A Markovian analytical approach to a repairable system under the mixed redundancy strategy with a repairman

Abstract

The mixed redundancy strategy is one of the most powerful techniques for improving system performance. This novel strategy has, however, been mostly studied in non-repairable redundant systems, while the present study aims to study, for the first time, its application to a repairable system with a repairman in availability and maintainability perspectives. In this system, a repairman is responsible for providing the repair services. The intended system simultaneously benefits from the repairman's vacation concept following different policies, namely: vacation interruption and multiple vacations. Moreover, the system consists of two types of repairs, specifically: regular and working vacation repair. Also, successive vacation times are governed by the Markovian arrival process. Accordingly, the system is analyzed by modeling a vector-valued Markov process and several performance measures are derived in both transient and stationary regimes following the matrix-analytic procedure. Finally, the performance of the proposed approach is verified using numerical examples that involve a system with three repairable non-identical components under the mixed strategy as well as a micro-grid system with three parallel subsystems as a real-life case study.

Research on the Reliability of a Two-Robot Security System with Early Warning Function

“…Here, it should be noted that although P i (t, x)(i � 2, 3) is only defned as 0⩽x < t, but for the sake of discussion, P i (t, x)(i � 2, 3) can be defned according to the actual physical background of the system and P i (t, x)(i � 2, 3) is extended on x > t, that is, supplementary defnition P i (t, x) � 0, x > t, i � 2, 3. At the same time, the system is out of state i(i � 2, 3) of the risk function; that is, the fx quotiety of the faulty component in the system in the state i(i � 2, 3) can be defned as follows by the conditional probability [21,22]:…”

“…For convenience, 􏽥 P i (t, x), 􏽥 P i (t), 􏽥 μ i (x) is still represented by P i (t, x), P i (t), μ i (x) in the following system equations. P i (t, x) can be obtained from the partial diferential equations (21):…”

“…In literatures [10][11][12][13][14][15], Kamranfar et al studied the stability of repairable systems. On the basis of discussing the asymptotic stability of the solutions of a repairable system with two diferent components connected in parallel, Wang et al studied the controllability of the system in the zero state and the criterion of using the controllability of the system in literatures [16][17][18][19][20][21][22][23][24], and obtained the corresponding optimal control element of the system by using the minimization sequence, thus solving the optimal control problem of the system solution. In other literatures, the reliability index of the system is obtained by quantitative analysis.…”