Reliability analysis of a single-unit repairable system with optional repairs and vacations

Abstract

Single‑unit repairable systems (e.g., purifiers, elevators) affect operational efficiency and maintenance costs. This paper studies a system with optional repairs and multiple vacations, assuming general repair times and exponential vacation times. The supplementary variable technique yields integro‑differential equations for state probabilities. Laplace transforms of availability, failure frequency, and renewal frequency are derived in closed form. Numerical examples for exponential repairs illustrate the effects of key parameters on transient reliability indices. The results provide theoretical support for maintenance strategy design and reliability analysis of similar systems.