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Comparative Analysis of 2-out-of-3 Cold Standby Reliability Systems with Perfect and Imperfect Automatic Repair Mechanisms

ABSTRACT

This paper presents a comparative study of two reliability models for a 2-out-of-3 cold standby system consisting of three identical units, of which two units are required for the successful operation of the system. In the first model, the Automatic Repair Machine (ARM) is assumed to be perfect and does not fail during the repair process. In the second model, the assumption of a perfect ARM is relaxed and the ARM itself is allowed to fail; an expert repairman is then employed to repair the failed ARM. Both models are analysed using the Regenerative Point Technique (RPT) and Markovian methods. The principal reliability measures considered are Mean Time to System Failure (MTSF), steady-state availability, busy period of the ARM, and profit function. The first model involves four states, whereas the second model requires seven states because additional states are introduced to represent ARM failure and its repair. The comparative analysis demonstrates that incorporating ARM failure provides a more comprehensive representation of the practical behaviour of the system. The second model therefore extends the first model by considering an additional source of system degradation and the corresponding repair mechanism.

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