ 2500B) and Project 8 ( H319003C_ McNeil Const. Co._ Tucson_ 0203-
15_ 4000) do not follow the normality assumption because Anderson- Darling statistics are
quite large in comparison to the other projects ( AD = 1.238 and 1.165).
Data
Percent
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
99.9
99
95
90
80
70
60
50
40
30
20
10
5
1
0.1
Mean
0.553
4026 767.0 14 0.249 0.693
4608 570.2 23 0.491
StDev
0.198
3849 415.3 31 1.238 < 0.005
5695 562.6 8 0.252
N
0.629
4065 194.5 6 0.530 0.101
5013 412.5 139 1.165
AD
< 0.005
5414 658.2 23 0.326 0.504
4515 266.7 42 0.412
P
0.325
5186 360.2 29 0.302
Variable
H416001CR_ CAMP_ LAKE_ 3500S_ 3500
H416001CR_ CAMP_ LAKE_ 2500S_ 2500
H407601C_ 60141_ 1332439_ 4000
H407601C_ 55041_ 14016_ 3500
H319003C_ TUCSON_ 0203- 15_ 4000
H319003C_ TUCSON_ 0203- 10_ 4000
H313401CR
H576801CR
H552501C
Probability Plot of H576801CR, H552501C, H416001CR_ CA, ...
Normal - 95% CI
Figure 4. Probability plot for Series 1
The next step is to assume that the data are normally distributed, and one can conduct a
hypothesis test and find the probability ( or P- value). The P value is calculated based on
the results by assuming the null hypothesis is true. The significance level ( or the alpha
( α) level) is the particular probability level that the evidence is either an irrational
estimate or the decisive factor used for rejecting the null hypothesis, as explained by
Hayes et al.[ 10] The P- value can be interpreted as the probability of a false rejection of
the null hypothesis or the chance of making a Type I error ( the error of rejecting a null
hypothesis when the null hypothesis is actually true). For example, the significant level of
0.05 corresponds to a 5% chance that the normality assumption was rejected due to the
Probability Plot of Series 1
13
sample specimen belonging to a normally distributed set of data. When comparing the
probability to the significance level, if the P- value is less than or equal to the alpha level,
one may conclude that the null hypothesis is ‘ statistically significant’ and rejected,
according to Lane.[ 11] In general, the popular levels of significance level are 0.05 and
0.01. The lower the significance level, the more the data significantly deviate from the
null hypothesis.[ 11]
Based on the above, it is clearly observed that Projects 5 and 8 might not fit the normal
distribution very well since P- values are quite small (< 0.005). For discussion purposes
of this report, the rest of the data set is assumed to be valid test data collected from
normally distributed populations. A summary of all the X- bar and S- Charts for these
samples are listed in Appendix B ( Figures B1 – B9).
An alternative method to present data is to show X- bar and S charts. The X- bar charts are
plotted in two sets, first by considering the lower limit as specified minimum strength
( F’c) which is the current approach of ADOT, and second by a method similar to ACI-
214 in which the mean ( center line) is the required jobsite strength ( F’cr) with lower and
upper limits. The second criterion of ACI- 214 is used in which:
n
F F s z cr c
' = ' + . , s is the standard deviation of the data set, z is associated with the
normality of the data set ( here z= 1.28 for 10%) and n= 3. The formula of the lower and
upper control limit ( LCL and UCL) is
n
CL k σ
± where
CL = the center line ( F’cr)
n = 3= the size of the subgroup
k = the number of standard deviations from the center line. In this situation, k = 3.
σ = the standard deviation that is calculated by the pooled standard deviation.
It is written as.
4
1
4
( )
ˆ
c
n
S
c
S
n
i
i Σ=
σ = = where c4 is the value from the table. The summary table
of the factors for constructing variable control charts is shown in Table 4.
Table 4: Factors used for Constructing Variable Control Charts
Factor for Central
Line
Factor for Control Limits of
the S chart
Sample size
c4 B3 B4
2
3
4
5
0.7979
0.8862
0.9213
0.9400
0
0
0
0
3.267
2.568
2.266
2.089
From Montgomery. Introduction to Statistical Quality Control. 4th ed. 2001. [ 6]
14
For instance, the standard deviation of project 8 ( Figure 5) is 658.2, but the sigma is
calculated by 233.58
0.8862
ˆ 207
4
= = =
c
σ S since the sample size = 3. Here,
4000 658 1 28 4486 psi
3 cr
F' . ×
= + =
Then: 4081.43
3
= − = 4486 − ( 3)( 233.58) =
n
LCL k σ
μ
4890.57
3
= + = 4486 + ( 3)( 233.58) =
n
UCL k σ
μ
0 20 40 60 80 100 120 140
3500
4000
4500
5000
5500
6000
6500
1
2
3
4
5
6
78
9
10
11
12
13
14
15
16
17
18
24
2527
28
29
30
31
32
33
34
35
36
37
3839
40 41
42
43
44
45
46
47
48
49
50
51
5354
56
5758
59
60
61
62
63
64
65
66
6769
70
71
72
73
74
75
76
77
78
79
80 81
86
87
88
89
91
92
93
94
95
96
97
98 99100
101
102
104
105 111114
111189
120
124
112267
128
129
113323
134
113356
LCL= 4000
X- bar Chart, Current ADOT
Samples
Sample Mean
Figure 5. X- bar and S Chart for Project 8 in Series1
15
The S chart demonstrates the instability and variability in several projects ( Project 1, 5, 6,
7, and 8). Figure 5 presents the S chart which is a running sequence of the average
strength values as a function of project time. The center line is the average of all
subgroup standard deviations. It is defined asCL = S . Then CL = 207. The lower and
upper control limits can be written as B S 3 and B S 4 respectively, where B3 and B4 are
values from a table above which depends on the subgroup size. Then
( 0)( 207) 0 3 LCL = B S = = and ( 2.568)( 207) 531.576 4 UCL = B S = = .
It should be mentioned that the real lower limit for concrete strength is the specified
design strength ( F’c) and the values for different samples can vary about the required
strength ( F’cr). However, in this analysis, the obtained lower limit ( e. g. 4081 psi) would
be slightly higher than the F’c ( e. g. 4000 psi).
The S chart detects the shifts that are above and below the target. Since there are several
points greater than the upper control limit, this indicates that the process is out- of- control
as shown above. Nevertheless, it is acceptable for the compressive strength data to be
above the specified strength, so this report focuses on the out- of- control signal,
particularly the lower specification. This means that this process can be considered as the
good process since there are no points that fall beyond the lower control limits. The
presence of an out- of- control signal shows the assignable causes ( effects that can be
corrected, adjusted, or removed, i. e, process control, extra cement factor, etc.) in the
process, so the process should be investigated to remove the variation and increase its
capability.
2.2. Exploratory Data Analysis of Series 2
This test case was selected based on a random selection of various suppliers, plants, and
mix specifications ( Series 2). There are some cases in this series where the data set is too
small ( less than 5 data points). Since such a data set was not appropriate to analyze,
several projects were discarded such as A12, A22, A23, B23, D11, and D22. Figure A2,
A3, A4, A5, and A6 represent the Normal Probability plot for Series 2 Project A, B, C, D,
and E data sets respectively ( see Appendix A). Using the Anderson- Darling statistic
( AD), Project A21, B11, B12, D21, D23, E11, and E12 do not follow the normality
assumption because the Anderson- Darling statistics are quite large in comparison to the
other projects ( AD = 1.054, 0.747, 0.625, 0.866, 0.622, 0.854, and 0.742). The large
Anderson- Darling values indicate that the distribution does not fit the normality
assumption. In addition, the P- values ( 0.008, 0.043, 0.053, 0.022, 0.088, 0.024, and 0.037
respectively) are smaller than the chosen α- level ( 0.05 and 0.10), so Project A21, B11,
B12, D21, D23, E11 and E12 might not follow the normal distribution very well either.
For the purposes of discussion in this report, other projects are assumed to be collected
from normally distributed populations. A summary of both the X- bar and S- Charts for
these samples are listed in Appendix C ( Figures C1 – C24). The S control chart presents
the variability by detecting an out- of- control signal in some cases including B22, C11,
C13, D12, D13, D23, and E23. Most cases however, had higher strength than the defined
upper limit and are considered over- designed.
16
2.3 Exploratory Data Analysis of Series 3
This test case ( Series 3) was supplied by the members of the ADOT/ ARPA committee.
Figure A7 represents the Normal Probability plot for Series 3 data sets ( see Appendix A).
In this set of data, project D22 was discarded since the number of observations was quite
small. All the Anderson- Darling values ( AD) are relatively small ( AD = 0.567, 0.537,
0.232, 0.445, 0.210, 0.171), therefore, all bridge projects are assumed to follow a normal
distribution. In addition, the p- values ( 0.117, 0.147, 0.757, 0.194, 0.833, and 0.907
respectively) are greater than the commonly chosen α- level ( 0.05 and 0.10). All bridge
projects seem to be normally distributed. For the purposes of discussion in this report,
most data sets within this series are assumed to be collected from normally distributed
populations. A summary of all the X- bar and S- Charts for these samples is listed in
Appendix D ( Figures D1 – D6). In this series, all the bridge projects had rejected lots
with strength lower than design strength ( F’c). They also had some strengths higher than
the upper limit.
