Heterogeneous Part Quality as a Source of Reliability Improvement in Repairable Systems

Abstract

Distributions of part life lengths are often seen to have a decreasing force of mortality during the early life of the part. This effect is known as the infant mortalify effect. A similar decrease in the rate of occurrence of failures has been observed in field-failure data for repairable systems. In this article, we show how this improvement of system reliability can be understood as a consequence of heterogeneity in the quality of parts. We present a superimposed-renewalprocess model based on this assumption. The model results in a simple analytical expression for the rate of occurrence of failures with parameters that admit a direct physical interpretation. We compare the statistical properties of this model with models based on a postulated structure for the peril rate of a nonhomogeneous Poisson process, and in an example we illustrate the estimation of parameters in our model.