In this article, reliability and maintenance models are developed for systems subjected to dependent competing risks and multiple time-scales. Multiple degradation processes and random shocks involve in system failure. The random shocks cause sudden increment jumps in the degradation processes. We use copula method to fit the dependent relationship among various degradation processes. We also study the impact of multiple random usage processes (time-scales) on reliability measures of systems subjected to competing risks. A time-based maintenance policy is proposed to maximize the availability of such systems. The time interval between two successive preventive maintenances and maximum number of preventive maintenances before replacement is found so that the availability of the system is maximized.
Lifetime of some systems can be measured based on multiple time scales. For instance, the lifetime of an airplane may be affected by its mileage or number of landings. Furthermore, most systems are exposed to competing risks. In this regard, time scales can accelerate the failure mechanism of these systems. In this paper, the behavior of systems is investigated under competing risks and multiple time scales. The time scales follow independent Poisson processes. As it is not straight forward obtaining closed-form relations for the system reliability, we have provided a parametric upper bound. Also, the upper bound can be tightened by considering an error function. The error function can be built by regression on a sample containing real values of system reliability for given time units. Performance of the upper bound is studied in two numerical examples and a case study. Results show that the obtained upper bound is very tight.
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