3. Pay Factor Determination
Once the normality assumptions were properly tested, all projects were examined for
various penalty/ bonus criteria by using four different approaches. These alternatives
were identified as: FHWA, Currently enforced ADOT guidelines ( ADOT), recently
proposed ADOT guidelines ( new ADOT), and Caltrans.
It should be mentioned that in the current ADOT method, only a lower limit ( F’c) is
considered as the criterion for the pay factor and the data history and statistical analysis is
not employed to determine the level of penalty. However, following a similar method to
ACI- 214 ( such as the FHWA method) would enhance the overall quality control of
concrete production in which lower and upper limits are defined and a lot is of good
quality if it is between the two limits and of poor quality otherwise. The summary of this
analysis is presented in the following table in which the out of control data are shown in
all series. “ L” means lower strength and “ H” means higher strength compared to the
mean strength ( F’c in ADOT and F’cr in ACI). Details for all four methods are shown in
Table 5.
17
Table 5: Out- of- Control Data in all Series
Number of out of control
data
Percentage of Out of Control
data
Series Code ADOT: L ACI: L ACI: H ADOT: L,
%
ACI: L,
%
ACI: H,
%
1 0 0 13 0.0 0.0 44.8
2 1 3 8 7.1 21.4 57.1
3 0 0 4 0.0 0.0 66.7
4 0 0 8 0.0 0.0 100.0
5 0 0 31 0.0 0.0 100.0
6 0 0 17 0.0 0.0 73.9
7 0 0 20 0.0 0.0 87.0
8 0 0 74 0.0 0.0 53.2
3
9 0 0 30 0.0 0.0 71.4
A11 0 0 7 0.0 0.0 100.0
A13 0 0 11 0.0 0.0 100.0
A21 0 0 47 0.0 0.0 94.0
B11 0 0 19 0.0 0.0 100.0
B12 0 0 3 0.0 0.0 50.0
B13 0 0 21 0.0 0.0 100.0
B21 0 0 8 0.0 0.0 100.0
B22 1 4 8 5.6 22.2 44.4
C11 1 1 45 1.4 1.4 62.5
C12 0 0 5 0.0 0.0 100.0
C13 5 5 6 17.9 17.9 21.4
C21 0 0 16 0.0 0.0 100.0
C22 0 0 20 0.0 0.0 100.0
C23 0 0 5 0.0 0.0 100.0
D12 1 1 1 16.7 16.7 16.7
D13 0 1 18 0.0 5.0 90.0
D21 0 0 22 0.0 0.0 91.7
D23 0 4 9 0.0 23.5 52.9
E11 0 0 28 0.0 0.0 100.0
E12 0 0 11 0.0 0.0 100.0
E13 0 0 21 0.0 0.0 100.0
E21 0 0 23 0.0 0.0 88.5
E22 0 0 55 0.0 0.0 94.8
2
E23 1 1 6 9.1 9.1 54.5
Wilson Wash 7 8 4 50.0 57.1 28.6
Sandy Bleven 2 2 7 10.5 10.5 36.8
Quail Springs 3 3 1 20.0 20.0 6.7
Poison 1 2 5 14.3 28.6 71.4
Deveore 2 3 1 11.8 17.6 5.9
3
Apprentice 1 3 5 9.1 27.3 45.5
18
3.1 FHWA- PWL Method
The Pay factor is calculated by using the PWL method. PWL ( percent conforming or percent
within limit) is the percentage of the lot that is in the specification: between the upper
specification limit and lower specification limit. The PWL is calculated based on normality
assumption. A lot is defined as a finite sample size. Within each lot, several sub- lots are
defined. Samples are collected at the sublot level. Within each lot the mean and standard
deviation are calculated. These values are used by means of statistical process control
procedures to compute the quality measures. Upper and lower specification limits are either
specified or calculated based on a number of standard deviations away from the mean. Instead
of using the Z- value, the quality index, Q, is used to estimate the PWL. The Q- value is given
by Burati, et al.[ 5] as:
s
Q x LSL L
( − )
= where LSL = lower specification limit
s
Q USL x U
( − )
= where USL = upper specification limit
The Q- value is used to determine the estimated PWL for the lot as shown in the table by
Specification Conformity Analysis.[ 12] Each QU and QL value will transform to PU and PL and
then used to calculate the PWL. The total estimated percentage of the lot within the U and L
is = + − 100 U L PWL P P . The lot strength PWL is related to the pay factor. Figure 6 represents
the relationship between the Q- value and the PWL when n ( sample size) is varied from 3 to 10.
100 90 80 70 60 50
0
0.5
1
1.5
2
2.5
3
PWL
Qvalue
Qvalue vs. PWL
n= 3
n= 4
n= 5
n= 6
n= 7
n= 8
n= 9
n= 10
Figure 6 Plot of the Relationship between the Q- value and the PWL
19
Subsequent to estimation of PWL, the next step is finding the pay factor for each sublot.
The pay factor is estimated by two ways: the Acceptable Quality Level and the OC
Curve.
• Pay Factor determination using acceptable quality level.
There are two important definitions by the FHWA.[ 5] First, the Acceptable Quality Level
( AQL) is the minimum percentage of the quality work that is considered acceptable for
payment. Second, the Rejectable Quality Level ( RQL) is the maximum percentage of the
quality work that is considered unacceptable. There are 2 categories: I and II. Category I
is based on an AQL of 95 percent whereas Category II is based on AQL of 90 percent.
The contractor’s risk is 5 percent in both cases. The seller’s risk ( or contractor’s risk) is
the chance of rejecting material that is at the AQL level. This is also called Type II Error
( or β) by Montgomery.[ 6] The Government Agency’s risk is defined as the probability of
accepting material if it is at the RQL level. It may be called the ‘ buyer’s risk’ by
Mahboub and Hancher [ 13] or Type I Error ( or α) by Montgomery.[ 6] Figure 7 shows
the defining table of Type I and Type II errors.
Result of Decision
Accept the lot Reject the lot
Good lot
( AQL)
Producer’s Risk
( Type I error)
Quality of lot
Bad lot
( RQL)
Consumer’s Risk
( Type II error)
Figure 7 The Defining table of Type I and Type II errors
from Mahboub and Hancher.[ 13]
20
In this report, we applied Category II to the data set. The pay factor depends on sample size
and the calculated PWL by Mahboub and Hancher [ 13] ( See Appendix E). Figure 8
represents the determining pay factor by using Category II and varying number of sample
size.
100 80 60 40 20 0
0.75
0.8
0.85
0.9
0.95
1
PWL
Pay factor
PWL and Pay factor
n= 3
n= 4
n= 5
n= 6
n= 7
n= 8
n= 9
n= 10
Figure 8 Plot of Relationship between PWL and Pay Factor by Category II
• OC curve
The OC curve plots the probability of acceptance against the true value or percent of
defectives. The probability of acceptance is the parameter on the vertical axis whereas the
percent defective is on the horizontal axis, according to Mahboub and Hancher.[ 13]
Figure 9 shows the OC curve for any plan.
Figure 9. OC Curve from Mahboub and Hancher [ 13]
21
OC curves are tools widely accepted to manage risk analysis since they allow one to
choose the number of samples to detect the particular probability, per Montgomery.[ 6] In
general, the payment adjustment is related to α and β risks. An alternative method for
acceptance is to consider the payment performance as mentioned in Mahboub and
Hancher [ 13] and shown in Figure 10.
Figure 10. The Payment Curve from Mahboub and Hancher [ 13]
In the present method we chose the Kentucky OC curve, as in Mahboub and
Hancher.[ 13] The table below and Figure 11 show the relationship between the PWL and
the pay factor. It is clear that a higher PWL would result in better pay factors.
Table 6: Relationship Between PWL and Pay Factor
Lot Strength PWL
(%)
Seller’s Risk for
rejecting the lot (%) Pay factor*
100 0 102.5
95 5.3 100
90 15.2 97.5
85 27.1 95
80 40.5 92
75 51.1 90
70 62.0 87.5
65 70.5 85
60 78.2 82.5
55 83.5 80
50 88.5 77.5
45 92.6 75
40 94.9 72.5
35 97.1 70
30 98.3 67.5
25 99 65
20 99.1 62.5
* Assuming a sample lot PWL of a given lot is approximately
equal to the population lot PWL
22
100 80 60 40 20
PWL
60
70
80
90
100
110
Pay Factor
Figure 11. Plot of the Relationship between PWL
and Pay Factor by Kentucky OC curve
3.2 Current ADOT Pay Factor Determination
The pay factor, according to the ADOT method, is calculated from the average of two com-pressive
strength samples representing a finite volume of concrete defined as a lot. Normally
the volume of concrete corresponds to approximately 100 cubic yards. The strength result is
the percentage of compressive strength as a function of the required and/ or specified strength.
The present ADOT method does not penalize or reward the various ready mix suppliers in
accordance to the statistics of the sampled data. The current technique is primarily focused on
meeting the minimum specified level.
The ADOT method is neither based on statistical methodology nor does it take into account the
variations that take place in normal operating conditions. Therefore, a sample may be slightly
above the required level, and that sample will be considered acceptable although a large pro-portion
of that population may actually fall below the specified strength level from a statistical
point of view. In conclusion, when the mistaken sample was chosen, it cannot represent the
true strength of cement. This misrepresented strength results in an invalid payment determina-tion.
