Setting probabilistic limits for the minimum thickness of uninspected feeder pipes

This paper describes a methodology for providing probabilistic limits at specified confidence for the probability that unobserved feeder wall thickness will be above a specified minimum value based on existing measurements. The objective is to determine whether the existing sample provides sufficient evidence to preclude the need for 100% inspection. The approach uses the joint distribution of the uninspected and inspected feeder thicknesses to estimate the probability that this minimum is exceeded in the uninspected feeders. In the normal case, the joint distribution is given by a multivariate t. Although the procedure can be applied to different population distributions, it appears that the Gumbel is the most appropriate model for the problem at hand and for which the required distribution can be obtained numerically by simulation. Mathematical details will be kept to a minimum in the presentation, and emphasis will be on explaining predictive intervals, which deal with observables, and contrasting them with the more commonly used confidence intervals, which deal with parameters. (author)