Nonparametric Methods for Analysis of Repair Data

Repair models specify the joint distribution of the failure times of a system subject to repair. Prominent models include the minimal repair model, the Brown–Proschan model, the Block–Borges–Savits model, the Kijima models, and the general Dorado–Hollander–Sethuraman model. For such models, failure-time data and data on the types of repairs performed allow inference for the distribution F of the time to first failure of the system and other features of the system that can be defined in terms of F. This article surveys some nonparametric inference procedures for repair data, including frequentist and Bayesian estimation of F, simultaneous confidence bands for F, two-sample tests, tests of the minimal repair assumption, and goodness-of-fit tests. Keywords: Bayes estimation; cumulative hazard function; destructive repair; distribution of the time to first failure; effective age; failure rate; goodness of fit; interfailure times; life supplement; simultaneous confidence band; testing the minimal repair assumption; two-sample test