IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v54y2007i5p568-582.html
   My bibliography  Save this article

On optimal system designs in reliability‐economics frameworks

Author

Listed:
  • Michael R. Dugas
  • Francisco J. Samaniego

Abstract

Reliability Economics is a field that can be defined as the collection of all problems in which there is tension between the performance of systems of interest and their cost. Given such a problem, the aim is to resolve the tension through an optimization process that identifies the system which maximizes some appropriate criterion function (e.g. expected lifetime per unit cost). In this paper, we focus on coherent systems of n independent and identically distributed (iid) components and mixtures thereof, and characterize both a system's performance and cost as functions of the system's signature vector (Samaniego, IEEE Trans Reliabil (1985) 69–72). For a given family of criterion functions, a variety of optimality results are obtained for systems of arbitrary order n. Approximations are developed and justified when the underlying component distribution is unknown. Assuming the availability of an auxiliary sample of N component failure times, the asymptotic theory of L‐estimators is adapted for the purpose of establishing the consistency and asymptotic normality of the proposed estimators of the expected ordered failure times of the n components of the systems under study. These results lead to the identification of ε‐optimal systems relative to the chosen criterion function. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • Michael R. Dugas & Francisco J. Samaniego, 2007. "On optimal system designs in reliability‐economics frameworks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 568-582, August.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:5:p:568-582
    DOI: 10.1002/nav.20245
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20245
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20245?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
    ---><---

    References listed on IDEAS

    as
    1. Subhash Kochar & Hari Mukerjee & Francisco J. Samaniego, 1999. "The “signature” of a coherent system and its application to comparisons among systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 507-523, August.
    2. A. D. Hutson & M. D. Ernst, 2000. "The exact bootstrap mean and variance of an L‐estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 89-94.
    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. Antonio Di Crescenzo & Franco Pellerey, 2011. "Improving series and parallel systems through mixtures of duplicated dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 411-418, August.
    2. Jorge Navarro & Francisco J. Samaniego & N. Balakrishnan & Debasis Bhattacharya, 2008. "On the application and extension of system signatures in engineering reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 313-327, June.
    3. Serkan Eryilmaz & Markos V. Koutras & Ioannis S. Triantafyllou, 2011. "Signature based analysis of m‐Consecutive‐k‐out‐of‐n: F systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 344-354, June.
    4. He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2021. "Comparisons of Multi-State Systems with Binary Components of Different Sizes," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1309-1321, December.
    5. Qianru Ge & Willem van Jaarsveld & Zümbül Atan, 2020. "Optimal redesign decisions through failure rate estimates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 254-271, June.
    6. Francisco J. Samaniego & N. Balakrishnan & Jorge Navarro, 2009. "Dynamic signatures and their use in comparing the reliability of new and used systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 577-591, September.
    7. Jorge Navarro & Antonio Guillamón & María del Carmen Ruiz, 2009. "Generalized mixtures in reliability modelling: Applications to the construction of bathtub shaped hazard models and the study of systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 323-337, May.
    8. 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.

    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. Lauer, Alexandra & Zähle, Henryk, 2017. "Bootstrap consistency and bias correction in the nonparametric estimation of risk measures of collective risks," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 99-108.
    2. Shuang Li & James Lynch, 2010. "Some elementary ideas concerning the complexity of system structure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 626-633, October.
    3. Serkan Eryilmaz & Markos V. Koutras & Ioannis S. Triantafyllou, 2011. "Signature based analysis of m‐Consecutive‐k‐out‐of‐n: F systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 344-354, June.
    4. Ioannis S. Triantafyllou, 2020. "On the Consecutive k 1 and k 2 -out-of- n Reliability Systems," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    5. Alan Hutson, 2000. "A composite quantile function estimator with applications in bootstrapping," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 567-577.
    6. Alan Hutson, 2009. "A distribution function estimator for the difference of order statistics from two independent samples," Statistical Papers, Springer, vol. 50(1), pages 203-208, January.
    7. Zarezadeh, Somayeh & Asadi, Majid, 2019. "Coherent systems subject to multiple shocks with applications to preventative maintenance," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 124-132.
    8. Weiyong Ding & Rui Fang & Peng Zhao, 2017. "Relative Aging of Coherent Systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 345-354, June.
    9. Jia, Xujie & Shen, Jingyuan & Xu, Fanqi & Ma, Ruihong & Song, Xueying, 2019. "Modular decomposition signature for systems with sequential failure effect," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 435-444.
    10. Ioannis S. Triantafyllou, 2022. "Signature-Based Analysis of the Weighted- r -within-Consecutive- k -out-of- n : F Systems," Mathematics, MDPI, vol. 10(15), pages 1-13, July.
    11. Jingwen Lu & He Yi & Xiang Li & Narayanaswamy Balakrishnan, 2023. "Joint Reliability of Two Consecutive-(1, l) or (2, k)-out-of-(2, n): F Type Systems and Its Application in Smart Street Light Deployment," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    12. Modarres, Reza & Hui, Terrence P. & Zheng, Gang, 2006. "Resampling methods for ranked set samples," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1039-1050, November.
    13. 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.
    14. Burkschat, M. & Samaniego, F.J., 2018. "Dynamic IFR concepts for coherent systems," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 1-7.
    15. Liling Ge & Yingjie Zhang, 2019. "Improving operational reliability of manufacturing systems by process optimization via survival signatures," Journal of Risk and Reliability, , vol. 233(3), pages 444-454, June.
    16. 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.
    17. Salehi, Ebrahim & Tavangar, Mahdi, 2019. "Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 327-337.
    18. Elham Khaleghpanah Noughabi & Majid Chahkandi & Majid Rezaei, 2022. "On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2801-2822, December.
    19. M. Kelkin Nama & M. Asadi, 2014. "Stochastic Properties of Components in a Used Coherent System," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 675-691, September.
    20. Diane L. Evans & Lawrence M. Leemis & John H. Drew, 2006. "The Distribution of Order Statistics for Discrete Random Variables with Applications to Bootstrapping," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 19-30, February.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:54:y:2007:i:5:p:568-582. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.