Probabilistic models of decreasing failure rate processes

The “infant mortality” effect observed in the statistical treatment of reliability consists of a decreasing with age of the conditional probability of equipment failure (failure rate). One widely applicable explanatory hypothesis is that of population heterogeneity. This is developed here as a basis for several specific models of decreasing failure rate processes. Since, in the case of repairable devices, decreasing failure rate is often observed after the occurrence of failure and repair, consideration is extended to include repair in an explicit way. This union of failure and repair models is a fruitful one in view of the interaction between the two processes and gives a complete picture of the life of the device in terms of a stochastic process, usually with non-independent interfailure times. Four models, of particular significance due to their plausibility, mathematical tractability, and frugality of parameterization, are presented.