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Burn-in and the performance quality measures in continuous heterogeneous populations

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  • Ji Hwan Cha
  • Maxim Finkelstein

Abstract

Burn-in is a method used to eliminate initial failures in field use. To burn-in a component or system means to subject it to a period of use prior to the time when it is to actually be used. Under the assumption of decreasing or bathtub-shaped population failure rate functions, various problems of determining optimal burn-in have been intensively studied in the literature. In this paper, we assume that a population is composed of stochastically ordered subpopulations, described by their own performance quality measures and study optimal burn-in, which optimizes overall performance measures. It turns out that this setting can justify burn-in even when it is not necessary in the framework of conventional approaches. For instance, it could be reasonable to perform burn-in even when the failure rate function that describes a heterogeneous population of items increases and this is one of the main and important findings of the current study.

Suggested Citation

  • Ji Hwan Cha & Maxim Finkelstein, 2012. "Burn-in and the performance quality measures in continuous heterogeneous populations," Journal of Risk and Reliability, , vol. 226(4), pages 417-425, August.
    • Handle: RePEc:sae:risrel:v:226:y:2012:i:4:p:417-425
    DOI: 10.1177/1748006X12443217
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    References listed on IDEAS

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    1. Maxim S. Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," MPIDR Working Papers WP-2009-031, Max Planck Institute for Demographic Research, Rostock, Germany.
    2. Sheu, Shey-Huei & Chien, Yu-Hung, 2005. "Optimal burn-in time to minimize the cost for general repairable products sold under warranty," European Journal of Operational Research, Elsevier, vol. 163(2), pages 445-461, June.
    3. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, March.
    4. Maxim Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 643-663, November.
    5. A. R. Thatcher, 1999. "The long‐term pattern of adult mortality and the highest attained age," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 5-43.
    6. Cha, Ji Hwan & Finkelstein, Maxim, 2011. "Burn-in and the performance quality measures in heterogeneous populations," European Journal of Operational Research, Elsevier, vol. 210(2), pages 273-280, April.
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