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

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
    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

[1] M. S. Kadyan, “Reliability and profit analysis of a single-unit system with preventive maintenance subject to maximum operation time”, Maintenance and Reliability 15 (2) (2013) 176.

[2] M. Kadyan, J. Kumar, S. P. Kadyan, X. Jin & L. Li, “Stochastic modeling of a single-unit repairable system with preventive maintenance under warranty”, International Journal of Computer Applications 75 (15) (2013) 36. https://doi.org/10.5120/13183-0906

[3] J. Kumar & M. Singh, “Analysis of a Single-Unit System with Preventive Maintenance and Degradation”, International Journal of Statistics and Re- liability Engineering 1 (1) (2014) 47.

[4] A. Kumar, M. Saini & S. Malik, “A single unit system with preventive maintenance and repair subject to maximum operation and repair times”, International Journal of Applied Mathematics and Computation 6 (1) (2014) 25.

[5] A. Kumar & M. Saini, “Cost-benefit analysis of a single-unit system with preventive maintenance and Weibull distribution for failure and repair activities”, Journal of Applied Mathematics, Statistics and Informatics 10 (2) (2014) 5. https://doi.org/10.2478/jamsi-2014-0009

[6] R. Kishan & D. Jain, “A two non-identical unit standby system model with repair, inspection and post-repair under classical and Bayesian view- points”, Journal of reliability and statistical studies (2012) 85. https://journals.riverpublishers.com/index.php/JRSS/article/view/21917

[7] R. Kishan & D. Jain, “Classical and Bayesian analysis of reliability characteristics of a two-unit parallel system with Weibull failure and repair laws”, International Journal of System Assurance Engineering and Management 5 (2014) 252. https://doi.org/10.1007/s13198-013-0154-9

[8] A. S. Rodrigues, T. C. M. Dias, M. S. Lauretto & A. Polpo, “Reliability analysis in series systems: An empirical comparison between Bayesian and classical estimators”, AIP Conference Proceedings 1443 (1) (2012) 214. https://doi.org/10.1063/1.3703638

[9] M. Li & W. Q. Meeker, “Application of Bayesian methods in reliability data analyses”, Journal of Quality Technology 46 (1) (2014) 1. https://doi.org/10.1080/00224065.2014.11917951

[10] B. Singh & P. K. Gupta, “Bayesian reliability estimation of a 1-out-of- k load-sharing system model”, International Journal of System Assurance Engineering and Management 5 (2014) 562. https://doi.org/10.1007/ s13198- 013- 0206- 1

[11] J. Lin, J. Pulido & M. Asplund, “Reliability analysis for preventive maintenance based on classical and Bayesian semi-parametric degradation approaches using locomotive wheel-sets as a case study”, Reliability Engineering & System Safety 134 (2015) 143. https://doi.org/10.1016/j.ress.2014.10.011

[12] E. I. Basri, I. H. Abdul Razak, H. Ab-Samat & S. Kamaruddin, “Pre- ventive maintenance (PM) planning: a review”, Journal of quality in maintenance engineering 23 (2) (2017) 114. https://doi.org/10.1108/JQME-04-2016-0014

[13] N. Ahlawat, S. K. Chauhan & S. C. Malik, “Reliability evaluation of a non series–parallel system of six components with Weibull failure laws”, Life Cycle Reliability and Safety Engineering 8 (1) (2019) 91. https://doi.org/10.1007/s41872-018-0066-4

[14] G. Kumar, V. Jain & U. Soni, “Modelling and simulation of repairable mechanical systems reliability and availability”, International Journal of System Assurance Engineering and Management 10 (2019) 1221. https://doi.org/10.1007/s13198-019-00852-3

[15] M. Rasekhi, M. M. Saber & H. M. Yousof, “Bayesian and classical infer- ence of reliability in multicomponent stress-strength under the general- ized logistic model”, Communications in Statistics - Theory and Methods 50 (21) (2020) 5114. https://doi.org/10.1080/03610926.2020.1726958

[16] T. Kayal, Y. M. Tripathi, S. Dey & S. J. Wu, “On estimating the reliability in a multicomponent stress-strength model based on Chen distribution”, Communications in Statistics-Theory and Methods 49 (10) (2020) 2429. https://doi.org/10.1080/03610926.2019.1576886

[17] A. B. Toroody, M. M. Abaei, E. Arzaghi, G. Song, F. De Carlo, N. Paltrinieri & R. Abbassi, “On reliability challenges of repairable systems using hierarchical bayesian inference and maximum likelihood estimation”, Process Safety and Environmental Protection 135 (2020) 157. https://doi.org/10.1016/j.psep.2019.11.039

[18] S. C. Malik, “Reliability Measures of Repairable Systems with Ar- rival Time of Server”, Annual Conference of the Society of Statistics, Computer and Applications 2 (2020) 231. https://doi.org/10.1007/978-981-16-7932-2 15

[19] M. Saini & A. Kumar, “Stochastic modeling of a single-unit system operating under different environmental conditions subject to inspection and degradation”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 90 (2020) 319. https://doi.org/10.1007/s40010-018-0558- 7

[20] Y. F. Li, H. Z. Huang, J. Mi, W. Peng & X. Han, “Reliability analysis of multi-state systems with common cause failures based on Bayesian network and fuzzy probability”, Annals of Operations Research (2022) 1. https://doi.org/10.1007/s10479-019-03247-6

[21] L. Wang, K. Wu, Y. M. Tripathi & C. Lodhi, “Reliability analysis of multicomponent stress–strength reliability from a bathtub-shaped distribution”, Journal of Applied Statistics 49 (1) (2022) 122. https://doi.org/10.1080/02664763.2020.1803808

[22] V. Saxena, R. Gupta & B. Singh, “Classical and Bayesian stochastic analysis of a two unit parallel system with working and rest time of repairman”, Reliability: Theory & Applications 18 (1) (2023) 43.

