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## Development and Implementation of a Performance-Related Specification for I-65 Tennessee: Final Report

### APPENDIX C: Expected Pay Information

#### EXPECTED PAY CHARTS

Information can be developed that shows the risks of using the plan to both the agency and the contractor. The PaveSpec software provides expected pay charts, which are graphical representations of an acceptance plan, that show the relation between the actual quality of a given lot and the pay the contractor can expect to receive (on average) for submitted lots of that quality. Figures C-1, C-2, C-3, and C-4 show the expected pay for strength (with two different standard deviations), thickness, and smoothness or profile index, respectively.

Focusing on strength as an example, if the contractor produces a lot with exactly the target mean strength of 4,500 lbf/in2 (31.03 MPa) and standard deviation of 500 lbf/in2 (3.45 MPa), figure C-1 (left side chart) shows that the probability of acceptance with, say, 100 percent pay or better is 50 percent (which of course is logical). If the contractor desires a higher probability to achieve an incentive, the mean strength of the lot could be increased to, say, 4,750 lbf/in2 (32.75 MPa). The probability of acceptance with at least 100 percent is then 95 percent. For this true lot mean strength of 4,750 lbf/in2 (32.75 MPa), the right hand chart of figure C-1 shows that the contractor would be expected to receive 102 percent 50 percent of the time. If the contractor wanted to greatly increase his pay factor, the mean lot strength would have to be increased to, say, 5,500 lbf/in2 (37.92 MPa) where the expected pay factor would be about 104 percent. Obviously many other statements could be created to analyze the risks using the acceptance plan. Also, changing the number of samples per sublot would change the slope of these curves.

 Figure C-1. Expected pay chart for compressive strength (standard deviation = 500 lbf/in2).

Figure C-2 shows the impact of increased variation of strength on the risks involved to the agency and contractor. This expected pay chart is developed for a standard deviation of 1,000 lbf/in2 (6.89 MPa) of strength or twice the variability of figure C-1. In this case, if the lot mean is truly at 4,500 lbf/in2 (31.03 MPa), the probability of receiving 100 percent pay is reduced to 30 percent rather than 50 percent with a standard deviation of 500 lbf/in2 (3.45 MPa). The mean expected pay factor is 99 percent.

 Figure C-2. Expected pay chart for compressive strength (standard deviation = 1,000 lbf/in2).
 Figure C-3. Expected pay chart for slab thickness (standard deviation = 0.5 in.).
 Figure C-4. Expected pay chart for profile index (standard deviation = 1.0 in.).

The expected pay curves developed by PaveSpec provide very useful information for the contractor and the agency to assess the risks associated with the performance-related specification.

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Updated: 02/20/2015