The adjustment in contract for the ADOT method is shown as follows:
Table 7: Adjustment in Contract for ADOT Method
Strength result (% of F’c) Reduction in Contract Unit Price (%)
100 or More 0
98 - 99 5
96 - 97 10
95 15
Less than 95* 45
* If allowed to remain in place
23
To check the sensitivity of the strength, the round- off numbers are applied to the
boundary values. The table below shows the new adjustment in contract.
Table 8: Sensitivity of Adjustment in
Contract for ADOT Method
Strength result (% of F’c) Reduction in Contract
Unit Price (%)
99.5 or more 0
97.5 – 99.5 5
95.5 – 97.5 10
94.5 - 95.5 15
Less than 94.5* 45
* If allowed to remain in place
3.3 Proposed ADOT Pay Factor Determination
This method is an improvement over the old ADOT method. It applies the same concept,
but also depends on the level of required compressive strength. The adjustment in
contract for strength is shown as follows:
Table 9: Adjustment in Contract for New ADOT Method
Adjustment in Contract Unit Price For Compressive Strength of Class S and Class B Concrete
3000 and Below 3000 and 4000 4000 and Above
Percent of
Specified 28- Day
Compressive
Strength Attained,
to the Nearest One
Percent
Percent
Reduction in
Contract Unit
Price
( See Note 1)
Percent of
Specified 28-
Day
Compressive
Strength
Attained, to the
Nearest One
Percent
Percent
Reduction in
Contract Unit
Price
( See Note 1)
Percent of
Specified 28-
Day
Compressive
Strength
Attained, to the
Nearest One
Percent
Percent
Reduction in
Contract Unit
Price
( See Note 1)
100 or More 0 100 or More 0 100 or More 0
99 1 99 1 99 1
98 2 98 2 98 2
97 3 97 3 97 3
96 4 96 4 96 4
95 5 95 5 95 5
94 6 94 6 94 30
93 7 93 7 93 30
92 8 92 8 92 30
91 9 91 9 91 30
90 10 90 10 90 30
89 11 89 30 89 30
88 12 88 30 88 30
87 13 87 30 87 30
86 14 86 30 86 30
85 15 85 30 85 30
Less than 85 30
( See Note 2)
Less than 90 30
( See Note 2)
Less than 95 30
( See Note 2)
Note1: For items measured and paid for by the cubic yard, the reduction shall not exceed $ 150 per cubic yard
Note2: If allowed to remain in place.
24
It is possible to write the simple linear regression for calculating the new ADOT penalty
by
100 1
70
, x
P x , x
, x
β
β
> ⎧⎪
= ≥ ⎨⎪
⎩ <
where P = penalty, and
specified strength
x = strength required
Table 10: The Value of β
Strength β
3000 and Below 85
3000 to 4000 90
4000 and Above 95
Figure 12 below shows the plot of percent reduction comparing the table to computations
from two different equations.
100 96 92 88 84
Percent of Compressive Strength
40
60
80
100
Percent of Payment in Contract
Strength 3000 psi and below
Strength between 3000 and 4000 psi
Strength 4000 psi and above
ADOT method
Figure 12. Comparison of the present ADOT Pay Factor equation ( shown in black) and
the proposed method which is dependant on the concrete strength class.
25
3.4 California Department of Transportation method
The California Department of Transportation ( Caltrans) method is based on the average
percent of strength of two cylinders by removing the improper one from the samples due
to any evidence of inappropriate sampling, molding, or testing. The test cylinder will be
molded, cured, and tested in conformance with the requirements of the California Test.
The assumptions in the estimation for the Caltrans penalty are: Lot size = 100 cubic yards
with 4 samples for each lot size. Unit cost = $ 150 per cubic yard. The penalty is
calculated by the cost per cubic yard as shown in Table 11.
Table 11: Penalty Calculated by the Cost per Cubic Yard
Strength result (% of F’c) Penalty
95 - 100 $ 10.70/ cy
85 - 94 $ 15.29/ cy
< 85 Reject
Note: No single test if the sample is more than 327 cy
26
27
III. Discussion of Results
1. Comparing two different methods for the PWL based analysis of the FHWA
method
The results are shown for three different scenarios ( Series 1, 2, and 3). The acceptable
quality level with Category II is more generous than the Kentucky OC curve. The starting
point for 100% payment for the first method, the minimum required PWL = 65 while the
required minimum PWL = 95 for the second method. An additional constraint is the
value of the standard deviation. For the purpose of analysis, if the standard deviation is
zero, then the appropriate value ( to avoid a divide by zero error) of the standard deviation
is assumed to be 0.000001. In addition, using the acceptable quality level with Category
II does not provide the bonus or award. The positive penalty represents the bonus/ award
or the amount that the supplier can potentially accumulate due to consistently above-average
strength values. In contrast, the negative penalty means the loss of payment since
the strength of concrete is lower than the minimum required level. Zero penalties
correspond to the full amount of payment.
To simplify the problem, some assumptions are applied to the penalty calculation for the
rejected sublot: Lot size = 100 cubic yards and unit cost = $ 150 per cubic yard. Then the
estimation of penalty for each unit in a rejected sublot is around $ 15,000. For the
calculation of penalty or bonus, the lower limit is set to be the design strength ( F’c) and
the upper limit is set to an arbitrary value such as 10,000 psi to make sure it would be
higher than all the design strengths. The penalties calculated from the FHWA method are
presented in the following tables for Series 1, 2, and 3 separately.
Table 12: Series 1.
The FHWA Penalty for both Kentucky OC Curve and Category II Pay Factor Methods.
Project TRACs
number
Supplier Required
strength
FHWA with
Kentucky OC, $
FHWA with Pay
factor category II, $
1 H576801 Rinker 4500 10,875 0
2 H552501 Sunshine Concrete 3000 1,610.6 0
3 H407601 Rinker 3500 2,250 0
4 Rinker material 4000 3,000 0
5 H416001C Cambell Redi- mix 2500B 11,625 0
6 3500S 7,529 0
7 H319003C McNeil Const. Co. 4000 5,398.9 0
8 H319003C McNeil Const. 4000 5,212 0
9 H313401C McNeil Const. 4000 13,226 0
Note: If any lot is rejected, the total penalty is computed as the cost of the lot.
28
Table 13: Series 2.
The Penalty from both the Kentucky OC and the Category II Methods
No Supplier Required
strength
FHWA with
Kentucky OC,$
FHWA with Pay factor
category II,$
A11 Chandler Ready Mix 3000 2,625 0
A13 2500 4,125 0
A21 4000 - 4,522.7 0
B11 Rinker 3500 7,125 0
B12 4000 2,250 0
B13 4500 7,875 0
B21 3000 3,000 0
B22 3500 - 4,628.4 0
C11 Arizona Materials 4500 23,900 0
C12 2500 1,875 0
C13 4000 - 123,230 - 120,000
C21 3000 6,000 0
C22 3000 7,500 0
C23 3000 1,875 0
D12 Hanson Aggregates
of AZ
4000 - 4,183.7 0
D13 3500 6,402.4 0
D21 4000 9,000 0
D23 4000 313.8 0
E11 TPAC 5000 12,375 0
E12 5500 4,125 0
E13 5500 7,875 0
E21 4500 9,750 0
E22 5000 21,750 0
E23 6000 - 228 0
Note: If any lot is rejected, the total penalty is computed as the cost of the lot.
The sensitivity of the specification to the penalty is investigated in the next step. In
addition, the table above clearly shows that if there was a PWL- based method in place,
then many of these problematic cases could have been identified during the construction
phase. One observation is that the huge penalties in project E come from many rejected
sublots. When the FHWA method is applied by converting the Q- value to the PWL,
either ql or qu become 100 and 0. Finally, PWL is 0 and this lot size will be rejected.
To clearly understand the behavior of the PWL, the category II method was tested by
varying the specification limits. Focusing on project E, the table below compares the
FHWA with LSL = required strength and USL = 10,000 psi, with LSL and USL within
± 2 sigma and ± 6 sigma respectively, based on overall data. The results are different for
these three sets of analyses. Some cases indicate the rejected sublot whereas the other
criteria do not show the rejected sublot. This means that setting the USL and LSL too
tight results in rejecting the sublot. The alternative to solving this problem is using the
LSL as the required strength and setting the USL at a high value such as 10,000 psi or
more.
29
Table 14: Pay Factor in the FHWA Method calculated using different LSL and USL
No Supplier Plant Required
strength
FHWA penalty with
LSL = required
strength and USL =
10,000
FHWA penalty
with LSL and
USL= CL ± 6s
overall σ
FHWA penalty
with LSL and
USL= CL ± 2s
overall σ
E11 TPAC PHX 5000 0 0 - 495,000
E12 5500 0 0 - 165,000
E13 5500 0 - 60,000 - 315,000
E21 TUCSON 4500 0 0 - 390,000
E22 5000 0 0 - 870,000
E23 6000 0 0 - 65,106
Note: If any lot is rejected, the total penalty is computed as the cost of the lot.
Table 15: Series 3. The Results for both Methods.
Supplier Required
strength, psi
FHWA with
Kentucky OC
FHWA with Pay
factor category II
1 Wilson Wash 4500 - 77,420 - 62,521
2 Sandy Blevens 4500 - 8,573.4 - 1,743.9
3 Quail Springs 4500 - 14,823 - 3,020.9
4 Poison 4500 - 6,151.2 0
5 Deveore 4500 - 4,891.2 0
6 Apprentice 4500 - 1,545.9 0
Note 1: If any lot is rejected, the total penalty is computed as the cost of the lot.
