IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v223y2012i1p141-149.html
   My bibliography  Save this article

Optimization problems of replacement first or last in reliability theory

Author

Listed:
  • Zhao, Xufeng
  • Nakagawa, Toshio

Abstract

This paper takes up age and periodic replacement last models with working cycles, where the unit is replaced before failure at a total operating time T or at a random working cycle Y, whichever occurs last, which is called replacement last. Expected cost rates are formulated, and optimal replacement policies which minimize them are discussed analytically. Comparisons between such a replacement last and the conventional replacement first are made in detail. It is determined theoretically and numerically which policy is better than the other according to the ratios of replacement costs and how the mean time of working cycles affects the comparison results. It is also shown that the unit can be operating for a longer time and avoid unnecessary replacements when replacement last is done. For further studies, expected cost rates of modified models and their applications in a standard cumulative damage model with working cycles are obtained and computed numerically. Finally, case studies on replacement last and first in maintaining electronic systems of naval ships under battle and non-battle statuses are given.

Suggested Citation

  • Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.
    • Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:141-149
    DOI: 10.1016/j.ejor.2012.05.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712004043
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.05.035?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, February.
    2. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2011. "Two shock and wear systems under repair standing a finite number of shocks," European Journal of Operational Research, Elsevier, vol. 214(2), pages 298-307, October.
    3. Moan, Torgeir & Ayala-Uraga, Efren, 2008. "Reliability-based assessment of deteriorating ship structures operating in multiple sea loading climates," Reliability Engineering and System Safety, Elsevier, vol. 93(3), pages 433-446.
    4. Sheu, Shey-Huei & Griffith, William S., 2002. "Extended block replacement policy with shock models and used items," European Journal of Operational Research, Elsevier, vol. 140(1), pages 50-60, July.
    5. Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    6. Deris, Safaai & Omatu, Sigeru & Ohta, Hiroshi & Shaharudin Kutar, Lt. Cdr & Abd Samat, Pathiah, 1999. "Ship maintenance scheduling by genetic algorithm and constraint-based reasoning," European Journal of Operational Research, Elsevier, vol. 112(3), pages 489-502, February.
    7. Taghipour, Sharareh & Banjevic, Dragan, 2012. "Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements," European Journal of Operational Research, Elsevier, vol. 220(3), pages 649-660.
    8. Berrade, M.D. & Cavalcante, Cristiano A.V. & Scarf, Philip A., 2012. "Maintenance scheduling of a protection system subject to imperfect inspection and replacement," European Journal of Operational Research, Elsevier, vol. 218(3), pages 716-725.
    9. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    10. Riccardo Manzini & Alberto Regattieri & Hoang Pham & Emilio Ferrari, 2010. "Maintenance for Industrial Systems," Springer Series in Reliability Engineering, Springer, number 978-1-84882-575-8, February.
    11. Toshio Nakagawa, 2008. "Advanced Reliability Models and Maintenance Policies," Springer Series in Reliability Engineering, Springer, number 978-1-84800-294-4, February.
    12. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, February.
    Full references (including those not matched with items on IDEAS)

    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. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2013. "Optimal policies for cumulative damage models with maintenance last and first," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 50-59.
    2. Zhao, Xufeng & Liu, Hu-Chen & Nakagawa, Toshio, 2015. "Where does “whichever occurs first†hold for preventive maintenance modelings?," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 203-211.
    3. Levitin, Gregory & Finkelstein, Maxim & Huang, Hong-Zhong, 2019. "Scheduling of imperfect inspections for reliability critical systems with shock-driven defects and delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 89-98.
    4. Hamidi, Maryam & Szidarovszky, Ferenc & Szidarovszky, Miklos, 2016. "New one cycle criteria for optimizing preventive replacement policies," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 42-48.
    5. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    6. Mingchih Chen & Xufeng Zhao & Toshio Nakagawa, 2019. "Replacement policies with general models," Annals of Operations Research, Springer, vol. 277(1), pages 47-61, June.
    7. Xufeng Zhao & Toshio Nakagawa, 2016. "Over-time and over-level replacement policies with random working cycles," Annals of Operations Research, Springer, vol. 244(1), pages 103-116, September.
    8. Seyedhosseini, Seyed Mohammad & Moakedi, Hamid & Shahanaghi, Kamran, 2018. "Imperfect inspection optimization for a two-component system subject to hidden and two-stage revealed failures over a finite time horizon," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 141-156.
    9. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George, 2012. "Optimal maintenance policy for a system subject to damage in a discrete time process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 1-10.
    10. Ali, Sajid & Pievatolo, Antonio, 2018. "Time and magnitude monitoring based on the renewal reward process," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 97-107.
    11. Levitin, Gregory & Finkelstein, Maxim, 2019. "Optimal loading of elements in series systems exposed to external shocks," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    12. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    13. Shafiee, Mahmood & Chukova, Stefanka, 2013. "Maintenance models in warranty: A literature review," European Journal of Operational Research, Elsevier, vol. 229(3), pages 561-572.
    14. Cha, Ji Hwan, 2011. "Comparison of combined stochastic risk processes and its applications," European Journal of Operational Research, Elsevier, vol. 215(2), pages 404-410, December.
    15. Zhao, Xufeng & Chen, Mingchih & Nakagawa, Toshio, 2016. "Replacement policies for a parallel system with shortage and excess costs," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 89-95.
    16. Taghipour, Sharareh & Banjevic, Dragan & Jardine, Andrew K.S., 2010. "Periodic inspection optimization model for a complex repairable system," Reliability Engineering and System Safety, Elsevier, vol. 95(9), pages 944-952.
    17. Xufeng Zhao & Syouji Nakamura & Toshio Nakagawa, 2012. "Optimal Tenuring And Major Collection Times For A Generational Garbage Collector," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-17.
    18. Huang, Yeu-Shiang & Fang, Chih-Chiang & Lu, Chang-Ming & (Bill) Tseng, Tzu-Liang, 2022. "Optimal Warranty Policy for Consumer Electronics with Dependent Competing Failure Processes," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    19. Hyunju Lee & Ji Hwan Cha, 2021. "On a multivariate IFR and positively dependent lifetime model induced by multiple shot-noise processes," Statistical Papers, Springer, vol. 62(2), pages 561-590, April.
    20. Miaomiao Yu & Yinghui Tang, 2017. "Optimal replacement policy based on maximum repair time for a random shock and wear model," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 80-94, April.

    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:eee:ejores:v:223:y:2012:i:1:p:141-149. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.