Abstract:

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engineering design, especially in applications where continuous operation is required. This study focuses on a three-unit standby system, in which two identical units operate simultaneously while the third remains in standby to improve fault tolerance. The objective is to evaluate key reliability metrics such as Steady state availability, Busy period, profit and mean time to failure (MTTF). To achieve this, a continuous-time Markov chain (CTMC) approach is employed, incorporating the system’s transition dynamics under both active and standby configurations. Explicit expressions are derived for the reliability indices, and numerical illustrations are provided to highlight the system’s performance under varying failure and repair rates. The results demonstrate that the standby unit significantly enhances the system’s dependability by prolonging operational lifetime and improving availability compared to non-redundant configurations. The study concludes that such a configuration is suitable for mission-critical applications where downtime must be minimized. The findings provide valuable insights for system designers, particularly in optimizing redundancy and repair strategies for cost-effective and resilient engineering systems

Keyward(s): Availability, Busy period, Mean time failure, And Reliability

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