Stochastic Evaluation of a Duplicate Standby System via Semi-Markov Processes
DOI:
https://doi.org/10.13052/jrss0974-8024.18210Keywords:
Stochastic modeling, MTSF, duplicate unit, reliability, regenerative point, probabilistic analysisAbstract
This paper presents a stochastic evaluation of a repairable system consisting of two identical operative units in parallel and one cold standby duplicate unit. The system is modeled using a Semi-Markov process framework combined with the regenerative point technique, which enables the treatment of general repair time distributions beyond the exponential assumption common in classical Markovian models. The novelty of the study lies in jointly analyzing reliability and economic measures-including Mean Time to System Failure (MTSF), steady-state availability, busy period of the repair facility, expected number of repairs, and long-run profit-under a unified framework. Instantaneous activation of the standby unit is incorporated without switchover delay, and its independence from the repair queue is explicitly considered. Numerical and graphical illustrations are provided to compare system performance across different redundancy strategies and to highlight the sensitivity of reliability indices to failure and repair rates. The results show that failures of original units exert a stronger impact on system reliability than those of the duplicate unit, while enhancing repair efficiency significantly improves both availability and profitability. The proposed modeling approach provides practical insights for the design of highly reliable and cost-effective systems in applications such as data centers, manufacturing, and safety-critical infrastructures.
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