0 10 20 30 40 50
Case Number
- 1200000
- 800000
- 400000
0
400000
Penalty, $
Kentucky OC
FHWA PWL
Series 1 Series 2 Series 3
Figure 13 Comparison of two methods ( FHWA PWL
and Kentucky DOT) penalties for all series.
30
Figure 13 implies that the FHWA PWL method calculated by the Kentucky OC curve is
more supplier friendly as compared to FHWA Category II. These two methods show the
different direction in some cases. Finally, Table 13 in Series 2 illustrates that many
problematic cases could be identified when the PWL based method is applied.
2. Sensitivity analysis of the PWL and the Q- value for FHWA method
To find the PWL, the Q- value is calculated and estimated from the table by a
Specification Conformity Analysis. Subsequently, the PU and PL values are computed
based on the value of Q and will lead to the estimation of the PWL. The Q- value is
variable and sensitive to the PWL depending on the sample size ( n = 3 to 10). The
tolerance value (± 0.25 and ± 0.50) is respectively added to the Q- value and to the PWL
table. Figure 14 represents the relationship between the Q- value and the PWL. Note that
when the Q- value is sufficiently low, one cannot reduce it further such that negative
values are obtained. In order to circumvent the problem, both the PU and PL values
correspond to 100 minus the table value for PU and PL.
100 90 80 70 60 50
- 0.5
0
0.5
1
1.5
2
2.5
3
3.5
PWL
Qvalue
Qvalue vs. PWL
n= 3
n= 4
n= 5
n= 6
n= 7
n= 8
n= 9
n= 10
Figure 14 Plot of Relationship between Q- value and PWL
For the FHWA method, each lot is assumed to have four sublots or four sample sizes
( measured in cubic yards). To understand this behavior clearly, the sample size of four is
explored by adding the small tolerance value (+ 0.05, + 0.10, + 0.15, and + 0.2) to the Q-value.
The result is shown in Figure 15 and Figure 16. It is noted that in Table 16, the
values of the lower limit and upper limit are set to be 2000 and 6000 psi respectively. If
other limits ( such as F’c for the lower limit) were used, we could have seen different
results. The details of the case numbers are presented in Appendix F.
Q- value + 0.5
Q- value + 0.25
Q- value
Q- value - 0.25
Q- value - 0.5
31
Table 16: Pay Factors in FHWA Category II Method calculated using different Q’s
Pay Factor with Category II ($)
Case Number Q+ 0 Q+ 0.05 Q+ 0.1 Q+ 0.15 Q+ 0.2
1 0 0 0 0 0
2 0 0 0 0 0
3 0 0 0 0 0
4 - 726 - 1463 - 2289 - 2863 - 3789
5 0 0 0 0 0
6 0 0 0 0 0
7 - 3275 - 4337 - 4875 - 6468 - 61231
8 0 0 0 0 0
9 0 0 0 0 0
14 0 0 0 0 0
15 0 0 0 0 0
16 0 0 0 0 0
17 0 0 0 0 0
18 0 0 0 0 0
19 - 315000 - 315000 - 315000 - 315000 - 315000
20 0 0 0 0 0
21 0 0 0 0 0
22 - 3381 - 4520 - 6304 - 7697 - 9562
23 0 0 0 0 0
24 0 0 0 0 0
25 0 0 0 0 0
26 0 0 0 0 0
27 0 0 0 0 - 404
28 0 0 0 0 0
29 0 0 0 0 0
30 0 0 0 0 0
31 0 0 0 0 0
32 - 495000 - 495000 - 495000 - 495000 - 495000
33 - 165000 - 165000 - 165000 - 165000 - 165000
34 - 315000 - 315000 - 315000 - 315000 - 315000
35 - 390000 - 390000 - 390000 - 390000 - 390000
36 - 870000 - 870000 - 870000 - 870000 - 870000
37 - 165000 - 165000 - 165000 - 165000 - 165000
42 0 0 0 0 0
43 - 1505 - 2405 - 2905 - 4382 - 5873
44 0 0 0 0 0
45 0 0 0 0 0
46 0 0 0 0 0
47 0 0 0 0 0
32
0 10 20 30 40 50
Case Number
- 800000
- 400000
0
400000
Penalty, $
PWL & Q- value + 0
PWL & Q- value + 0.05
PWL & Q- value + 0.1
PWL & Q- value + 0.15
PWL & Q- value + 0.2
Series 1 Series 2 Series 3
Pay Factor with Category II
Figure 15 Plot of Pay Factor ( Penalty) between
Q- value and the PWL by Category II
0 10 20 30 40 50
Case Number
- 800000
- 400000
0
400000
Penalty, $
PWL & Q- value + 0
PWL & Q- value + 0.05
PWL & Q- value + 0.1
PWL & Q- value + 0.15
PWL & Q- value + 0.2
Series 1 Series 2 Series 3
Pay Factor with Kentucky OC Curve
Figure 16 Plot of Pay Factor ( Penalty) between
Q- value and PWL by the Kentucky OC Curve
33
Table 17: Pay Factors in the FHWA Kentucky OC Method
calculated by using different Q’s
Pay Factor with Kentucky OC Curve
Case Number Q+ 0 Q+ 0.05 Q+ 0.1 Q+ 0.15 Q+ 0.2
1 8775 8410 8004 7576 7070
2 5233 5168 5102 5037 4913
3 2250 2250 2250 2250 2250
4 - 12450 - 13422 - 14484 - 15537 - 16607
5 11625 11625 11625 11625 11625
6 7599 7378 7128 6878 6589
7 - 18797 - 20275 - 21764 - 23486 - 71368
8 34000 32215 30251 27979 25557
9 15750 15750 15750 15750 15750
14 2625 2625 2625 2625 2625
15 4125 4125 4125 4125 4125
16 2250 2250 2250 2250 2250
17 - 249 - 1009 - 1811 - 2752 - 3686
18 2250 2250 2250 2250 2250
19 - 315000 - 315000 - 315000 - 315000 - 315000
20 3000 3000 3000 3000 3000
21 6750 6746 6681 6590 6492
22 - 10320 - 13628 - 17160 - 20892 - 24951
23 1875 1875 1875 1875 1875
24 10500 10500 10500 10500 10500
25 6000 6000 6000 5970 5905
26 6402 6107 5732 5321 4884
27 - 6929 - 7429 - 7929 - 8429 - 9029
28 2250 2250 2250 2250 2250
29 7500 7500 7440 7375 7310
30 8844 8730 8549 8286 8005
31 5362 5143 4893 4643 4356
32 - 495000 - 495000 - 495000 - 495000 - 495000
33 - 165000 - 165000 - 165000 - 165000 - 165000
34 - 315000 - 315000 - 315000 - 315000 - 315000
35 - 390000 - 390000 - 390000 - 390000 - 390000
36 - 870000 - 870000 - 870000 - 870000 - 870000
37 - 165000 - 165000 - 165000 - 165000 - 165000
42 5250 5250 5250 5250 5250
43 - 18532 - 20208 - 21789 - 23706 - 25465
44 5625 5625 5625 5625 5625
45 2423 2358 2251 2101 1933
46 - 530 - 1007 - 1568 - 2202 - 2908
47 4125 4125 4125 4125 4125
34
3. Comparing Current and New ADOT methods
Table 18: Series 1. Comparison of Pay Factors for Current and New ADOT
Methods
TRAC
No
TRACs
number
Supplier Total Cost,
$
Penalty
of New
Method
% Penalty
of the
Total Cost
Penalty of
Current
Method
% Penalty
of the
Total Cost
1 H576801 Rinker 435,000 0 0.0 0 0.0
2 H552501 Sunshine
concrete 210,000 - 2250 1.1 - 6750 3.2
3 H407601 Rinker 90,000 0 0.0 0 0.0
4 Rinker
material 120,000 0 0.0 0 0.0
5 H416001C Cambell
Redi- mix 465,000 0 0.0 0 0.0
6 345,000 0 0.0 0 0.0
7 H319003C McNeil
Const. Co. 345,000 0 0.0 0 0.0
8 2,085,000 0 0.0 0 0.0
9 H313401C McNneil
Const. Co. 630,000 0 0.0 0 0.0
35
Table 19: Series 2. Comparison of Pay Factors for Current and New ADOT methods
Project
No
Name Supplier Total Cost Penalty
of New
ADOT
Method
% Penalty of
the Total
Cost
Penalty of
Current
ADOT
Method
% penalty of
the total cost
1 A11 Chandler
Ready Mix 10,5000
0 0.0 0 0.0
2 A13 165,000 0 0.0 0 0.0
3 A21 750,000 0 0.0 0 0.0
4 B11 Rinker 285,000 0 0.0 0 0.0
5 B12 90,000 0 0.0 0 0.0
6 B13 315,000 0 0.0 0 0.0
7 B21 120,000 0 0.0 0 0.0
8 B22 270,000 - 1500 0.6 - 6750 2.5
9 C11 Arizona
Materials 1,080,000 - 600 0.1 - 1500 0.1
10 C12 75,000 0 0.0 0 0.0
11 C13 420,000 - 4100 1.0 - 21750 5.2
12 C21 240,000 0 0.0 0 0.0
13 C22 300,000 0 0.0 0 0.0
14 C23 7,5000 0 0.0 0 0.0
15 D12 Hanson
Aggregates
of AZ 90,000
- 150 0.2 - 750 0.8
16 D13 300,000 0 0.0 0 0.0
17 D21 360,000 0 0.0 0 0.0
18 D23 255,000 0 0.0 0 0.0
19 E11 TPAC 495,000 0 0.0 0 0.0
20 E12 165,000 0 0.0 0 0.0
21 E13 315,000 0 0.0 0 0.0
22 E21 390,000 0 0.0 0 0.0
23 E22 870,000 0 0.0 0 0.0
24 E23 165,000 - 450 0.3 - 1500 0.9
36
Table 20: Series 3. Comparison of Pay Factors for Current and New ADOT Methods
Bridge
Project
Supplier Total
Cost
Penalty
of New
Method
% Penalty
of the Total
Cost
Penalty of
Current
Method
% penalty
of the total
cost
1 Wilson Wash 210,000 - 10950 5.2 - 18750 8.9
2 Sandy Blevens 285,000 - 4500 1.6 - 6750 2.4
3 Quail Springs 225,000 - 5250 2.3 - 21750 9.7
4 Poison 105,000 - 4500 4.3 - 6750 6.4
5 Deveore 255,000 - 1200 0.5 - 16500 6.5
6 Apprentice 165,000 - 750 0.5 - 15000 9.1
- 25000 - 20000 - 15000 - 10000 - 5000 0 5000
Penalty by Current ADOT Specification, in dollars
- 25000
- 20000
- 15000
- 10000
- 5000
0
5000
Penalty by Proposed ADOT Specification, in dollars
Current ADOT Penalty = $ 124,500
Proposed ADOT Penalty = $ 36,200
Total Material Cost= $ 13,590,000
New Penalty to
Old Penalty ratio= 25.9%
Figure17 Penalty from both ADOT methods
The penalty of the two ADOT methods from all series is plotted in Figure17. A
straight line relationship with a 45 degree angle and a zero intercept represents the same
amount of penalty of both ADOT methods. A slope steeper than 1: 1 value means that the
penalty from the proposed ADOT method is higher than the current ADOT method. On
the other hand, a slope flatter than 1: 1 implies that the proposed ADOT penalty is less
than the current ADOT penalty, which is the case here.
