Zero failure data

Abstract

Estimating failure probabilities or risk in the absence of observed failures is a recurring challenge in reliability engineering, especially for prototype systems or highly reliable components. Three primary methodologies address this “zero-failure-data” problem. Pessimistic estimates utilize upper confidence limits or Bayesian distributions based on noninformative priors, such as the Jeffreys prior, to establish conservative risk bounds. Alternatively, data from similar equipment can be integrated using empirical or hierarchical Bayes methods, which often yield more accurate posterior distributions than noninformative priors. In cases where data is generic or limited to summary form, constrained noninformative priors provide a way to incorporate engineering judgment by maximizing entropy subject to known mean constraints. Finally, complex systems may be analyzed by decomposing them into constituent parts or processes where failure data is available, a technique essential to probabilistic safety assessment and load-strength interference modeling. While zero-failure scenarios typically restrict estimates to conservative upper bounds, the observation of even a few failures significantly improves the stability of Bayesian conclusions and reduces the sensitivity of results to the specific details of the prior distribution. – AI-generated abstract.