Determining Optimum Sample Size for Percent-Within-Limits Specifications

Abstract

Highway construction and materials acceptance plans use a sample size that is often established on the basis of practical considerations such as personnel and time constraints. Commonly used sample sizes range between three and seven units. While a sample size within this range may be practical, it may not be economically optimal. If this sample size is too small, the probability of making erroneous acceptance or pay adjustment decisions (and thus the expected cost consequences of these decisions) would be too high for state departments of transportation (DOTs). If this sample size is too large, the cost of sampling and testing would be unnecessarily high, especially where destructive testing is used. A computational model for determining the optimum sample size was developed and is presented in this paper. This model is intended to help highway agencies determine how much to sample to minimize their total acceptance cost (cost of sampling and testing plus the cost of erroneously accepting poor-quality materials and construction). Inputs to this model can be obtained from an agency's specifications book, historical data on quality, prevalent unit bid prices, and prevalent sampling and testing prices. The developed model was applied to determine the optimum sample size for the AASHTO acceptance plan for binder content and density of hot-mix asphalt concrete pavements. The model shows that, when historical quality levels are satisfactory, the state DOT may consider reducing sample size as much as practically possible (in most cases, a sample size of three per lot for each acceptance quality characteristic is optimal). Only in the case of large lot size, combined with historically extremely poor quality and high unit bid price, was a larger sample size found to be optimal (n = 7 to 8).