Assessing Quality of Asphalt
Paving Jobs to Determine
Contractor Pay
Robin C. Wurl
James R. Lundy
2003 Quality & Productivity
Research Conference
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
2
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)
3
Pay Factor is a Function of the
Expected Quality Level
Pay Factor
1.05
Expected Quality Level Exceeded
1.00
Expected Quality Level Attained
0.95
0.90
0.85
0.80
0.75
Quality Level Unacceptable:
Tear out and replace
4
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
Job Pay
Factor
5
Nature 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
6
The Measure of Quality is Based
on Loss Function
• Consider univariate case:
X – mix quality characteristic
T – target of quality characteristic
• Quadratic Loss Function:
L   X T 
2
• Expected Loss:
E  L   E  X   T   V  X 
2
7
Quality Measures
E X T 
Measure of
Deviation from
Target
2
V X 
Measure of
Variability
8
Multiple QCs and
Target Changes During Job
kth QC
jth target change within
kth QC
X i jk
ith observation within
jth target change within
kth QC
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Quality Measures are Estimated for
Each QC and Target
• Estimate deviation
from target
 E  X
ijk
  T jk 
• Estimate variability
with
   X jk  T jk 
2
jk
V  X ijk 
2
with
2
S 2jk
10
Quality Measures are Averaged
Over Target Changes
• Use number of observations per target in
weighted average of quality measures
1
 
Nk
2
k
mk
 n jk 
j 1
2
jk
1
S 
Nk
2
k
mk
n
j 1
jk
S
2
jk
Nk – total # of obs. for kth QC
njk – # of obs. for jth target change in kth QC
mk – # of target changes in kth target 
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Individual 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
1.05
1.00
0.75
Specific Point Values
of Quality Measures
 k 1.05
 k 1.00
 k  0.75
Sk 1.05
Sk 1.00
Sk  0.75
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Linear Interpolation is Used Create
Continuous Mapping Function
F k
1.1
1.05
Pay Factor
1
0.95
0.9
0.85
0.8
0.75
0.7



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
k 1.00 
k 1.05 
k  0.75
Deviation from Target
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Account for Unequal Importance
of QCs
• Assign weights to QCs to account for
different relative importance
• wk - relative importance weight of QC
p
w
k 1
k
1
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Intermediate “Pay Factor” Values
Computed for Quality Measures
• Deviation from target:
p
F   wk Fk
k 1
• Variability:
p
FS   wk FSk
k 1
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Intermediate “Pay Factor” Value
Computed for a Specific QC
• For kth QC:
Fk  wk  Fk  FSk 
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Pay Factor for the Overall Job
is Computed
• Overall:
p
1
F   Fk
p k 1
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Example 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
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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
X 11  3.48
X 21  5.43
   3.48  4   0.27
 221   5.43  4.3  1.27
S112  0.08
S212  0.14
2
11
2
2
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Quality Measures Averaged Over
Target Changes
Weighted Averages
Air Voids (%) Density (%)
2
S2
0.71
0.61
0.11
0.54
12   5  0.27    4 1.27  9  0.71
Number of
observations for
target 1
Number of
Observations
for target 2
S12   5 0.08   4  0.14  9  0.11
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Deviation from Target for Air Voids
Mapped to Individual “Pay Factor”
Air Voids (%)
1.10
F1
1.05
Pay Factor
1.00
0.95
0.90
0.85
0.80
0.75
0.70
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
Deviation from Target
12 
0.71  0.84  F1  0.95
1.6 1.7
1
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Quality Measures Mapped to
Pay Factor Values
Air Voids (%)
Density (%)
Quality Measure Pay Factor
Quality Measure
Pay Factor
1  0.84
0.95
2  0.79
1.01
0.99
S1  0.33
1.05
S2  0.74
1.01
1.03
1.21
1.01
0.80
Intermediate Pay Factor
for Deviation from Target:
 
 
F   w1  F1   w2  F2
Overall Pay Factor
F   0.80  1.21 2  1.01
  0.4  0.95    0.6 1.01
 0.99
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