Assessing Quality of Asphalt Paving Jobs to Determine

Contractor Pay

Assessing Quality of Asphalt Paving Jobs to Determine

Contractor Pay

Robin C. WurlJames R. Lundy

2003 Quality & Productivity Research Conference

22

Contractors Employed for Asphalt Paving Jobs in Oregon

Contractors Employed for Asphalt Paving Jobs in Oregon

• Job price established prior to commencing

• At job completion, quality of pavement assessed– If pavement quality exceeds expectations

• Contractor receives pay bonus

– If pavement quality below expectations• Contractor is given a pay penalty

33

Bonus or Penalty is Determined by a Pay Factor

Bonus or Penalty is Determined by a Pay Factor

• Pay Factor

– Index between 0.75 and 1.05

– Multiplied by original job price to determine final payout figure

• Final Payout = (Job Price) x (Pay Factor)

44

Pay Factor is a Function of the Expected Quality Level

Pay Factor is a Function of the Expected Quality Level

Quality Level Unacceptable:Tear out and replace

0.75

Expected Quality Level Attained

Expected Quality Level Exceeded

1.00

1.05

Pay FactorPay Factor

0.80

0.85

0.90

0.95

55

Goal: Map Job Quality to a Pay Factor

Goal: Map Job Quality to a Pay Factor

• Statistically quantify quality of pavement job

• Map statistical quality measure of job to pay factor

Statistical Quality Level of Job

Statistical Quality Level of Job

Job Pay Factor

Job Pay Factor

66

Nature of Pavement MixesNature of Pavement Mixes

• Multiple Quality Characteristics (QCs)– X1, X2, …, Xp

• Target values for QCs may change during job• Process adjustments in beginning of production• Changes in raw materials during production

• QCs not all equally important

77

The Measure of Quality is Based on Loss Function

The Measure of Quality is Based on Loss Function

• Consider univariate case: X – mix quality characteristicT – target of quality characteristic

• Quadratic Loss Function:

• Expected Loss:

2L X T

2E L E X T V X

88

Quality MeasuresQuality Measures

2E X T

Measure of Deviation from

Target

Measure of Deviation from

Target

Measure of Variability

Measure of Variability

V X

99

Multiple QCs and Target Changes During Job

Multiple QCs and Target Changes During Job

i j kX

ith observation within jth target change within

kth QC

ith observation within jth target change within

kth QC

jth target change within kth QC

jth target change within kth QC

kth QCkth QC

1010

Quality Measures are Estimated for Each QC and Target

Quality Measures are Estimated for Each QC and Target

• Estimate deviation from target

with

• Estimate variability

with

2

ijk jkE X T

22jk jk jkX T

ijkV X

2jkS

1111

Quality Measures are Averaged Over Target Changes

Quality Measures are Averaged Over Target Changes

• Use number of observations per target in weighted average of quality measures

2 2

1

1 km

k jk jkjk

nN

Nk – total # of obs. for kth QC

njk – # of obs. for jth target change in kth QC

mk – # of target changes in kth target

2 2

1

1 km

k jk jkjk

S n SN

1212

Individual Quality Measures are Mapped to “Pay Factor” ValuesIndividual Quality Measures are Mapped to “Pay Factor” Values

• Specific point values of quality measures mapped to “equitable” pay factor– Mappings determined from expertise about process– Straight units (not squared) for quality measures

Pay Factor

Specific Point Values of Quality Measures

1.05 1 05.k 1 05.kS

1.00 1 00.k 1 00.kS

0.75 0 75.k 0 75.kS

1313

Linear Interpolation is Used Create Continuous Mapping Function

Linear Interpolation is Used Create Continuous Mapping Function

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Deviation from Target

Pay

Fac

tor

1.05k 1 00.k 0 75.k

kF

1414

Account for Unequal Importance of QCs

Account for Unequal Importance of QCs

• Assign weights to QCs to account for different relative importance

• wk - relative importance weight of QC

1

1p

kk

w

1515

Intermediate “Pay Factor” Values Computed for Quality Measures

Intermediate “Pay Factor” Values Computed for Quality Measures

• Deviation from target:

• Variability:

1k

p

kk

F w F

1k

p

S k Sk

F w F

1616

Intermediate “Pay Factor” Value Computed for a Specific QC

Intermediate “Pay Factor” Value Computed for a Specific QC

• For kth QC:

k kk k SF w F F

1717

Pay Factor for the Overall Job is Computed

Pay Factor for the Overall Job is Computed

• Overall:

1

1 p

kk

F Fp

1818

Example Asphalt Paving JobExample Asphalt Paving Job

• X1 Air voids in pavement mix (%)• Target: T1 = 4% and changes to 4.3%

• Relative importance: w1 = 0.4

• X2 In-place density of pavement (%)• Target: T2 = 93%

• Relative importance: w2 = 0.6

1919

Quality Measures Computed within Each Target

Quality Measures Computed within Each Target

Observation Xijk Target Tjk

Air Voids (%) Density (%) Air Voids (%) Density (%)

1 3.9 91.0 4.0 93

2 3.6 92.2 4.0 93

3 3.4 91.6 4.0 93

4 3.3 92.1 4.0 93

5 3.2 92.9 4.0 93

6 5.5 92.6 4.3 93

7 4.9 93.1 4.3 93

8 5.5 4.3

9 5.8 4.3

2211 3 48 4 0 27. .

11 3 48.X

211 0 08.S

2221 5 43 4 3 1 27. . .

21 5 43.X

221 0 14.S

2020

Quality Measures Averaged Over Target Changes

Quality Measures Averaged Over Target Changes

Weighted Averages

Air Voids (%) Density (%)

0.71 0.61

0.11 0.54

22S

21 5 0 27 4 1 27 9 0 71 . . .

21 5 0 08 4 0 14 9 0 11S . . .

Number of observations for target 1

Number of observations for target 1

Number of Observations for target 2

Number of Observations for target 2

2121

Deviation from Target for Air Voids Mapped to Individual “Pay Factor”Deviation from Target for Air Voids Mapped to Individual “Pay Factor”

Air Voids (%)

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Pa

y F

ac

tor

Deviation from Target 1

1F

1

21 0 71 0 84 0 95F . . .

2222

Air Voids (%) Density (%)

Quality Measure Pay Factor Quality Measure Pay Factor

0.95 1.01 0.99

1.05 1.01 1.03

0.80 1.21 1.01

Quality Measures Mapped to Pay Factor Values

Quality Measures Mapped to Pay Factor Values

2 0 79 .1 0 84 .

1 0 33S . 2 0 74S .

Intermediate Pay Factorfor Deviation from Target:

Intermediate Pay Factorfor Deviation from Target:

1 21 2

0 4 0 95 0 6 1 01

0 99

F w F w F

. . . .

.

Overall Pay FactorOverall Pay Factor

0 80 1 21 2 1 01F . . .