Reliability analysis of fail-safe systems with heterogeneous and dependent components subject to random shocks

In many significant safety systems, the fault tolerance of a fail-safe system has been a fundamental design attributed to obtaining more higher reliability. However, in most practical scenarios, the components in a fail-safe system suffer from additional random shocks, and one component's failure may increase the failure probability of other surviving components. This article analyzes the effects of survived probabilities and components lifetimes on the reliability of fail-safe systems with statistically dependent components subject to random shocks in terms of the usual stochastic and hazard rate orderings. Sufficient conditions are established by means of transformation functions, underlying component lifetime distributions, and majorization orders. Some numerical examples are also presented for illustrating our theoretical findings.