Weibull-based reliability and profitability analysis of an industrial multi-state repairable system

Authors

  • Priya Dahiya
    Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab 140401, India
  • Jasdev Bhatti
    Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab 140401, India
  • Pankaj Thakur
    Department of Mathematics, Faculty of Science and Technology, ICFAI University Baddi, Solan 174103, India
    https://orcid.org/0000-0001-8119-2697

Keywords:

Reliability analysis, Weibull distribution, Cold standby redundancy, Regenerative point technique, Profit analysis

Abstract

Reliability is a primary concern in industrial manufacturing because operational interruptions can reduce production, cause substantial economic losses, and create workplace-safety risks. This study applies the two-parameter Weibull distribution and the regenerative point technique (RPT) to a repairable system comprising two non-identical units: a primary unit operating in parallel with a secondary unit arranged in cold standby. The model incorporates inspection, repair, and replacement activities and is used to derive transition probabilities, mean sojourn times, mean time to system failure (MTSF), steady-state availability, maintenance busy periods, and a profit function. Numerical results show that system profitability decreases as the failure rate and Weibull shape parameter increase, whereas a higher repair rate improves profitability. For the reported parameter set, profit increases from 7325.258 to 8726.043 when the repair rate rises from 0.1 to 1.0 at a=0.01, and from 4879.802 to 6970.602 at a=0.05. The analysis also identifies reported zero-profit thresholds near a=1.45, 1.38, and 1.21 for k=0.8, 1.0, and 2.0, respectively. The framework supports maintenance planning and economic assessment of multi-state repairable systems. 

Dimensions

[1] S. Jayatilleka & G. Okogbaa, ``Use of accelerated life tests on transmission belts for predicting product life, identifying better designs, materials and suppliers'', Proceedings of the Annual Reliability and Maintainability Symposium, Tampa, FL, USA, 2003, pp. 101--105. https://ieeexplore.ieee.org/document/1181909.

[2] H. Cui, ``Accelerated temperature cycle test and Coffin--Manson model for electronic packaging'', Proceedings of the Annual Reliability and Maintainability Symposium, Alexandria, VA, USA, 2005, pp. 556--560. https://ieeexplore.ieee.org/document/1408421.

[3] J. P. Zhang & X. M. Geng, ``Constant-step stress accelerated life test of VFD under Weibull distribution case'', Journal of Zhejiang University Science A 6 (2005) 722. https://doi.org/10.1631/jzus.2005.A0722.

[4] S. Charruau, F. Guerin, J. H. Dominguez & J. Berthon, ``Reliability estimation of aeronautic component by accelerated tests'', Microelectronics Reliability 46 (2006) 1451. https://www.sciencedirect.com/science/article/pii/S0026271406002186.

[5] R. Manzini, M. Gamberi & A. Regattieri, ``Applying mixed integer programming to the design of a distribution logistic network'', International Journal of Industrial Engineering: Theory, Applications and Practice 13 (2006) 207. https://doi.org/10.23055/ijietap.2006.13.2.438.

[6] G. Casella & R. L. Berger, Statistical Inference, 2nd ed., Duxbury, 2007. https://pages.stat.wisc.edu/~shao/stat610/Casella_Berger_Statistical_Inference.pdf.

[7] S. Voiculescu, F. Guerin, M. Barreau & A. Charki, ``Bayesian estimation in accelerated life testing'', International Journal of Product Development 7 (2009) 246. https://doi.org/10.1504/IJPD.2009.023321.

[8] D. H. Jung, H. J. Kim, Y. S. Pyoun, A. Gafurov, G. C. Choi & J. M. Ahn, ``Reliability prediction of the fatigue life of a crankshaft'', Journal of Mechanical Science and Technology 23 (2009) 1071. https://doi.org/10.1007/s12206-009-0343-2.

[9] S. Zacks, Introduction to Reliability Analysis: Probability Models and Statistical Methods, Springer, 2011. https://doi.org/10.1007/978-1-4612-2854-7.

[10] M. Scott, Applied Stochastic Processes in Science and Engineering, lecture notes, Department of Applied Mathematics, University of Waterloo, 2013. https://www.e-booksdirectory.com/details.php?ebook=9320.

[11] S. Gupta & S. K. Gupta, ``Stochastic analysis of a reliability model of one-unit system with post inspection, post repair, preventive maintenance and replacement'', International Journal of Mechanical Engineering and Robotics Research 2 (2013) 178. https://www.ijmerr.com/v2n2/ijmerr_v2n2_20.pdf.

[12] M. D. Berrade, P. A. Scarf, C. A. V. Cavalcante & R. A. Dwight, ``Imperfect inspection and replacement of a system with a defective state: A cost and reliability analysis'', Reliability Engineering & System Safety 120 (2013) 80. https://www.sciencedirect.com/science/article/pii/S0951832013000598.

[13] S. Gupta & S. K. Gupta, ``Optimization of cost maintenance and replacement for one-unit system reliability model with post repair'', International Journal of Mechanical Engineering and Robotics Research 2 (2013) 154. https://www.ijmerr.com/v2n4/ijmerr_v2n4_19.pdf.

[14] A. K. Azad, M. G. Rasul, M. M. Alam, S. M. A. Uddin & S. K. Mondal, ``Analysis of wind energy conversion system using Weibull distribution'', Energy Procedia 75 (2015) 722. https://doi.org/10.1016/j.egypro.2015.07.499.

[15] R. Kishan & M. Jain, ``Classical and Bayesian analysis of a two-unit parallel system with Weibull failure and repair laws'', International Journal of System Assurance Engineering and Management 5 (2014) 303. https://doi.org/10.1007/s13198-013-0154-9.

