Prediction of Reliability of an Arbitrary System from a Finite Population

摘要

When analyzing single-use nonrepairable systems that degrade over time, summaries of reliability as a function of age often are naturally formulated for individual systems to answer the question "For a given system of a particular age, what is its reliability with its associated uncertainty?" However, in other cases, the natural summary of interest is to predict the probability that an arbitrary system randomly selected from the population works. This second question is a function of both the probability of individual systems working at their given ages as well as the demographics of the population of interest. In this article we discuss the relevance of both these questions for two applications, describe a method for predicting population reliability, and illustrate how the second summary can be efficiently obtained from individual reliability estimates for analyses based on the Probit and Weibull models.