1. Assessing Quality of Asphalt Paving Jobs to Determine Contractor Pay Robin C. Wurl James R. Lundy 2003 Quality & Productivity Research Conference

2. 2 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

3. 3 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)

4. 4 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 Factor 0.80 0.85 0.90 0.95

5. 5 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

6. 6 Nature of Pavement Mixes Multiple Quality Characteristics (QCs) – X 1, X 2, …, X p 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

7. 7 The Measure of Quality is Based on Loss Function Consider univariate case: X – mix quality characteristic T – target of quality characteristic Quadratic Loss Function: Expected Loss:

8. 8 Quality Measures Measure of Deviation from Target Measure of Variability

9. 9 Multiple QCs and Target Changes During Job i th observation within j th target change within k th QC j th target change within k th QC k th QC

10. 10 Quality Measures are Estimated for Each QC and Target Estimate deviation from target with Estimate variability with

11. 11 Quality Measures are Averaged Over Target Changes Use number of observations per target in weighted average of quality measures

12. 12 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

13. 13 Linear Interpolation is Used Create Continuous Mapping Function

14. 14 Account for Unequal Importance of QCs Assign weights to QCs to account for different relative importance w k - relative importance weight of QC

15. 15 Intermediate Pay Factor Values Computed for Quality Measures Deviation from target: Variability:

16. 16 Intermediate Pay Factor Value Computed for a Specific QC For k th QC:

17. 17 Pay Factor for the Overall Job is Computed Overall:

18. 18 Example Asphalt Paving Job X 1 Air voids in pavement mix (%) Target: T 1 = 4% and changes to 4.3% Relative importance: w 1 = 0.4 X 2 In-place density of pavement (%) Target: T 2 = 93% Relative importance: w 2 = 0.6

19. 19 Quality Measures Computed within Each Target Observation X ijk Target T jk Air Voids (%)Density (%)Air Voids (%)Density (%) 13.991.04.093 23.692.24.093 33.491.64.093 43.392.14.093 53.292.94.093 65.592.64.393 74.993.14.393 85.54.3 95.84.3

20. 20 Quality Measures Averaged Over Target Changes Weighted Averages Air Voids (%)Density (%) 0.710.61 0.110.54 Number of observations for target 1 Number of Observations for target 2

21. 21 Deviation from Target for Air Voids Mapped to Individual Pay Factor Deviation from Target

22. 22 Air Voids (%)Density (%) Quality MeasurePay FactorQuality MeasurePay Factor 0.951.010.99 1.051.011.03 0.801.211.01 Quality Measures Mapped to Pay Factor Values Intermediate Pay Factor for Deviation from Target: Intermediate Pay Factor for Deviation from Target: Overall Pay Factor