IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v222y2012i2p273-277.html
   My bibliography  Save this article

On the mean residual life of a k-out-of-n:G system with a single cold standby component

Author

Listed:
  • Eryilmaz, Serkan

Abstract

The concept of mean residual life is one of the most important characteristics that has been widely used in dynamic reliability analysis. It is a useful tool for investigating ageing properties of technical systems. In this paper, we define and study three different mean residual life functions for k-out-of-n:G system with a single cold standby component. In particular, we obtain explicit expressions for the corresponding functions using distributions of order statistics. We also provide some stochastic ordering results associated with the lifetime of a system. We illustrate the results for various lifetime distributions.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:222:y:2012:i:2:p:273-277
    DOI: 10.1016/j.ejor.2012.05.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171200361X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2012.05.012?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. Navarro, Jorge & Rychlik, Tomasz, 2010. "Comparisons and bounds for expected lifetimes of reliability systems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 309-317, November.
    2. Bairamov, Ismihan & Arnold, Barry C., 2008. "On the residual lifelengths of the remaining components in an n-k+1 out of n system," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 945-952, June.
    3. Leung, Kit Nam Francis & Zhang, Yuan Lin & Lai, Kin Keung, 2011. "Analysis for a two-dissimilar-component cold standby repairable system with repair priority," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1542-1551.
    4. Papageorgiou, Effie & Kokolakis, George, 2007. "A two-unit general parallel system with (n - 2) cold standbys--Analytic and simulation approach," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1016-1032, January.
    5. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    6. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, December.
    7. 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.
    8. Mohammad Raqab & Tomasz Rychlik, 2011. "Bounds for the mean residual life function of a k-out-of-n system," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(3), pages 361-380, November.
    9. Zhang, Zhengcheng & Yang, Yonghong, 2010. "Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 711-717, April.
    10. Khaledi, Baha-Eldin & Kochar, Subhash, 1999. "Stochastic orderings between distributions and their sample spacings - II," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 161-166, August.
    11. Kochar, Subhash C., 1999. "On stochastic orderings between distributions and their sample spacings," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 345-352, May.
    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. Longlong Liu & Xiaochuan Ai & Jun Wu, 2024. "Reliability and Residual Life of Cold Standby Systems," Mathematics, MDPI, vol. 12(10), pages 1-22, May.
    2. Frank PA Coolen & Tahani Coolen-Maturi & Abdullah H Al-nefaiee, 2014. "Nonparametric predictive inference for system reliability using the survival signature," Journal of Risk and Reliability, , vol. 228(5), pages 437-448, October.
    3. Krzysztof Jasiński, 2021. "Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1241-1251, November.
    4. Navarro, Jorge & Pellerey, Franco & Di Crescenzo, Antonio, 2015. "Orderings of coherent systems with randomized dependent components," European Journal of Operational Research, Elsevier, vol. 240(1), pages 127-139.
    5. Davies, Katherine & Dembińska, Anna, 2019. "On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 47-61.
    6. Jorgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2021. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Papers 2112.10672, arXiv.org.
    7. Aboalkhair, Ahmad M. & Coolen, Frank P.A. & MacPhee, Iain M., 2013. "Nonparametric predictive reliability of series of voting systems," European Journal of Operational Research, Elsevier, vol. 226(1), pages 77-84.
    8. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2022. "Optimal preventive switching of components in degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    9. Xiaojun Liang & Yinghui Tang, 2019. "The improvement upon the reliability of the k-out-of-n:F system with the repair rates differentiation policy," Operational Research, Springer, vol. 19(2), pages 479-500, June.
    10. Zohreh Pakdaman & Jafar Ahmadi, 2019. "Switching time of the standby component to the k-out-of-n:G system in the stress–strength setup," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 225-248, March.
    11. Mohamed Kayid & Mashael A. Alshehri, 2023. "Stochastic Comparisons of Lifetimes of Used Standby Systems," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    12. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03634370, HAL.
    13. Gupta, Nitin & Misra, Neeraj & Kumar, Somesh, 2015. "Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components," European Journal of Operational Research, Elsevier, vol. 240(2), pages 425-430.
    14. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Post-Print hal-03634370, HAL.
    15. Zarezadeh, S. & Asadi, M. & Balakrishnan, N., 2014. "Dynamic network reliability modeling under nonhomogeneous Poisson processes," European Journal of Operational Research, Elsevier, vol. 232(3), pages 561-571.
    16. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    17. Li, Chen & Li, Xiaohu, 2023. "On k-out-of-n systems with homogeneous components and one independent cold standby redundancy," Statistics & Probability Letters, Elsevier, vol. 203(C).
    18. Li, Xiaohu & Fang, Rui & Mi, Jie, 2015. "On the timing to switch on the standby in k-out-of-n:G redundant systems," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 10-20.
    19. Eryilmaz, Serkan, 2017. "The effectiveness of adding cold standby redundancy to a coherent system at system and component levels," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 331-335.
    20. Roy Cerqueti, 2022. "A new concept of reliability system and applications in finance," Annals of Operations Research, Springer, vol. 312(1), pages 45-64, May.
    21. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2019. "Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1120-1131.
    22. Zhao, Fei & Peng, Rui & Zhang, Nan, 2023. "Inspection policy optimization for a k-out-of-n/Cl(k′,n′;F) system considering failure dependence: a case study," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    23. Jia, Xiang & Chen, Hao & Cheng, Zhijun & Guo, Bo, 2016. "A comparison between two switching policies for two-unit standby system," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 109-118.
    24. Achintya Roy & Nitin Gupta, 2020. "Reliability of a coherent system equipped with two cold standby components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 677-697, August.
    25. Jorgen-Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Annals of Operations Research, Springer, vol. 326(1), pages 295-316, July.

