On Estimating Component Reliability for Systems with Random Redundancy Levels

Redundancy is a well understood and widely used design factor which can contribute appreciably to improve the reliability of a system. Reliability is improved, for example, when any fixed component is replaced by a parallel system of independent, identically distributed components. In this study, we discuss and treat problems in which the level of redundancy, K, is a random variable governed by a (known or unknown) discrete probability model. Given repeated observations on K and on the lifetime of a parallel system with K independent, identically distributed components, an estimator is derived for the reliability of the individual components. The consistency of the estimator is established, and its asymptotic distribution theory is discussed.