Probabilistic analysis of a multi-state warm standby k-outof-n: G system in a series configuration using copula linguists.

This paper discusses the reliability analysis of repairable complex system comprising of two subsystems in series configuration together with the controllers. The two subsystems, consisting of three undistinguishable units in a parallel arrangement and functioning under 1-out-of-3: G operational policy. Controllers control both the subsystems and can be unstable, and the malfunction result in the controller prevents system operation. The system may have an unforeseeable catastrophic failure due to which the system may not perform its function once the situation arises. The failure rate of the units is constant, and the exponential distribution is assumed to obey. The two forms of repair namely general repair and Goumbel-Hougard copula repair are used to restore the existing failed units of the system. The supplementary variable technique with Laplace transformation is used to evaluate the output of the system. Using Stochastic theory, differential equations are derived to obtain essential features of reliability such as availability of the system, reliability of the system, MTTF, and profit analysis. Graphs were drawn to highlight the behavior of the results. Tables and figures display the findings and suggest that copula repair is a more efficient repair policy for the improved performance of repairable systems. It brings a different aspect to the research world to adopt multi-dimensional repair in the form of the copula. Besides, the findings of the model are useful for system engineers and maintenance managers. [ABSTRACT FROM AUTHOR]