Availability of a General Repairable k-out-of-n:G System Considering Shut-Off Rules

The k-out-of-n:G system is a common form of redundancy, widely used in reliability and maintenance engineering. The k-out-of-n:G system has a wide range of applications in industrial systems, military services and communication systems. In this work, the number of repairmen is assumed to be r (1 ≤ r ≤ n – k + 1) and the shut-off rule could involve suspended animation, continuous operation, or a mixture of these two shut-off rules. Components can have different or similar repair priorities. The objective of this work is to address the problem of efficient evaluation of the system’s availability in a way that steady state solutions can be obtained systematically in a reasonable computational time. This problem is modeled as a finite state-dependent non-homogeneous quasi-birth-death (QBD) process. An algorithm is introduced to automatically generate the system state vectors and transition rate matrix. An iterative solution procedure based on the Block Gauss–Seidel method is employed to determine the steady state measures of the system. Numerical examples are applied to demonstrate the correctness and efficiency of the proposed method. Our method exhibits very high efficiency on large problems in terms of correctness and computational time. Our result can facilitate the analyses of similar reliability models in terms of finding the optimum design for a repairable system.

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