System Reliability with Multiple Failure Modes and Time Scales

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.