[16] M. Doostparast, F. Kolahan & M. Doostparast, ``A reliability-based approach to optimize preventive maintenance scheduling for coherent systems'', Reliability Engineering & System Safety 126 (2014) 98. https://www.sciencedirect.com/science/article/pii/S0951832014000118.

[17] D. Singh & G. Taneja, ``Reliability and economic analysis of a power generating system comprising one gas and one steam turbine with random inspection'', Journal of Mathematics and Statistics 10 (2014) 436. https://doi.org/10.3844/jmssp.2014.436.442.

[18] M. K. Kakkar, J. Bhatti, R. Malhotra, M. Kaur & D. Goyal, ``Availability analysis of an industrial system under the provision of replacement of a unit using genetic algorithm'', International Journal of Innovative Technology and Exploring Engineering 9 (2019) 1236. https://doi.org/10.35940/ijitee.L3302.119119.

[19] J. Salomon, N. Winnewisser, P. Wei, M. Broggi & M. Beer, ``Efficient reliability analysis of complex systems in consideration of imprecision'', Reliability Engineering & System Safety 216 (2021) 107972. https://doi.org/10.1016/j.ress.2021.107972.

[20] J. Bhatti, M. K. Kakkar, N. Bhardwaj, M. Kaur & D. Goel, ``Reliability analysis to industrial active standby redundant system'', Malaysian Journal of Science 39 (2020) 74. https://doi.org/10.22452/mjs.vol39no3.6.

[21] J. Bhatti, M. K. Kakkar & M. Kaur, ``Stochastic analysis to a power supply system through reliability modelling'', Transactions Issue Mathematics, Azerbaijan National Academy of Science 41 (2021) 35. https://trans.imm.az/volumes/41-1/4101-04.pdf.

[22] J. Bhatti, M. K. Kakkar, M. Kaur, D. Goel & P. Khanna, ``Stochastic analysis to mechanical system to its reliability with varrying repairing services'', Chebyshevskii Sbornik 22 (2021) 92. https://www.researchgate.net/publication/351929050_Stochastic_analysis_to_mechanical_system_to_its_reliability_with_varrying_repairing_services.

[23] J. Bhatti & M. K. Kakkar, ``Reliability analysis of cold standby parallel system possessing failure and repair rate under geometric distribution'', Recent Advances in Computer Science and Communications 14 (2021) 962. https://doi.org/10.2174/2666255813666191219110504.

[24] A. S. Maihulla & I. Yusuf, ``Performance analysis of photovoltaic systems using RAMD analysis'', Journal of the Nigerian Society of Physical Sciences 3 (2021) 172. https://doi.org/10.46481/jnsps.2021.194.

[25] M. A. Mellal & A. Salhi, ``System reliability-redundancy allocation by the multiobjective plant propagation algorithm'', International Journal of Quality & Reliability Management 39 (2022) 902. https://doi.org/10.1108/IJQRM-10-2018-0285.

[26] R. Pang, D. Zai, B. Xu, J. Liu, C. Zhao, Q. Fan & Y. Chen, ``Stochastic dynamic and reliability analysis of AP1000 nuclear power plants via DPIM subjected to mainshock-aftershock sequences'', Reliability Engineering & System Safety 235 (2023) 109217. https://doi.org/10.1016/j.ress.2023.109217.

[27] T. O. Alamri & J. P. T. Mo, ``Optimisation of preventive maintenance regime based on failure mode system modelling considering reliability'', Arabian Journal for Science and Engineering 48 (2023) 3455. https://doi.org/10.1007/s13369-022-07174-w.

[28] H. Kaur & S. K. Sharma, ``Reliability and mean time to system failure of a parallel system by using one or two decimal random data point'', EAI Endorsed Transactions on Scalable Information Systems 11 (2024) 1. https://doi.org/10.4108/eetsis.5071.

[29] R. Malhotra, Reliability and availability analysis of a standby system with activation time and varying demand, in Advances in Reliability Science: Engineering Reliability and Risk Assessment, Garg & Ram (Eds.), Elsevier, 2023, pp. 35--51. https://www.sciencedirect.com/science/article/pii/B9780323919432000046.

[30] Pankaj, J. Bhatti & M. K. Kakkar, ``Profit analysis to an industrial system possessing active redundancy form using geometric distribution'', Contemporary Mathematics 4 (2025) 423. https://doi.org/10.37256/cm.4320232515.

[31] M. A. Khanday, A. A. Saji, S. U. Rasool & M. Ahmad, ``Reliability and risk analysis of technical systems: A probabilistic modeling approach'', Reliability: Theory and Applications 21 (2026) 99. https://doi.org/10.24412/1932-2321-2026-190-99-108.

[32] N. Bhardwaj, M. Saini & A. Kumar, ``Estimation of reliability characteristics of single-unit repairable system with preventive maintenance and server arrival time'', Journal of the Nigerian Society of Physical Sciences 8 (2026) 3062. https://doi.org/10.46481/jnsps.2026.3062.

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Published

2026-07-22

How to Cite

Weibull-based reliability and profitability analysis of an industrial multi-state repairable system. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3426. https://doi.org/10.46481/jnsps.2026.3426

Issue

Volume 8, Issue 3, August 2026

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 Priya Dahiya, Jasdev Bhatti, Pankaj Thakur (Author)

Creative Commons License

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

How to Cite

Weibull-based reliability and profitability analysis of an industrial multi-state repairable system. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3426. https://doi.org/10.46481/jnsps.2026.3426

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