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PurposeThe present paper analyzed a model consisting of one unit with a warm standby unit where the main unit has three states: up, degraded and down.Design/methodology/approachThe semi-Markov model under the regenerative method is used to construct the mathematical model for the system.FindingsThe effectiveness measures of the system are discussed such as availability, reliability, steady-state availability and mean time to system failure. The life and repair times of the system units are assumed to be discrete follow discrete Weibull distribution. Also, the parameters of the discrete Weibull distribution are assumed to be fuzzy with bell-shaped membership function. An application is introduced to show the results obtained for the system and the profit of the presented model.Originality/valueRarely papers in literature treated the topic of the discrete-time semi-Markov process using a regenerative point technique.

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This paper presents a mathematical model for performing availability and reliability analysis of a parallel repairable system consisting of n identical components with degradation facility and common-cause failures. In addition, system repair time is assumed to be arbitrarily distributed. Markov and supplementary variable techniques are used to develop equations for the model. As an illustration, system of four-identical/repairable components is analysed.

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