Stochastic Analysis of a Cold Standby System with Installation and Maximum Repair Time
Kuldeep , Puran Rathi, S.C. Malik
Abstract
A stochastic analysis of a cold standby system comprising two identical units has been conducted. In this system
a constant failure rate for the units is assumed. Here, a failed unit is sent for repair, and if the repair is not completed
within a specified maximum repair time, the unit is replaced with a new one. Additionally, the repaired unit
requires a certain installation time before becoming operational when needed. The rates of repair, installation, and
replacement are governed by distinct probability density functions with arbitrary lifetime distributions. The semi-
Markov process and regenerative point technique have been employed to derive expressions for key reliability
measures, including mean time to system failure (MTSF), system availability, expected number of server visits
and busy periods attributable to repair, installation & replacement activities in steady state. The profit of the
system has also been evaluated based on these reliability measures. The behavior of MTSF, availability, and the
profit function has been analyzed for specific parameter values related to failure, repair, and installation rates.
Finally, the practical application of this model has been demonstrated in the context of a healthcare system.
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