Reliability Analysis of Limited Failure One-Shot Devices

Meeker introduced the concept of limited failure population (LFP) while studying integrated circuits, where most devices exhibit a near-zero probability of failure throughout their technological life, while a small subset contains latent defects that manifest only after prolonged operation. In this article, we extend the LFP framework to the context of one-shot device testing, wherein devices get destroyed or must be rebuilt after testing. We propose a model that incorporates a relationship between defect probability and a set of covariates and develop an expectationmaximization algorithm for estimating the model parameters. The effectiveness of the proposed method is then assessed through a Monte Carlo simulation study, assuming the lifespan of defective devices follow a log-location-scale distribution. Finally, the developed methods are applied to three real datasets.