Generalized renewal process for analysis of repairable systems with limited failure experience

Repairable systems can be brought to one of possible states following a repair. These states are: 'as good as new', 'as bad as old', 'better than old but worse than new', 'better than new', and 'worse than old'. The probabilistic models traditionally used to estimate the expected number of failures account for the first two states, but they do not properly apply to the last three, which are more realistic in practice. In this paper, a robust solution to a probabilistic model that is applicable to all of the five after repair states, called generalized renewal process (GRP), is presented. This research demonstrates that the GRP offers a general approach to modeling repairable systems and discusses application of the classical maximum likelihood and Bayesian approaches to estimation of the GRP parameters. This paper also presents a review of the traditional approaches to the analysis of repairable systems as well as some applications of the GRP and shows that they are subsets of the GRP approach. It is shown that the proposed GRP solution accurately describes the failure data, even when a small amount of failure data is available. Recent emphasis in the use of performance-based analysis in operation and regulation of complex engineering systems (such as those in space and process industries) require use of sound models for predicting failures based on the past performance of the systems. The GRP solution in this paper is a promising and efficient approach for such performance-based applications