Estimation of the mean cumulative number of failures in a repairable system with mixed exponential component lifetimes

Abstract

AbstractComponents in electronic systems are often observed to be likely to fail at an early age, an effect well known as the ‘infant mortality’ effect. Similarly, for systems composed of such components, a decrease in the rate of occurrence of failures, usually called the ‘reliability improvement’ effect, is seen in the early operating period. In this paper we show that such improvement may be considered as a simple consequence of the heterogeneity among the components in the population. We present a simple three‐parameter model for the distribution of the component lifetime, which has a simple physical interpretation, and from which we obtain methods for statistical inference, suitable for implementation on even small computers. The methods have been applied successfully to field failure data, collected from an industrial company.