Accounting for Measurement Uncertainty in Alternative Sampling Plans for Verification of Pipeline Material Properties

Abstract The statistical formulations of alternative sampling plans to achieve “at least a 95% confidence level that material properties used in the operation and maintenance of the pipeline are valid” under US 49 CFR 192 have been studied previously. The resulting conservative lower bounds on yield strength (YS) have been presented under both frequentist and Bayesian approaches. Every physical measurement of YS, whether in the field or in the laboratory, embodies at least two components of variation. First, the YS itself varies throughout the material under test across the many pipe joints in a population. Second, the measurement method has an associated uncertainty inherent in the technology employed to accomplish it. The observed results reported from the measurement method necessarily contain contributions from both sources of variation. The previous formulations for statistical lower bounds on YS remain conservative in the presence of measurement uncertainty by bounding the total material and measurement uncertainties taken together. But those bounds might be an overly conservative bound on YS if the measurement uncertainty is not negligible. This paper presents a study of statistical approaches to developing a lower bound on YS that explicitly account for the presence of measurement uncertainty, separating out the effects of measurement uncertainty to arrive at a less conservative bound on just the YS variation. The study employs simulations of alternative sampling plans under various YS and measurement uncertainty conditions across a range of YS and measurement uncertainties that might be typical in actual pipeline applications. The study examines the effectiveness of the statistical approaches at separating the components of the combined uncertainty, recovering both the true lower bound on YS and the true associated measurement uncertainty. A comparison against truth is possible since full knowledge for the simulated populations is available. The resulting YS bounds are also compared against the more conservative statistical bounds developed previously that combine both sources of uncertainty into the bound.