A Monte Carlo approach to modeling and estimation of the generalized renewal process in repairable system reliability analysis

In repairable system reliability analysis, one can consider five states to which a system can be repaired upon a failure. These are (1) "as-good-as-new", (2) "same-as-old", (3) "better-than-old-but-worse-than-new", (4) "better-than-new" and (5) "worse-than-old".; Probabilistic models accounting for "as-good-as-new" and "same-as-old" repair assumptions (Ordinary Renewal Process - ORP and Non-Homogeneous Poisson Process - NHPP, respectively) have been extensively studied and discussed by many investigators. Although more realistic in practice, repair states 3, 4 and 5 have received much less attention in reliability theory. The reason being the difficulty of developing a mathematically tractable, closed form probabilistic model to represent other than the two "limiting" assumptions.; This dissertation considers a numerical approximation method of developing such a probabilistic model called a Generalized Renewal Process (GRP) and offers a statistical procedure for its estimation. The suggested estimation procedure is based on Monte Carlo (MC) simulation. This is a rather unique approach in statistical science, since normally the MC simulation is used for modeling or validation purposes.; The dissertation provides a probabilistic framework for treating epistemic and aleatory uncertainty of the GRP rejuvenation parameter, which brings the GRP to an even higher generalization level. Quantification of each of the two uncertainties is illustrated through numerical examples.; The analytical results obtained have high practical importance. It is shown that the application of GRP in statistical warranty forecasting provides a significantly lower prediction error as compared to the ORP or the NHPP. The same is true when the GRP is applied to warranty coverage optimization, an example of which is considered in detail. Also discussed is the use of the GRP in the estimation of repair effectiveness, allowing for the evaluation of the quality of a repair facility/technique and design for better repairability and serviceability. (The application of the ORP and the NHPP in this latter context turns out to be impossible in principle.); This dissertation concludes with an outline of the trends for future research related to both theoretical and practical aspects of the generalized renewal process application in repairable system reliability analysis.