IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i6p852-d766398.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/6/852/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/6/852/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guglielmo D’Amico & Raimondo Manca & Filippo Petroni & Dharmaraja Selvamuthu, 2021. "On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems," Mathematics, MDPI, vol. 9(5), pages 1-23, March.
    2. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "New reliability indices for first- and second-order discrete-time aggregated semi-Markov systems with an application to TT&C system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    3. Hanagal David D. & Kanade Rupali A., 2010. "Optimal Replacement Policy Based on the Number of Down Times," Stochastics and Quality Control, De Gruyter, vol. 25(1), pages 3-12, January.
    4. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2018. "Constructing a Markov process for modelling a reliability system under multiple failures and replacements," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 34-47.
    5. Wu, Shaomin & Do, Phuc, 2017. "Editorial," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 1-3.
    6. Bo, Yimin & Bao, Minglei & Ding, Yi & Hu, Yishuang, 2024. "A DNN-based reliability evaluation method for multi-state series-parallel systems considering semi-Markov process," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    7. Çekyay, B. & Özekici, S., 2010. "Mean time to failure and availability of semi-Markov missions with maximal repair," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1442-1454, December.
    8. Mohamed Kayid & Mashael A. Alshehri, 2023. "Stochastic Comparisons of Lifetimes of Used Standby Systems," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    9. Fang, Chen & Cui, Lirong, 2021. "Balanced Systems by Considering Multi-state Competing Risks Under Degradation Processes," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    10. Gao, Hongda & Cui, Lirong & Yi, He, 2019. "Availability analysis of k-out-of-n: F repairable balanced systems with m sectors," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    11. Kayedpour, Farjam & Amiri, Maghsoud & Rafizadeh, Mahmoud & Shahryari Nia, Arash, 2017. "Multi-objective redundancy allocation problem for a system with repairable components considering instantaneous availability and strategy selection," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 11-20.
    12. Wang, Naichao & Li, Mingyuan & Xiao, Boping & Ma, Lin, 2019. "Availability analysis of a general time distribution system with the consideration of maintenance and spares," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    13. Chatterjee, Debolina & Sarkar, Jyotirmoy, 2020. "Computing limiting average availability of a repairable system through discretization," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    14. Eryilmaz, Serkan, 2012. "On the mean residual life of a k-out-of-n:G system with a single cold standby component," European Journal of Operational Research, Elsevier, vol. 222(2), pages 273-277.
    15. Guan Jun Wang & Yuan Lin Zhang, 2016. "Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1021-1031, April.
    16. Yu, Miaomiao & Tang, Yinghui & Liu, Liping & Cheng, Jiang, 2013. "A phase-type geometric process repair model with spare device procurement and repairman’s multiple vacations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 310-323.
    17. Wang, Wei & Wu, Zhiying & Xiong, Junlin & Xu, Yaofeng, 2018. "Redundancy optimization of cold-standby systems under periodic inspection and maintenance," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 394-402.
    18. Wu, Bei & Cui, Lirong & Fang, Chen, 2019. "Reliability analysis of semi-Markov systems with restriction on transition times," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    19. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Optimal loading of system with random repair time," European Journal of Operational Research, Elsevier, vol. 247(1), pages 137-143.
    20. Fang, Chen & Cui, Lirong, 2021. "Reliability evaluation for balanced systems with auto-balancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:852-:d:766398. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.