Vol. 7, Issue 2, Part D (2025)

This paper related to analyze the reliability of a stochastic system consisting of two identical units, one of which acts as a cold standby. A maintenance policy is applied to the standby unit before it is brought into operation. The proposed system model assumes that when the active unit fails, the standby unit may require maintenance with a certain probability before it can be used. According to the adopted policy, the server first inspects the original unit to determine whether it can be restored. If the failed unit is found unfit for further operation, the server initiates its replacement after a specified delay. A single server is responsible for performing all maintenance, inspection, replacement, and repair tasks. Both maintenance and repair activities are assumed to be perfect. The failure time of the units follows a negative exponential distribution, while the maintenance, inspection, and repair times follow arbitrary distributions with distinct probability density functions. All random variables are considered statistically independent. Using a semi-Markov process and regenerative point graphical technique, expressions for various steady-state reliability measures are derived. The behavior of key performance indicators is examined graphically for selected parameter values. Additionally, the profit function of the system is evaluated to assess the effectiveness of the maintenance and inspection policies.