Reliability analysis of repairable systems using stochastic point processes

In order to analyze the failure data from repairable systems, the homogeneous Poisson process(HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system because the rate of occurrence of failures (ROCOF) of the system changes over time rather thanremains stable. However, from a practical point of view, it is always preferred to apply the simplest methodto address problems and to obtain useful practical results. Therefore, we attempted to use the HPP model toanalyze the failure data from real repairable systems. A graphic method and the Laplace test were also usedin the analysis. Results of numerical applications show that the HPP model may be a useful tool for the entirelife cycle of repairable systems.     

Nonlinear Mixed-Effects Models for Repairable Systems Reliability

Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.