37
4. Exploring the Comparison of Four Different Methods
Applying these four methods, the penalty is calculated based on the following data: lot
size = 100 cubic yards and unit cost = $ 150 per cubic yards. The sample is assumed to be
four ( each lot has four samples). Both sides of specification limits are selected. The upper
specification is 6000 and the lower specification is 2000. The results are shown in Table
21.
Table 21: Series 1. Comparison of Pay Factors for the different Methods
Project TRACS
number
Supplier Required
strength
FHWA with Pay
Factor Category
II
Current
ADOT
New
ADOT
CA
1 H576801 Rinker 4500 0 0 0 0
2 H552501 Sunshine
Concrete
3000 0 - 6750 - 2250 - 6116
3 H407601 Rinker 3500 0 0 0 0
4 Rinker
Material
4000 0 0 0 0
5 H416001C Cambell
Redi- mix
2500B 0 0 0 0
6 3500S 0 0 0 0
7 H319003C McNeil
Const. Co.
4000 0 0 0 0
8 4000 0 0 0 0
9 H313401C McNeil
Const. Co.
4000 0 0 0 0
Note: If any lot is rejected, the total penalty is computed as the cost of the lot.
38
Table 22: Series 2. Comparison of Pay Factors for different Methods
No Supplier Require
strength
FHWA with Pay
factor category II
Current
ADOT
New
ADOT
CA
A11 Chandler Ready Mix 3000 0 0 0 0
A13 2500 0 0 0 0
A21
4000 0 0 0 0
B11 Rinker 3500 0 0 0 0
B12 4000 0 0 0 0
B13 4500 0 0 0 0
B21 3000 0 0 0 0
B22 3500 0 - 6750 - 1500 - 6116
C11 Arizona Materials 4500 0 - 1500 - 600 - 4280
C12 2500 0 0 0 0
C13 4000 - 120000 - 21750 - 4100 - 20792
C21 3000 0 0 0 0
C22 3000 0 0 0 0
C23 3000 0 0 0 0
D12 Hanson Aggregates
of AZ
4000 0 - 750 - 150 - 4280
D13 3500 0 0 0 0
D21 4000 0 0 0 0
D23 4000 0 0 0 0
E11 TPAC 5000 0 0 0 0
E12 5500 0 0 0 0
E13 5500 0 0 0 0
E21 4500 0 0 0 0
E22 5000 0 0 0 0
E23 6000 0 - 1500 - 450 - 4280
Note: If any lot is rejected, the total penalty is computed as the cost of the lot.
Table 23: Series 3. Comparison of Pay Factors for different Methods
Supplier Require
strength
FHWA with Pay
factor category II
Current
ADOT
New ADOT CA
1 Wilson Wash 4500 - 62521 - 18750 - 10950 - 29352
2 Sandy Blevens 4500 - 1743.9 - 6750 - 4500 - 6116
3 Quail Springs 4500 - 3020.9 - 21750 - 5250 - 10396
4 Poison 4500 0 - 6750 - 4500 - 6116
5 Deveore 4500 0 - 16500 - 1200 - 8560
6 Apprentice 4500 0 - 15000 - 750 - 4280
Note: If any lot is rejected, the total penalty is computed as the cost of the lot.
39
0 10 20 30 40 50
Case Number
$- 200,000
$- 100,000
$ 0
$ 100,000
Penalty, $
FHWA, $ 187,000
Current ADOT, $ 124,500
New ADOT, $ 36,200
CA , $ 110,684
Series 1 Series 2 Series 3
Figure 18 Plot Comparing four methods for all series
Figure18 presents that the FHWA penalty method is signifigant in Series 2. This can be
attributed to the chosen specification limits ( USL = 10,000 psi and LSL = F’c). Other
methods look similar and show the same direction. Considering the project cost, the
percentages of the total penalty for all four methods are low compared to the total
material cost of each series. It can be observed that the penalty given by FHWA is higher
than the other methods; however, the new ADOT method gives the lowest penalties. The
values in Table 24 show the summation of all the data in each series.
Table 24: All Series. Comparison of Pay Factors for different Methods
Case
Total Cost
of All the
Lots in the
Series, $
Total
Penalty
from
FHWA, $
Total
Penalty
from
FHWA,
%
Total
Penalty
from
New
ADOT, $
Total
Penalty
from
New
ADOT, %
Total
Penalty
from
Current
ADOT, $
Total
Penalty
from
Current
ADOT, %
Total
Penalty
from
CA, $
Total
Penalt
y from
CA, %
Series 1 4,725,000 0 0 - 2,250 0.05 - 6,750 0.14 - 6,116 0.13
Series 2 7,620,000 - 120,000 1.57 - 6,800 0.09 - 32,250 0.42 - 39,748 0.52
Series 3 1,245,000 - 67,285 5.40 - 27,150 2.18 - 85,500 6.87 - 64,820 5.21
Total 13,590,000 - 187,285 1.38 - 36,200 0.27 - 124,500 0.92 - 110,684 0.81
40
41
IV. Conclusions
• A majority of the samples evaluated meet or exceed the strength requirements
specified for the ADOT jobs. The overall process is satisfied, except for Series 3.
• There are excessive variations in the trends of the data which do not correlate with
the specified strength of the concrete and the areas of its applications. There are
potential opportunities to reduce the average and standard deviations of the
strength data. Reduction of the mean strength values delivered at the expense of
better quality control will translate into significant raw materials savings.
• The FHWA- PWL penalty is based on many factors such as the Q- value table and
the specification’s upper and lower limit. These factors lead to the rejection of a
sublot. This means that the FHWA approach should be employed carefully
because of the sensitivity of the method.
• In cases where an entire sublot is rejected, certain assumptions were applied to the
penalty calculation. For example, lot size = 100 cubic yards and unit cost = $ 150
per cubic yard. Then the estimation of penalty for each rejected sublot is around
$ 15,000. Such calculations may affect the comparison of the various
methodologies used.
• For the TRACs number samples ( Series 1), the FHWA- PWL method with Pay
Factor Category II resulted in two potential penalties, whereas there was only one
potential penalty for the other methods. Nevertheless, the total penalties for all
four methods are quite low when the total costs are considered ($ 0, $ 6,750,
$ 2,250 and $ 6116 for FHWA with Pay Factor Category II, current ADOT, new
ADOT, and CA methods, respectively).
• In the case of the randomly selected samples ( Series 2), the FHWA method with
Pay Factor Category II gave a 1.57% penalty of the total costs, the current ADOT
and CA methods gave an average of 0.45% penalty, while the new ADOT method
gave the lowest penalty which was 0.09% of the total costs.
• In the six bridge cases ( Series 3), all cases had lots rejected by the current ADOT,
new ADOT, and CA methods, although the FHWA method with Pay Factor
Category II showed only three cases that were penalized. The penalties given by
FHWA, current ADOT, and CA methods were similar and averaged 6% of the
total costs. The penalty from the new ADOT method was the lowest and resulted
in a 2.2% penalty.
• The estimation of pay factor by two different methods shows that they are quite
similar. The PWL method which was computed by the Kentucky OC curve was
generally friendlier to the supplier compared to the Category II method. In
addition, the Kentucky OC curve provided an award or bonus to the supplier
whereas there was no extra payment by using Category II. On the other hand, the
42
required PWL strength for the Category II method is 65%, but 95% to get the full
payment by the Kentucky OC curve.
