A Distribution-Free Bayesian Approach for Determining the Joint Probability of Failure of Materials Subject to Multiple Proof Loads

Abstract

Survival of manufacturing materials or component parts may depend on two or more variables, and yet joint strength tests can be difficult to perform. For many such materials, multiple strength properties can be estimated only using destructive testing. This problem gives rise to a technique called proof loading—stressing units up to a prescribed load, destroying only the weaker units, and leaving the survivors for further tests. We propose a distribution-free Bayesian approach for estimating the probability of joint failure under two proof loads. Our method does not assume that proof-load survivors are undamaged.