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On optimal system designs in reliability‐economics frameworks

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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