• The average cost comparisons between the current and proposed ADOT equations
indicate that the approximate penalties in the new ADOT method are in the range
of 26% of the present penalty levels.
• Comparing the current and proposed ADOT methods, the penalties were assessed
in all six bridge cases supplied by the ADOT/ ARPA committee. The average
level of penalty was in the range of 6.9%. This level of penalty could be reduced
to 2.2% upon adoption of the new ADOT cost factor policy.
• The total amount of penalties in comparison to the cost of the projects is
insignificant. Out of total materials cost of $ 13,590,000 for the projects studied,
the total penalties are $ 124,000 ( 0.91% of total) and $ 36,200 ( 0.26% of total)
depending on the use of present or proposed ADOT formulas, respectively.
• The FHWA method presents a higher penalty than the other methods ( 1.38% of
the total cost of the projects) whereas the CA method shows a lower penalty
( 0.81%). The huge penalty is related to the rejection of several sublots. The
penalties are less than 1% for current ADOT, proposed ADOT, and CA methods.
• The proposed ADOT method seems to be friendly to the supplier and provide a
stable penalty. The 0.27% penalty is slightly lower than the current ADOT
method ( 0.92%). Applying these methods with quality control criteria would help
in enhancing concrete on jobsites with less out- of- control strength and thus
obtaining required strength and quality with less materials consumption.
APPENDIX A ( Probability plots) ( Note that the labeling for different series in the following pages are in Appendix F)
Data
Percent
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
99.9
99
95
90
80
70
60
50
40
30
20
10
5
1
0.1
Mean
0.553
4026 767.0 14 0.249 0.693
4608 570.2 23 0.491
StDev
0.198
3849 415.3 31 1.238 < 0.005
5695 562.6 8 0.252
N
0.629
4065 194.5 6 0.530 0.101
5013 412.5 139 1.165
AD
< 0.005
5414 658.2 23 0.326 0.504
4515 266.7 42 0.412
P
0.325
5186 360.2 29 0.302
Variable
H416001CR_ CAMP_ LAKE_ 3500S_ 3500
H416001CR_ CAMP_ LAKE_ 2500S_ 2500
H407601C_ 60141_ 1332439_ 4000
H407601C_ 55041_ 14016_ 3500
H319003C_ TUCSON_ 0203- 15_ 4000
H319003C_ TUCSON_ 0203- 10_ 4000
H313401CR
H576801CR
H552501C
Probability Plot of H576801CR, H552501C, H416001CR_ CA, ...
Normal - 95% CI
F
Figure A1 Probability Plot for Series 1
43
Data
Percent
2000 3000 4000 5000 6000 7000
99
95
90
80
70
60
50
40
30
20
10
5
1
Mean
0.629
4004 422.1 11 0.448 0.224
5301 477.2 50 1.054
StDev
0.008
N AD P
4700 390.1 7 0.247
Variable
A21
A11
A13
Probability Plot of A11, A13, A21
Normal - 95% CI
Figure A2 Probability plot for Project A: A11, A13 and A21
44
Data
Percent
2000 3000 4000 5000 6000 7000
99
95
90
80
70
60
50
40
30
20
10
5
1
Mean
0.043
4788 431.3 6 0.625 0.053
6254 307.4 21 0.344
StDev
0.453
4524 390.6 8 0.239 0.677
4446 757.5 19 0.260
N
0.673
AD P
5096 635.5 19 0.747
Variable
B13
B21
B22
B11
B12
Probability Plot of B11, B12, B13, B21, B22
Normal - 95% CI
Figure A3 Probability plot of Project B: B11, B12, B13, B21 and B22
45
Data
Percent
3000 4000 5000 6000 7000 8000
99.9
99
95
90
80
70
60
50
40
30
20
10
5
1
0.1
Mean
0.543
4565 452.7 73 0.205 0.868
4244 374.9 28 0.608
StDev
0.103
5183 271.6 16 0.299 0.542
4948 483.2 20 0.190
N
0.887
5770 354.7 6 0.276 0.518
AD P
5423 422.4 72 0.312
Variable
C13
C21
C22
C23
C11
C12
Probability Plot of C11, C12, C13, C21, C22, C23
Normal - 95% CI
Figure A4 Probability plot of Project C: C11, C12, C13, C21, C22 and C23
46
Data
Percent
2000 3000 4000 5000 6000 7000
99
95
90
80
70
60
50
40
30
20
10
5
1
Mean
0.250
4696 508.4 20 0.283 0.595
5146 452.2 24 0.866
StDev
0.022
4820 579.0 17 0.622 0.088
N AD P
4427 504.0 6 0.394
Variable
D21
D23
D12
D13
Probability Plot of D12, D13, D21, D23
Normal - 95% CI
Figure A5 Probability plot of Project D: D12, D13, D21 and D23
47
Data
Percent
4000 5000 6000 7000 8000 9000 10000 11000
99
95
90
80
70
60
50
40
30
20
10
5
1
Mean
0.024
7113 491.9 11 0.742 0.037
8631 620.3 20 0.593
StDev
0.108
6691 786.0 26 0.492 0.199
6876 524.3 57 0.382
N
0.388
6883 536.3 11 0.225 0.762
AD P
8251 809.1 28 0.854
Variable
E13
E21
E22
E23
E11
E12
Probability Plot of E11, E12, E13, E21, E22, E23
Normal - 95% CI
Figure A6 Probability plot of Project E: E11, E12, E13, E21, E22 and E23
48
Data
Percent
3000 4000 5000 6000 7000 8000
99
95
90
80
70
60
50
40
30
20
10
5
1
Mean
0.117
5414 712.3 19 0.537 0.147
4751 342.9 15 0.232
StDev
0.757
5029 532.9 7 0.445 0.194
5154 524.7 17 0.210
N
0.833
4919 364.4 11 0.171 0.907
AD P
4629 458.2 14 0.567
Variable
Quail Springs
Poison
Deveore
Apprentice
Wilson Wash
Sandy Blevens
Normal - 95% CI
Probability Plot of Series 3
Figure A7 Probability plot for Series 3
49
50
APPENDIX B ( X bar- S charts for Series 1)
Note: in the following pages, the top graph shows the X bar chart, which includes the
current ADOT criterion setting F’c as the lower limit ( LCL) equal to the X bar. The
bottom graph shows the S charts for modified ACI- 214 second criterion assuming
n
F F s z cr c
' = ' + . is the mean ( X ).
Figure B1. TRACs number: H576801C
S am p le
Sample Mean
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 4 9 5 1
LC L= 4 0 4 9
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 6 9 .8
U C L= 5 5 4 .6
L C L= 0
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
51
Figure B2. TRACs number: H552501C
S am p le
Sample Mean
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
2 5 0 0
__
X = 3 5 0 0
U C L= 3 6 8 5
LC L= 3 3 1 5
1
1
1
1
1
1
1
1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 6 9 .7
U C L= 2 2 7 .8
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
52
Figure B3. TRACs number: H407601C from plant 55041 and mix specification 14016
S am p le
Sample Mean
1 2 3 4 5 6
4 4 0 0
4 2 0 0
4 0 0 0
3 8 0 0
3 6 0 0
3 4 0 0
3 2 0 0
__
X = 3 5 0 0
U C L= 3 7 8 8
L C L = 3 2 1 2
1
1
1
1
1 1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 0 8 .3
U C L= 3 5 3 .6
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
53
Figure B4. TRACs number: H407601C from plant 60141and mix specification 1332439.
