Maintenance-policy cost-analysis for a series system with highly-censored data

Abstract

This paper considers the problem of estimating the optimal age-replacement time for a series arrangement of functional subsystems when data are subject to high levels of random censoring on the right. The system does not have redundant components. Simulation is used to compare the performance of the Kaplan-Meier Estimator (KME), the Piecewise Exponential Estimator (PEXE) and the Maximum Likelihood Estimator (MLE) in estimating the optimal replacement time for the system, as well as for each component, under high levels of random censorship. Monte Carlo analysis is used to estimate 'average optimal age replacement times' determined using total time on test (TTT) transforms based on the KME, PEXE, and MLE methods. The optimal replacement time is used to calculate a value which is used to compare the relative long-run cost per unit-time for each method. The differences between using system-level data vs. component-level data to construct a maintenance policy are examined. With respect to cost effectiveness, the results identify the crucial factor in determining whether to perform system-level maintenance or component-level maintenance; that factor is the ratio of the 'cost of performing preventive maintenance' and the 'penalty cost of experiencing a system failure'. For the ratios used in this study (0.1 to 0.5) a 'component-level maintenance policy' is more cost effective than a 'system-level maintenance policy'. The results also show that for a correctly specified model and for large sample sizes, the age replacement times provided by the MLE are more accurate than those provided by the KME and PEXE, especially under high levels of censoring.