Availability of K-out-of-N:G systems with non-identical components subject to repair priorities

• Published in: Reliability engineering & system safety Vol. 94; no. 2; pp. 142 - 151
• Main Authors: Khatab, A., Nahas, N., Nourelfath, M.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier 01.02.2009
• Subjects: Applied sciences; Exact sciences and technology; Operational research and scientific management; Operational research. Management science; Reliability theory. Replacement problems; Availability; Monte Carlo method; Automaton; K-out-of-N:G system; Redundancy; Priority; Order statistic; Operator algebra; Markov model; Failure rate; Modeling; Stationary condition; Generalized Kronecker algebra; K out of n system; Active redundancy; State diagram; Transition state; Automatic construction; Automatic system; State dependence; Reliability; Repair
• ISSN: 0951-8320
• DOI: 10.1016/j.ress.2008.02.017

In this paper, a K-out-of-N:G system with N categories of components is studied. Each component category is characterized by its own failure and repair rates. There are R repair facilities, and repair priorities are specified between the N non-identical components. An algorithm for automatic construction of the system state transition diagram is presented. The stationary availability of each component and that of the system are evaluated by using a multi-dimensional Markov model. We show how this model can be represented as a network of stochastic automata with state-dependent transitions that can be implemented via generalized tensor (or Kronecker) algebra. For the efficiency assessment, an analog Monte Carlo simulation model is developed. Experiments are then conducted and simulation results are compared to those obtained by the proposed approach.