Estimation of reliability characteristics of single-unit repairable system with preventive maintenance and server arrival time

Nikita Bhardwaj; Monika Saini; Ashish Kumar

doi:10.46481/jnsps.2026.3062

Authors

Nikita Bhardwaj
Department of Mathematics & Statistics Manipal University Jaipur, Jaipur-303007, India

Great Lakes Institute of Management, Bilaspur, India
Monika Saini
Department of Mathematics & Statistics Manipal University Jaipur, Jaipur-303007, India
Ashish Kumar
[email protected]

Department of Mathematics & Statistics Manipal University Jaipur, Jaipur-303007, India

Keywords:

Single unit system, Preventive maintenance, Maximum likelihood estimation, Bayesian estimation, MCMC algorithm

Abstract

The study seeks to determine the reliability features of the single unit repairable systems around the roles of the maximum operating time, preventive maintenance (PM), and the server arrival time. The main objective is to analyze trade-offs between scheduled maintenance outage and system availability. With that in mind, two Weibull-distributed stochastic models Model-1 with PM and Model-2 without PM are compared with Semi-Markovian and Regenerative Point methods to calculate such metrics as MTSF, availability and profit. In addition, we utilized Maximum likelihood estimation (MLE) and Bayesian models to estimate reliability characteristics with the validation of the solution by Markov Chain Monte Carlo (MCMC) simulations. The numerical analysis shows that in both models, a rise in the rate of failures will cause a reduction in MTSF, availability and profit. Critical comparison reveals that Model $2$ (without PM) surprisingly generates higher availability and MTSF as compared to Model 1. Also, the numerical and graphical outcomes prove that the MLE findings are very close to the true availability of the system. The research provides a strong framework on which the precise boundary of planned maintenance exceeding downtime.

Dimensions

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