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A System with Two Spare Units, Two Repair Facilities, and Two Types of Repairers

Author

Listed:
  • Vahid Andalib

    (Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Cir, Baltimore, MD 21250, USA
    These authors contributed equally to this work.)

  • Jyotirmoy Sarkar

    (Department of Mathematical Sciences, Indiana Universiry-Purdue University Indianapolis, Indianapolis, IN 46202, USA
    These authors contributed equally to this work.)

Abstract

Assuming exponential lifetime and repair time distributions, we study the limiting availability A ∞ as well as the per unit time-limiting profit ω of a one-unit system having two identical, cold standby spare units using semi-Markov processes. The failed unit is repaired either by an in-house repairer within an exponential patience time T or by an external expert who works faster but charges more. When there are two repair facilities, we allow the regular repairer to begin repair or to continue repair beyond T if the expert is busy. Two models arise accordingly as the expert repairs one or all failed units during each visit. We show that (1) adding a second spare to a one-unit system already backed by a spare raises A ∞ as well as ω ; (2) thereafter, adding a second repair facility improves both criteria further. Finally, we determine whether the expert must repair one or all failed units to maximize these criteria and fulfill the maintenance management objectives better than previously studied models.

Suggested Citation

  • Vahid Andalib & Jyotirmoy Sarkar, 2022. "A System with Two Spare Units, Two Repair Facilities, and Two Types of Repairers," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:852-:d:766398
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    References listed on IDEAS

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    1. Sarkar, Jyotirmoy & Li, Fang, 2006. "Limiting average availability of a system supported by several spares and several repair facilities," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1965-1974, December.
    2. Cui, Lirong & Chen, Jianhui & Wu, Bei, 2017. "New interval availability indexes for Markov repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 12-17.
    3. Cha, Ji Hwan & Finkelstein, Maxim, 2019. "Stochastic modeling for systems with delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 118-124.
    4. Yu, Haiyang & Yalaoui, Farouk & Châtelet, Ėric & Chu, Chengbin, 2007. "Optimal design of a maintainable cold-standby system," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 85-91.
    5. Bruno Bieth & Liang Hong & Jyotirmoy Sarkar, 2010. "A standby system with two types of repair persons," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(5), pages 577-594, September.
    6. Zhang, Yuan Lin & Wang, Guan Jun, 2007. "A deteriorating cold standby repairable system with priority in use," European Journal of Operational Research, Elsevier, vol. 183(1), pages 278-295, November.
    7. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
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    Cited by:

    1. Monika & Garima Chopra, 2024. "Reliability assessment of an industrial system considering failures in its raw material inventory," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2704-2714, June.
    2. Ernesto Armando Pacheco-Velázquez & Manuel Robles-Cárdenas & Saúl Juárez Ordóñez & Abelardo Ernesto Damy Solís & Leopoldo Eduardo Cárdenas-Barrón, 2023. "A Heuristic Model for Spare Parts Stocking Based on Markov Chains," Mathematics, MDPI, vol. 11(16), pages 1-21, August.

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