Reliability analysis of a complex repairable system in series configuration with switch and catastrophic failure using copula repair

Abstract

This paper describes an analytical framework for in-depth investigation of a complex system consisting of two subsystems (namely L and M) in series configuration. Subsystem-L is composed of three identical units in parallel configuration that are working under 1-out-of-3: G policy, while subsystem-M has two non-identical units that are working under 1-out-of-2: G: policy. In subsystem-M, priority in operation is given to M1 unit whereas M2 unit put into cold standby mode if not in use. Moreover, both the subsystems are connected with controllers that may be perfect or imperfect at the time of need. We have considered a catastrophic failure due to frequent change in environmental conditions or man-made disruption. Failure rates of units in both the subsystems are constant and assumed to follow exponential distribution, but their repair supports two types of distributions namely general distribution and Gumbel-Hougaard family copula distribution. The system is studied by using the supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula to derive differential equations and obtain important reliability indexes such as availability of the system, reliability of the system and profit analysis. The results have shown by tables and graphs. Conclusive part have been discussed in the last section of this study.