Performance Assessment of Complex System Under the k-out-of-n: G Type Configuration with k Consecutive Degraded States through the Copula Repair Approach

Abstract

This paper is the stochastic analysis of a complex repairable system comprising of subsystems in a series arrangement under the [Formula: see text]-out-of-[Formula: see text]: [Formula: see text] type configuration. Both of the subsystems are in series arrangement and having auto transfer switches when some unit fails. Subsystem 1 is supposed to work under the [Formula: see text]-out-of-[Formula: see text]: [Formula: see text], scheme, and subsystem 2 which has four indistinguishable units in parallel arrangement with an auto switch functioning under the 1-out-of-4: [Formula: see text] scheme. A catastrophic failure is characterized as causing damage to the entire system. Units’ failure, switch failures, and catastrophic failure rates are constant, but repair rates are treated as variables with two types of distributions: general distribution and copula distribution. The model is analyzed using a supplementary variables approach, with probabilistic measures such as availability, reliability, MTSF, and profit functions derived.