Semi-parametric PWP model robustness for log-linear increasing rates of occurrence of failures

Repairable systems have reliability (failure) and maintainability (restoration) processes that tend to improve or deteriorate over time depending on life-cycle phase. External variables (covariates) can explain differences in event rates and thus provide valuable information for engineering analysis and design. In some cases, the processes may be modeled by a parametric non-homogeneous Poisson process (NHPP) with proportional intensity function, incorporating the covariates. However, the true underlying process may not be known, in which case a distribution-free or semi-parametric model may be very useful. The Prentice, Williams and Peterson (PWP) family of proportional intensity models has been proposed for application to repairable systems. This paper reports results of a study on the robustness of one PWP reliability model over early failure history. The assessment of robustness was based on the semi-parametric PWP modelʹs ability to predict the successive times of occurrence of events when the underlying process actually is parametric (specifically a NHPP having log-linear proportional intensity function with one covariate). A parametric method was also used to obtain maximum likelihood estimates of the log-linear parameters, for purposes of validation and as a reference for comparison. The PWP method provided accurate estimates of the time to next event for NHPP log-linear processes with moderately increasing rates of occurrence of events. Potential engineering applications to repairable systems, with increasing rates of event occurrence, include reliability (failure) processes in the wear-out phase and maintainability (restoration) processes in the learning phase. A real example of a maintainability (restoration) process (log-linear NHPP with two explanatory covariates) for US Army M1A2 Abrams Main Battle Tank serves to demonstrate the engineering relevance of the methods evaluated in this research.