Lower Confidence Bounds for System Reliability from Binary Failure Data Using Bootstrapping

We consider the problem of determining a (1 – A) 100% lower confidence bound on the system reliability for a coherent system of k components using the failure data (yi, ni), where yi is the number of components of type i that pass the test and ni is the number of components of type i on test, i1, 2, …, k. We assume throughout that the components fail independently, e.g. no common-cause failures. The outline of the article is as follows. We begin with the case of a single (k1) component system where n components are placed on a test and y components pass the test. The Clopper-Pearson lower bound is used to provide a lower bound on the reliability. This model is then generalized to the case of multiple (k1) components. Bootstrapping is used to estimate the lower confidence bound on system reliability. We then address a weakness in the bootstrapping approach-the fact that the sample size is moot in the case of perfect test results, e.g. when yi ni for some i. This weakness is overcome by using a beta prior distribution to model the component reliability before performing the bootstrapping. Two subsections consider methods for estimating the parameters in the beta prior distribution for components with perfect test results. The first subsection considers the case when previous test results are available, and the second subsection considers the case when no previous test results are available. A simulation study compares various algorithms for calculating a lower confidence bound on the system reliability. The last section contains conclusions.https://scholarworks.wm.edu/asbookchapters/1110/thumbnail.jp