[23] S. Gurler, D. Goksuluk & D. Tursel Eliiyi, “Reliability-based optimization of imperfect preventive maintenance with Bayesian estimation”, Quality Engineering 35 (3) (2023) 457. https://doi.org/10.1080/08982112.2022.2150085

[24] N. Abbas, “On classical and Bayesian reliability of systems using bivariate generalized geometric distribution”, Journal of Statistical Theory and Applications 22 (3) (2023) 151. https://doi.org/10.1007/s44199-023-00058-4

[25] K. S. Bhat & M. K. Simon, “Stochastic analysis of a complex repairable system with a constrain on the number of repairs”, Reliability: Theory & Applications 19 (2) (2024) 178.

[26] N. Kumar, “Stochastic Approach in Performance Modelling of a Re- pairable Industrial System”, International Journal for Engineering Modelling 37 (1) (2024) 15. https://doi.org/10.31534/engmod.2024.1.ri.02f

[27] S. Saini, “Advancements in reliability estimation for the exponentiated Pareto distribution: a comparison of classical and Bayesian methods with lower record values”, Computational Statistics 3 (2024) 1. https://doi.org/10.1007/s00180-024-01497-y

[28] S. Saini, R. Garg, N. Tiwari & C. Swaroop, “Classical and Bayesian estimation of multicomponent stress–strength reliability with power Lindley distribution under progressive first-failure censored samples”, Journal of Statistical Computation and Simulation 94 (15) (2024) 3341. https://doi.org/10.1080/00949655.2024.2383989

[29] S. Saini, “Estimation of multi-stress strength reliability under progressive first failure censoring using generalized inverted exponential distribution”, Journal of Statistical Computation and Simulation 94 (14) (2024) 3177. https://doi.org/10.1080/00949655.2024.2374829

[30] A. Kumari, I. Ghosh & K. Kumar, “Bayesian and likelihood estimation of multicomponent stress–strength reliability from power Lindley distribution based on progressively censored samples”, Journal of Statistical Computation and Simulation 94 (5) (2024) 923. https://doi.org/10.1080/00949655.2023.2277331

[31] S. Kadyan & S. C. Malik, “Stochastic analysis of a non-identical repairable system with (n+1) units subject to MRT of type-I unit”, International Journal of Operational Research 52 (2) (2025) 211. https://doi.org/10.1504/IJOR.2025.144338

[32] R. Gupta & S. Kumar, “Availability analysis of imperfect repairable system subject to inspection”, International Journal of Quality & Reliability Management 42 (1) (2025) 299. https://doi.org/10.1108/IJQRM-10-2023-0335

[33] A. Kumar & C. Shekhar,“Bayesian Modeling of Repairable Systems with Imperfect Coverage and Delayed Detection Dynamics”, Quality and Reliability Engineering International 3 (2025) 13. https://doi.org/10.1002/qre.3742

[34] R. Chaudhary, M. Saini, A. Kumar & K. Kumar, “Reliability character- istics analysis of Ready-Mix Cement plant under classical and bayesian inferential framework: A Comparative Analysis”, Brazilian Journal of Biometrics 43 (3) (2025) 12. https://doi.org/10.28951/bjb.v43i3.790

[35] A. S. Yadav, M. Saha & S. Dey, “Classical and Bayesian estimation of the reliability characteristics for logistic-exponential distribution”, Afrika Matematika 36 (1) (2025) 34. https://doi.org/10.1007/s13370-025-01250-8

[36] M. A. Sargazi, A. Heidari, J. Davtalab & J. Piri, “Comparative reliability assessment of PET and UTCI thermal comfort indices using Monte Carlo simulation in urban microclimates”, Scientific Reports 4 (2025) 7. https://doi.org/10.1038/s41598-025-33440-6

[37] D. H. Son, C. E. Oh, H. W. Lee, C. Y. Jeong, J. M. Jang, B. D. Ahn, et al., “Analysis of physical mechanisms for channel-length-dependent PBTS reliability in SA TG coplanar IGZO TFTs”, Scientific Reports 15 (1) (2025) 43556. https://doi.org/10.1038/s41598-025-27549-x

Published

2026-04-06

How to Cite

Estimation of reliability characteristics of single-unit repairable system with preventive maintenance and server arrival time. (2026). Journal of the Nigerian Society of Physical Sciences, 8(2), 3062. https://doi.org/10.46481/jnsps.2026.3062

Issue

Volume 8, Issue 2, May 2026

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 Nikita Bhardwaj, Monika Saini, Ashish Kumar (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Estimation of reliability characteristics of single-unit repairable system with preventive maintenance and server arrival time. (2026). Journal of the Nigerian Society of Physical Sciences, 8(2), 3062. https://doi.org/10.46481/jnsps.2026.3062

Similar Articles

101-110 of 205

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)