A semi-Markov model for reliability and cost analysis of two-unit cold standby systems considering operator fatigue, preventive maintenance and imperfect repairs
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".