Reliability Analysis and Optimization of Multi-Component Redundant Repairable Systems with Replacement Policies

Abstract: This paper presents a reliability analysis and optimization framework for multi-component redundant repairable systems with preventive replacement policies. The system is modeled as a k-out-of-N repairable redundant structure in which at least k components must remain operational for successful system performance. A continuous- time Markov chain (CTMC) approach is employed to describe the stochastic behavior of component failures, repairs, and preventive replacements. The Chapman–Kolmogorov differential equations are formulated and solved using matrix analytical and Laplace transform techniques to obtain transient and steady-state solutions. Important reliability measures such as reliability function, availability, Mean Time to System Failure (MTTF), steady-state probabilities, repair rate, replacement rate, and system failure frequency are derived analytically. A threshold-based preventive replacement policy is incorporated to minimize long-run operational cost while improving system reliability and availability. Numerical illustrations and graphical analyses are presented to study the effects of failure rate, repair rate, redundancy level, and replacement threshold on system performance. The results indicate that preventive replacement policies significantly reduce downtime and operational cost compared with corrective maintenance alone. The optimal replacement threshold is obtained by minimizing the expected total cost and maximizing system availability. The proposed model provides an effective decision-making framework for maintenance optimization in complex industrial and engineering repairable systems.

Keywords: Multi-component repairable system, Redundant systems, Reliability analysis, Continuous-time Markov chain, Preventive replacement policy