Abstract
Power supply system models are commonly used in industrial and manufacturing sectors to assess performance metrics. This paper conducts a cost-benefit analysis of four different unreliable retrial systems featuring warm standby components and setup times. The systems differ in the quantity of primary (operative) and warm standby (backup) components they contain. The failure and repair times for both primary and standby components are assumed to follow an exponential distribution. For each system, we present the state-transition diagram along with the corresponding differential-difference equations. Employing the Laplace stieltjes transform and the matrix-analytical method, we derive explicit formulas for key performance metrics, including the mean time to failure (MTTF) and steady-state availability, which serve as vital indicators of system reliability. Numerical examples are provided to examine the influence of system parameters on steady state availability, mean time to failure, and the cost-benefit ratio. The results are presented in both tabular and graphical formats, accompanied by a detailed cost-benefit comparative analysis. The findings provide decision-makers with valuable insights for ensuring system stability and optimizing cost efficiency.
