| Prentice, Williams and Peterson (1981) proposed a semi-parametric proportional intensity model for life studies on individuals experiencing a point process of repeated events. The PWP model is attractive for reliability applications, because it incorporates covariates and is semi-parametric, thus requiring no assumptions about the underlying stochastic process. There have been a few attempts to apply the PWP model to engineering reliability problems, but there have been no studies of the robustness of the PWP model.; The primary objective of this research was to investigate the robustness of the PWP model for the case where the underlying process is a NHPP with power-law intensity function. Sample data sets were generated by Monte Carlo simulation, for values of the power-law shape parameter from 0.5 to 3.0, and for 10 failures per unit in samples of 20 units (10 per class defined by a discrete indicator covariate), 60 units (30 per class) and 120 units (60 per class). The measure of merit for the robustness was the ability of the PWP model to estimate the expected times to successive failures. The performance metrics were the relative bias, mean absolute deviation, and mean squared error. A parametric estimation model proposed by Lawless (1987) was also used as a benchmark for comparison with the semi-parametric PWP model.; The research concluded that the PWP model performs well for values of the power-law shape parameter between 0.6 and 1.5, with a moderate tendency toward positive bias for values of the shape parameter greater than 1.5. The PWP model performed poorly for a shape parameter of 0.5, with positive bias of up to 60%. In general, the PWP model showed increasing positive bias with decreasing values of the shape parameter below 1.0. These results suggest that the PWP model is applicable for constant and increasing rates of occurrence of failures (ROCOF), which represent most cases in operational reliability of repairable systems. However, the PWP model should be used cautiously in reliability growth situations such as development testing on prototype hardware for which a rapidly decreasing ROCOF is anticipated. The PWP model performance improves for increasing sample sizes. |
