On Steady State Reliability and Sensitivity Analysis of a k-out-of-n System Under Full Repair Scenario

Abstract

The paper is devoted to the investigation of a k-out-of-n system under full repair scenario after its failure. This regime implies the restoration of all failed components for some random time. As a result, the system runs like a new one. A repairable system is one that is repaired not only after a component failure (partial repair), but also after the failure of the entire system (full repair). It is supposed that these repair times have both arbitrary and different distributions, while the components’ lifetime is exponentially distributed. In some previous works, time-dependent reliability characteristics have been obtained with the theory of decomposable semi-regenerative processes [1] and method of characteristics [2] in the same assumptions about life and repair time distributions. Markovization method in particular method of supplementary variables [3] has been applied for some special cases of parameters k and n for calculation of the stationary characteristics. In the current paper, the closed-form representations for the steady state system reliability characteristics for arbitrary k and n under similar assumptions about life and repair time distributions are presented. The obtained expressions are demonstrated in terms of Laplace transform of components’ partial repair time. The results are validated on an example of a 3-out-of-6 system by substituting the exponential distribution of repair time. In addition, the probabilistic characteristics of this system in the case of rare failures, as well as some numerical example to show their insensitivity are considered.