    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. Serkan Eryilmaz, 2014. "A new look at dynamic behavior of binary coherent system from a state-level perspective," Annals of Operations Research, Springer, vol. 212(1), pages 115-125, January.
    2. Sadiya & Mangey Ram & Akshay Kumar, 2022. "A New Approach to Compute System Reliability with Three-Serially Linked Modules," Mathematics, MDPI, vol. 11(1), pages 1-18, December.
    3. Gaofeng Da & Lvyu Xia & Taizhong Hu, 2014. "On Computing Signatures of k-out-of-n Systems Consisting of Modules," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 223-233, March.
    4. Heidrun C. Hoppe & Benny Moldovanu & Aner Sela, 2009. "The Theory of Assortative Matching Based on Costly Signals," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 253-281.
    5. Said, Maher, 2011. "Sequential auctions with randomly arriving buyers," Games and Economic Behavior, Elsevier, vol. 73(1), pages 236-243, September.
    6. Navarro, Jorge & Rychlik, Tomasz, 2010. "Comparisons and bounds for expected lifetimes of reliability systems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 309-317, November.
    7. 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.
    8. Belzunce, Félix & Mercader, José-Angel & Ruiz, José-María & Spizzichino, Fabio, 2009. "Stochastic comparisons of multivariate mixture models," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1657-1669, September.
    9. Sareh Goli, 2019. "On the conditional residual lifetime of coherent systems under double regularly checking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 352-363, June.
    10. Zhu, Xiaojun & Balakrishnan, N., 2023. "Non-parametric inference based on reliability life-test of non-identical coherent systems with application to warranty time," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    11. Hon Ng & Jorge Navarro & Narayanaswamy Balakrishnan, 2012. "Parametric inference from system lifetime data under a proportional hazard rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 367-388, April.
    12. Jorge Navarro, 2018. "Distribution-free comparisons of residual lifetimes of coherent systems based on copula properties," Statistical Papers, Springer, vol. 59(2), pages 781-800, June.
    13. Serkan Eryilmaz & Frank P.A. Coolen & Tahani Coolen‐Maturi, 2018. "Mean residual life of coherent systems consisting of multiple types of dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 86-97, February.
    14. Jorge Navarro & Yolanda Águila, 2017. "Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 627-648, November.
    15. Jorge Navarro & Rafael Rubio, 2011. "A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 478-489, August.
    16. Serkan Eryilmaz, 2014. "A study on reliability of coherent systems equipped with a cold standby component," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 349-359, April.
    17. Y Takemoto & I Arizono, 2016. "A study of MTTF in two-unit standby redundant system with priority under limited information about failure and repair times," Journal of Risk and Reliability, , vol. 230(1), pages 67-74, February.
    18. M. Kelkinnama & M. Asadi, 2019. "Stochastic and ageing properties of coherent systems with dependent identically distributed components," Statistical Papers, Springer, vol. 60(3), pages 805-821, June.
    19. Zhang, Zhengcheng & Yang, Yonghong, 2010. "Ordered properties on the residual life and inactivity time of (n-k+1)-out-of-n systems under double monitoring," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 711-717, April.
    20. Tavangar, Mahdi & Bairamov, Ismihan, 2015. "On conditional residual lifetime and conditional inactivity time of k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 225-233.

    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:222:y:2012:i:2:p:273-277. 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.