Maximum Likelihood Estimation and the Multivariate Bernoulli Distribution : An Application to Reliability

Abstract

We investigate systems designed using redundant component configurations. If external events exist in the working environment that cause two or more components in the system to fail within the same demand period, the designed redundancy in the system can be quickly nullified. In the engineering field, such events are called common cause failures (CCFs), and are primary factors in some risk assessments. If CCFs have positive probability, but are not addressed in the analysis, the assessment may contain a gross over-estimation of the system reliability. We apply a discrete, multivariate shock model for a parallel system of two or more components, allowing for positive probability that such external events can occur. The methods derived are motivated by attribute data for emergency diesel generators from various U. S. nuclear power plants. Closed form solutions for maximum likelihood estimators exist in some cases; statistical tests and confidence intervals are discussed for the different test environments considered.