S am p le
Sample Mean
1 2 3 4 5 6 7 8
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 0 0 0
U C L= 4 2 1 1
L C L = 3 7 8 9
1
1
1
1
1 1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6 7 8
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 7 9 .2
U C L= 2 5 8 .8
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
54
Figure B5. TRACs number: H416001C from the Lake Havasu plant and mix
specification 2500S
S am p le
Sample Mean
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
2 5 0 0
2 0 0 0
__
X = 2 5 0 0
U C L= 2 7 2 8
L C L = 2 2 7 2
1
1
1
1
1
1 1 1 1
1
1
1 1
1
1
1 1
1
1
1
1
1 1
1
1
1 1 1
1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8 3 1
3 5 0
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 8 5 .9
U C L= 2 8 0 .6
L C L= 0
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
55
Figure B6. TRACs number: H416001C from the Lake Havasu plant and mix
specification 3500S
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
__
X = 3 5 0 0
U C L= 3 8 6 6
L C L= 3 1 3 4
1
1
1
1
1 1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 3 7 .7
U C L= 4 4 9 .7
L C L= 0
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
56
Figure B7. TRACs number: H319003C from the Tucson plant and mix
specification0203- 10
S a m p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
__
X = 4 0 0 0
U C L= 4 3 7 5
LC L= 3 6 2 5
1
1
1 1 1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S a m p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 9 2 .1
U C L= 4 9 3 .4
L C L = 0
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
57
Figure B8. TRACs number: H319003C from the Tucson plant and
mix specification0203- 15
S am p le
Sample Mean
1 1 5 2 9 4 3 5 7 7 1 8 5 9 9 1 1 3 1 2 7
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
__
X = 4 0 0 0
U C L= 4 4 0 5
L C L= 3 5 9 5
1
11
1
11
1
1
1
1
1
1
1
1
1
11
1
11
111
1
1
1
1
111
1
1
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
111
11
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
1
1
11
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
11
1
1
1
1
1
1
T e s ts p e r fo rm e d w i th u n e q u a l s a m p le s iz e s
X b a r C h a r t
S am p le
Sample StDev
1 1 5 2 9 4 3 5 7 7 1 8 5 9 9 1 1 3 1 2 7
9 0 0
8 0 0
7 0 0
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 2 0 7
U C L= 5 3 2
L C L= 0
1
1
1
1
11
1
T e s ts p e r fo rm e d w i th u n e q u a l s am p le s iz e s
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
58
Figure B9. TRACs number: H313401C
S a m p le
Sample Mean
1 5 9 1 3 1 7 2 1 2 5 2 9 3 3 3 7 4 1
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 0 0 0
U C L= 4 2 2 5
L C L = 3 7 7 5
1
1
1
1
1
1 1
1
1
1
1 1
1
1
1 1
1
1 1
1 1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 5 9 1 3 1 7 2 1 2 5 2 9 3 3 3 7 4 1
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 8 4 .8
U C L= 2 7 7 .0
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
59
APPENDIX C ( X bar- S charts for Series 2)
Figure C1. Project A11
S am p le
Sample Mean
1 2 3 4 5 6 7
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
__
X = 3 0 0 0
U C L= 3 2 7 6
L C L= 2 7 2 4
1
1
1
1 1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 2 3 4 5 6 7
3 5 0
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 1 0 3 .8
U C L= 3 3 9 .0
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
60
Figure C2. Project A13
S am p le
Sample Mean
1 2 3 4 5 6 7 8 9 1 0 1 1
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
2 5 0 0
2 0 0 0
__
X = 2 5 0 0
U C L= 2 7 5 2
L C L= 2 2 4 8
1
1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6 7 8 9 1 0 1 1
3 5 0
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 9 4 .6
U C L= 3 0 9 .1
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
61
Figure C3. Project A21
S am p le
Sample Mean
1 6 1 1 1 6 2 1 2 6 3 1 3 6 4 1 4 6
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 0 0 0
U C L= 4 2 2 3
L C L= 3 7 7 7
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1 1 1
1
1
1
1
1
1
1
1
1
1
1
1
1 1
X b a r C h a rt
S am p le
Sample StDev
1 6 1 1 1 6 2 1 2 6 3 1 3 6 4 1 4 6
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 8 3 .9
U C L= 2 7 4 .2
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
62
Figure C4. Project B11
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
__
X = 3 5 0 0
U C L= 3 8 9 3
L C L= 3 1 0 7
1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 4 7 .9
U C L= 4 8 3 .1
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
63
Figure C5. Project B12
S am p le
Sample Mean
1 2 3 4 5 6
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
__
X = 4 0 0 0
U C L= 4 2 3 7
L C L= 3 7 6 3
1
1
1
1
1
1
T e s ts p e r fo rm e d w i th u n e q u a l s a m p le s iz e s
X b a r C h a r t
S am p le
Sample StDev
1 2 3 4 5 6
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 2 1 .2
U C L= 3 1 1 .4
L C L= 0
T e s ts p e r fo rm e d w ith u n e q u a l sam p le s iz e s
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
64
Figure C6. Project B13
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1
7 0 0 0
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 4 8 7 2
L C L= 4 1 2 8
1
1 1
1 1
1
1
1
1
1
1
1
1
1
1
1 1 1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 4 0 .0
U C L= 4 5 7 .3
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
65
Figure C7. Project B21
S am p le
Sample Mean
1 2 3 4 5 6 7 8
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
__
X = 3 0 0 0
U C L= 3 1 7 7
LC L= 2 8 2 3
1
1
1
1
1
1 1
1
X b a r C h a r t
S am p le
Sample StDev
1 2 3 4 5 6 7 8
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 3 1 .3
U C L= 4 2 9 .1
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
66
Figure C8. Project B22
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
__
X = 3 5 0 0
U C L= 3 9 0 5
LC L= 3 0 9 5
1 1
1
1
1
1
1
1
1
1
1
1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 5 2 .3
U C L= 4 9 7 .5
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
67
Figure C9. Project C11
S am p le
Sample Mean
1 8 1 5 2 2 2 9 3 6 4 3 5 0 5 7 6 4 7 1
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 4 9 5 9
L C L= 4 0 4 1
1 1
1
1
1
1
1
1
1
1
1 1 1
1
1
1
1
1 1
1 1
1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1 1
1
1
1
1
1
1
1 1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1 1 1
X b a r C h a rt
S am p le
Sample StDev
1 8 1 5 2 2 2 9 3 6 4 3 5 0 5 7 6 4 7 1
7 0 0
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 7 2 .5
U C L= 5 6 3 .5
L C L= 0
1
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
68
Figure C10. Project C12
S am p le
Sample Mean
1 8 1 5 2 2 2 9 3 6 4 3 5 0 5 7 6 4 7 1
6 0 0 0
5 0 0 0
4 0 0 0
3 0 0 0
2 0 0 0
__
X = 2 5 0 0
U C L= 2 9 2 2
L C L= 2 0 7 8
1
1
1
1
1 1
1
1
1
1
1
1
11
1
1
1
1
1
1
1
11
1
1
1
1
1 1
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
11 1
1
1 1
1
1
11
1
1
1
11
1
1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 8 1 5 2 2 2 9 3 6 4 3 5 0 5 7 6 4 7 1
7 0 0
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 5 8 .7
U C L= 5 1 8 .6
L C L = 0
1
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
69
Figure C11. Project C13
S am p le
Sample Mean
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
__
X = 4 0 0 0
U C L= 4 2 7 6
L C L= 3 7 2 4
1
1 1
1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 0 4 .0
U C L= 3 3 9 .6
L C L = 0
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
70
Figure C12. Project C21
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
2 5 0 0
__
X = 3 0 0 0
U C L= 3 3 5 6
L C L= 2 6 4 4
1
1
1 1
1
1 1
1
1
1
1 1
1
1
1 1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 3 3 .8
U C L= 4 3 7 .0
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
71
Figure C13. Project C22
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
2 5 0 0
__
X = 3 0 0 0
U C L= 3 3 2 4
L C L= 2 6 7 6
1
1 1
1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 2 1 .8
U C L= 3 9 7 .9
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
72
Figure C14. Project C23
S am p le
Sample Mean
1 2 3 4 5
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
2 5 0 0
__
X = 3 0 0 0
U C L= 3 3 6 2
L C L= 2 6 3 8
1
1
1 1
1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 3 6 .3
U C L= 4 4 5 .1
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
73
Figure C15. Project D12
S am p le
Sample Mean
1 2 3 4 5 6
5 2 5 0
5 0 0 0
4 7 5 0
4 5 0 0
4 2 5 0
4 0 0 0
3 7 5 0
3 5 0 0
__
X = 4 0 0 0
U C L= 4 4 3 4
LC L= 3 5 6 6
1
1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 6 3 .2
U C L= 5 3 3 .1
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
74
Figure C16. Project D13
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
3 0 0 0
__
X = 3 5 0 0
U C L= 3 8 2 8
L C L= 3 1 7 2
1
1
1
1
1
1
1
1
1
1
1 1
1
1 1
1 1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 2 3 .4
U C L= 4 0 3 .0
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
75
Figure C17. Project D21
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 0 0 0
U C L= 4 2 4 7
L C L= 3 7 5 3
1 1 1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3
3 5 0
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 1 2 6 .5
U C L= 3 2 4 .9
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
76
Figure C18. Project D23
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 0 0 0
U C L= 4 1 8 1
L C L= 3 8 1 9
1
1
1
1
1
1
1 1 1
1
1
1
1 1
1 1
T e s ts p e r fo rm e d w i th u n e q u a l s am p le s iz e s
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 9 2 .7
U C L= 2 3 8 .2
L C L = 0
T e s ts p e r fo rm e d w ith u n e q u a l s am p le s iz e s
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
77
Figure C19. Project E11
S am p le
Sample Mean
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8
1 0 0 0 0
9 0 0 0
8 0 0 0
7 0 0 0
6 0 0 0
5 0 0 0
__
X = 5 0 0 0
U C L= 5 2 0 6
L C L= 4 7 9 4
1
1
1 1
1
1
1
1
1
1
1
1 1
1 1
1
1
1 1
1 1
1 1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5 2 8
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 7 7 .3
U C L= 2 5 2 .6
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
78
Figure C20. Project E12
S am p le
Sample Mean
1 2 3 4 5 6 7 8 9 1 0 1 1
8 0 0 0
7 5 0 0
7 0 0 0
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
__
X = 5 5 0 0
U C L= 5 7 6 7
L C L= 5 2 3 3
1
1 1
1
1
1 1
1
1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 2 3 4 5 6 7 8 9 1 0 1 1
3 5 0
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 1 0 0 .5
U C L= 3 2 8 .3
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
79
Figure C21. Project E13
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
1 0 0 0 0
9 0 0 0
8 0 0 0
7 0 0 0
6 0 0 0
5 0 0 0
__
X = 5 5 0 0
U C L= 5 7 9 5
L C L= 5 2 0 5
1
1
1
1
1 1
1
1
1
1
1 1 1
1
1
1
1 1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 1 0 .8
U C L= 3 6 1 .9
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
80
Figure C22. Project E21
S am p le
Sample Mean
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5
8 0 0 0
7 0 0 0
6 0 0 0
5 0 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 5 0 6 1
L C L= 3 9 3 9
1
1
1 1
1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1 1
1 1
1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 4 7 1 0 1 3 1 6 1 9 2 2 2 5
9 0 0
8 0 0
7 0 0
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 2 1 1 .1
U C L= 6 8 9 .6
L C L = 0
1
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
81
Figure C23. Project E22
S am p le
Sample Mean
1 7 1 3 1 9 2 5 3 1 3 7 4 3 4 9 5 5
9 0 0 0
8 0 0 0
7 0 0 0
6 0 0 0
5 0 0 0
4 0 0 0
__
X = 5 0 0 0
U C L= 5 7 1 3
L C L= 4 2 8 7
1
1
1
1
1
1
1
1
1
1
1
1
1
1 1
1 1
1
1 1
1
1
1
1
1 1 1 1
1 1
1
1 1
1
1
1
1
1 1
1
1
1
1
1
1
1
1
1
1
1
1 1
1
1
1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 7 1 3 1 9 2 5 3 1 3 7 4 3 4 9 5 5
1 2 0 0
1 0 0 0
8 0 0
6 0 0
4 0 0
2 0 0
0
_
S = 2 6 8
U C L= 8 7 6
L C L= 0
1
1 1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
82
Figure C24. Project E23
S am p le
Sample Mean
1 2 3 4 5 6 7 8 9 1 0 1 1
8 0 0 0
7 5 0 0
7 0 0 0
6 5 0 0
6 0 0 0
5 5 0 0
__
X = 6 0 0 0
U C L= 6 4 3 6
L C L= 5 5 6 4
1
1
1
1
1
1
1
1
1 1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6 7 8 9 1 0 1 1
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 6 4 .2
U C L= 5 3 6 .2
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
83
APPENDIX D ( X bar- S charts for Series 3)
Figure D1. Wilson Wash.
