Statistical Modeling and Analysis of Repairable Systems

Abstract

A repairable system can briefly be characterized as a system which is repaired rather than replaced after a failure. The most commonly used models for the failure process of a repairable system are nonhomogeneous Poisson processes (NHPP), corresponding to minimal repairs, and renewal processes (RP), corresponding to perfect repairs. The paper reviews models for more general repair actions, often called “better-than-minimal repair” models. In particular we study the class of so called trend-renewal processes (TRP), which has both the NHPP and the RP as special cases. Parametric inference in TRP models is considered, including cases with several systems involving unobserved heterogeneity. Trend testing is discussed when the null hypothesis is that the failure process is an RP. It is shown how Monte Carlo trend tests for this case can be made from the commonly used trend tests for the null hypothesis of a homogeneous Poisson process (e.g. the Laplace test and the Military Handbook test). Simulations show that the Monte Carlo tests have favorable properties when the sample sizes are not too small.Keywords and phrasesRepairable systemnonhomogeneous Poisson processrenewal processbetter-than-minimal repairheterogeneitytrendMonte Carlo test