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.

Lz‐transform approach to evaluate reliability indices of multi‐state repairable weighted K‐out‐of‐n systems

“…investigated the covariance and reliability of weighted K ‐out‐of‐ n MSSs. Recently, the coupla approach has been used in reliability estimation of repairable k ‐out‐of‐ n systems 10–14 . In general, UGF technique and recursive methods are used to estimate reliability indices of weighted system.…”

“…Recently, the coupla approach has been used in reliability estimation of repairable k-out-of-n systems. [10][11][12][13][14] In general, UGF technique and recursive methods are used to estimate reliability indices of weighted system. Further, in the aforementioned research work, the system considered were binary systems.…”

Performance Modeling and Estimation of Serial System Exhibiting k-out-of-n: G Scheme with Controller Failure

“…Poonia et al [15] used the copula repair approach to examine the performance of a warm standby k-out-of-n: G and 2-out-of-4: G system. Singh et al [22] reported a reliability assessment of a multi-computer system with n clients and the k-out-of-n: G operation scheme with copula repair policy.To analyze the availability of the butteroil production system, Mehta et al [31] developed a mathematical model that took into account the reliability of each subsystem and the system as a whole. The model also considered the time required for repair and maintenance of the subsystems.…”

“…Such literatures present different types of system architectures employing the k-out-of-n: G scheme in form of standby, series or parallel configurations. Motivated by the work ofPoonia and Sirohi [14], Poonia et al [21], Singh and Ram [19], Singh and Gahlot [20], Singh et al [21] and Singh et al [22], in which the system design consisting of only one subsystem with a k-out-of-n: G operational scheme. Little is known on performance evaluation of serial system consisting of two subsystems in which each subsystem possesses n units working under k-out-of-n: G scheme attended by a controller whose error can lead to system failure.…”