S am p le
Sample Mean
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 4 7 3 9
LC L= 4 2 6 1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 8 9 .7
U C L= 2 9 3 .1
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
84
Figure D2. Sandy Blevens
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
7 0 0 0
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
3 5 0 0
__
X = 4 5 0 0
U C L= 5 2 6 9
L C L= 3 7 3 1
1
1 1
1 1
1 1
1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9
1 6 0 0
1 4 0 0
1 2 0 0
1 0 0 0
8 0 0
6 0 0
4 0 0
2 0 0
0
_
S = 2 8 9
U C L= 9 4 4
L C L= 0
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
85
Figure D3. Quail Springs
S am p le
Sample Mean
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5
5 4 0 0
5 2 0 0
5 0 0 0
4 8 0 0
4 6 0 0
4 4 0 0
4 2 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 4 9 0 8
L C L= 4 0 9 2
1 1
1
1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5
7 0 0
6 0 0
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
0
_
S = 1 5 3 .6
U C L= 5 0 1 .7
L C L= 0
1
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
86
Figure D4. Poison
S am p le
Sample Mean
1 2 3 4 5 6 7
5 8 0 0
5 6 0 0
5 4 0 0
5 2 0 0
5 0 0 0
4 8 0 0
4 6 0 0
4 4 0 0
4 2 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 4 6 7 8
L C L= 4 3 2 2
1
1 1
1
1
1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6 7
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 6 7 .1
U C L= 2 1 9 .1
L C L= 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
87
Figure D5. Deveore
S am p le
Sample Mean
1 3 5 7 9 1 1 1 3 1 5 1 7
6 5 0 0
6 0 0 0
5 5 0 0
5 0 0 0
4 5 0 0
4 0 0 0
__
X = 4 5 0 0
U C L= 4 7 4 5
L C L= 4 2 5 5
1
1
1
1
1
1
1
1
1
1
1 1
1
1
X b a r C h a r t
S am p le
Sample StDev
1 3 5 7 9 1 1 1 3 1 5 1 7
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
_
S = 9 2 .1
U C L= 3 0 0 .9
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
88
Figure D6. Apprentice
S am p le
Sample Mean
1 2 3 4 5 6 7 8 9 1 0 1 1
5 8 0 0
5 6 0 0
5 4 0 0
5 2 0 0
5 0 0 0
4 8 0 0
4 6 0 0
4 4 0 0
4 2 0 0
__
X = 4 5 0 0
U C L= 4 6 1 8
L C L= 4 3 8 2
1
1
1
1
1
1
1
1
1 1
X b a r C h a rt
S am p le
Sample StDev
1 2 3 4 5 6 7 8 9 1 0 1 1
1 6 0
1 4 0
1 2 0
1 0 0
8 0
6 0
4 0
2 0
0
_
S = 4 4 .6
U C L= 1 4 5 .6
L C L = 0
S C h a r t
Sample mean and standard deviations represent statistical measures of compressive
strength in psi.
89
APPENDIX E ( Pay Factors)
Pay Factor Minimum Required PWL for a Given Pay Factor
Category II n= 3 n= 4 n= 5 n= 6 n= 7 n= 8 n= 9 n= 10 to n= 11
100 59 65 68 71 72 74 75 76
99 58 63 67 69 71 72 73 75
98 57 62 65 67 69 71 72 73
97 55 60 63 66 68 69 70 72
96 54 59 62 64 66 68 69 70
95 53 57 61 63 65 66 67 69
94 51 56 59 62 63 65 66 68
93 50 55 58 60 62 64 65 66
92 49 53 57 59 61 62 63 65
91 48 52 55 58 59 61 62 64
90 46 51 54 56 58 60 61 62
89 45 49 53 55 57 58 60 61
88 44 48 51 54 56 57 58 60
87 43 47 50 53 54 56 57 59
86 41 46 49 51 53 55 56 58
85 40 44 48 50 52 54 55 56
84 39 43 46 49 51 52 54 55
83 38 42 45 48 50 51 52 54
82 36 41 44 46 48 50 51 53
81 35 39 43 45 47 49 50 52
80 33 38 42 44 46 48 49 51
79 32 37 40 43 45 47 48 49
78 30 36 39 42 44 45 47 48
77 28 34 38 41 43 44 46 47
76 27 33 37 39 42 43 45 46
75 35 32 36 38 40 42 43 45
90
APPENDIX F ( Data information)
Series No Data Case
TRACSNo
1 1 H576801CR_ Rinker_ 33341_ 1333115_ 4500_ 672h
2 2 H552501C_ Sunshine_ Kingman_ S3000A_ 3000_ 672h
3 3 H407601C_ Rinker_ 55041_ 14016_ 3500_ 672h
4 4 H407601C_ RinkerMat_ 60141_ 1332439_ 4000_ 672h
5 5 H416001CR_ CAMPBELL_ LAKEHAVASU_ 2500S_ 2500_ 672h
6 6 H416001CR_ CAMPBELL_ LAKEHAVASU_ 3500S_ 3500_ 672h
7 7 H319003C_ McNeil_ Constco_ TUCSON_ 0203- 10_ 4000_ 672h
8 8 H319003C_ McNeil_ Constco_ TUCSON_ 0203- 15_ 4000_ 672h
1
9 9 H313401CR_ McNeil_ ConstCo_ TUCSON_ 9710- 3_ 4000_ 672h
Project
14 1 A11_ ChandlerReady_ 3_ 130624_ 3000_ 672h
15 2 A13_ ChandlerReady_ 3_ 4425_ 2500_ 672h
16 3 A21_ ChandlerReady_ 1_ 140204_ 4000_ 672h
17 4 B11_ Rinker_ 11241_ 14030_ 3500_ 672h
18 5 B12_ Rinker_ 11241_ 1333066_ 4000_ 672h
19 6 B13_ Rinker_ 11241_ 14504_ 4500_ 672h
20 7 B21_ Rinker_ 33341_ 14016_ 3000_ 672h
21 8 B22_ Rinker_ 33341_ 1333004_ 3500_ 672h
22 9 C11_ AZMat_ ValVista_ 15030_ 4500_ 672h
23 10 C12_ AZMat_ ValVista_ 13008_ 2500_ 672h
24 11 C13_ AZMat_ ValVista_ 14030A_ 4000_ 672h
25 12 C21_ AZMat_ QueenCreek_ 13008_ 3000_ 672h
26 13 C22_ AZMat_ QueenCreek_ 14030_ 3000_ 672h
27 14 C23_ AZMat_ QueenCreek_ 13530_ 3000_ 672h
28 15 D12_ HansonAggreofAZ_ ValleyPlant_ C40501_ 4000_ 672h
29 16 D13_ HansonAggreofAZ_ ValleyPlant_ C35501A_ 3500_ 672h
30 17 D21_ HansonAggreofAZ_ 40_ D402521_ 4000_ 672h
31 18 D23_ HansonAggreofAZ_ 40_ 840913_ 4000_ 672h
32 19 E11_ TPAC_ PHX_ 447_ 5000_ 672h
33 20 E12_ TPAC_ PHX_ 444_ 5500_ 672h
34 21 E13_ TPAC_ PHX_ 448M_ 5500_ 672h
35 22 E21_ TPAC_ TUCSON_ 2245_ 4500_ 672h
36 23 E22_ TPAC_ TUCSON_ 2248_ 5000_ 672h
2
37 24 E23_ TPAC_ TUCSON_ 2250_ 6000_ 672h
Bridge
42 1 Apprentice_ S4500
43 2 Deveore_ S4500
44 3 Poison_ S4500
45 4 Quail_ springs_ S4500
46 5 sandy_ blevens_ s4500
3
47 6 wilson_ wash_ S4500
91
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