Alternative Sampling Plans for Verification of Pipeline Material Properties: Frequentist and Bayesian Statistical Approaches

The creation and retention of accurate records reflecting the makeup of a pipeline is a critical aspect of pipeline safety. In the U.S., 49 CFR 192 provides guidance on the verification of pipeline material properties for populations of like pipe, including the development of alternative sampling plans for populations that lack complete documentation. But the code provides little guidance on how to formulate such a plan and how to process the samples as they arrive. Various statistical approaches exist for developing lower bounds on material properties based upon measurements. On one hand, frequentist (or classical) approaches are sometimes simpler to understand and implement. On the other hand, Bayesian approaches allow for the incorporation of natural prior information to improve the estimate. Estimating the yield strength (YS) is often one of the most important objectives of an alternative sampling plan. This paper presents a study of frequentist and Bayesian statistical approaches to developing a lower bound on YS using simulations of alternative sampling plans. Various hypothetical pipe populations with different distribution assumptions, indicative of different possible manufacturing patterns at the pipe mill, are simulated then alternative sampling plans are conducted for each simulated population under both frequentist and Bayesian statistical approaches. For each approach, the resulting lower bound on YS is estimated and compared with the true population lower bound. This direct comparison is possible since full information on the simulated populations is available. The relative merits of each statistical approach are compared, and recommendations about which approaches are most suitable are provided.