A semi-Markov model for reliability and cost analysis of two-unit cold standby systems considering operator fatigue, preventive maintenance and imperfect repairs

Purpose This study aims to investigate a two-unit cold standby system subject to practical operational factors, including operator fatigue, preventive maintenance and imperfect repairs. The system operates under a policy requiring the operator to rest after a stochastically determined work period, resulting in temporary downtime that does not constitute a failure. An integrated modeling framework based on a semi-Markov process is proposed to evaluate the joint impact of these factors on key reliability and cost metrics, thereby supporting informed maintenance optimization decisions. Design/methodology/approach The system is modeled using a bivariate exponential distribution to capture the correlation between each unit's failure and repair times, while accounting for additional factors such as imperfect repairs and operator fatigue. The model is analyzed at regenerative epochs, enabling the derivation of mean time to system failure, availability, repairman busy period and cost functions. Numerical experiments demonstrate how varying the preventive maintenance probability, the likelihood of imperfect repair and the fatigue parameters affect system performance. Findings Results demonstrate that preventive maintenance enhances system availability and reduces long-term costs when initiated with a sufficiently high probability. However, imperfect repairs accelerate system degradation by failing to fully restore failed units, while operator fatigue contributes to extended downtime through reduced repair efficiency. The interaction of these factors reveals a trade-off between investing in maintenance activities and mitigating the operational consequences of system unavailability. These findings highlight the importance of considering fatigue and repair quality when developing cost-effective maintenance strategies. Originality/value This research presents a more realistic and comprehensive model of standby system reliability by integrating correlated failures, operator fatigue-induced repair inefficiencies, imperfect repairs and preventive maintenance within a unified semi-Markov framework. The study expands existing reliability models by modeling fatigue through stochastic rest-work cycles and capturing repair dependencies via bivariate exponential distributions. Practitioners can leverage the model's quantitative insights to refine maintenance policies, assess trade-offs between reliability and cost and enhance decision-making in environments where human limitations and non-ideal repairs significantly impact overall system performance.