Reliability and sensitivity analysis of a repairable k-out-of-n:F system with general life-and repair times distribution

The study of a k-out-of-n system's reliability is interesting both from theoretical and practical points of view. There are many investigations devoted to reliability centric analysis of a k-out-of-n:F systems, i.e., systems consisting of n components which are operable while at least k of system's components are functioning Shepherd (2008). Another problem deals with the previous issue is the sensitivity of k-out-of-n system reliability characteristics to the shape of their elements’ life and repair times distribution Sevast’yanov (1957). In some previous works, closed-form representations for reliability characteristics of redundant systems with an exponential distribution of their elements lifetime and general distribution of their repair time have been found in Rykov (2018), Rykov et al. (2020). Such results show systems' asymptotic insensitivity to the shape of repair time distributions. In the recent paper the analytical model of a k-out-of-n:F system in the case of exponential distribution of their elements lifetime and a general repair time distribution is considered using the supplementary variables method (also called as the markovization method) Cox (1955) as well as sensitivity analysis of some reliability characteristics of such a system for the general distributions of life-and repair times is carried out with the help of simulation modeling. Numerical analysis is performed on the example of the 3-out-of-6:F system. © ESREL2020-PSAM15 Organizers. Published by Research Publishing, Singapore.