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Optimum Burn-in Time for a Bathtub Shaped Failure Distribution

Author

Listed:
  • Mark Bebbington

    (Massey University)

  • Chin-Diew Lai

    (Massey University)

  • Ričardas Zitikis

    (University of Western Ontario)

Abstract

An important problem in reliability is to define and estimate the optimal burn-in time. For bathtub shaped failure-rate lifetime distributions, the optimal burn-in time is frequently defined as the point where the corresponding mean residual life function achieves its maximum. For this point, we construct an empirical estimator and develop the corresponding statistical inferential theory. Theoretical results are accompanied with simulation studies and applications to real data. Furthermore, we develop a statistical inferential theory for the difference between the minimum point of the corresponding failure rate function and the aforementioned maximum point of the mean residual life function. The difference measures the length of the time interval after the optimal burn-in time during which the failure rate function continues to decrease and thus the burn-in process can be stopped.

Suggested Citation

  • Mark Bebbington & Chin-Diew Lai & Ričardas Zitikis, 2007. "Optimum Burn-in Time for a Bathtub Shaped Failure Distribution," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 1-20, March.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:1:d:10.1007_s11009-006-9001-7
    DOI: 10.1007/s11009-006-9001-7
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    References listed on IDEAS

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    1. Murari Mitra & Sujit Basu, 1995. "Change point estimation in non-monotonic aging models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 483-491, September.
    2. Henry W. Block & Thomas H. Savits & Harshinder Singh, 2002. "A Criterion for Burn-in that Balances Mean Residual Life and Residual Variance," Operations Research, INFORMS, vol. 50(2), pages 290-296, April.
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    Citations

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    Cited by:

    1. Gupta, Ashutosh & Mukherjee, Bhaswati & Upadhyay, S.K., 2008. "Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1434-1443.
    2. Rachele Foschi & Fabio Spizzichino, 2012. "Interactions Between Ageing and Risk Properties in the Analysis of Burn-in Problems," Decision Analysis, INFORMS, vol. 9(2), pages 103-118, June.
    3. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    4. Jinsong Yu & Jie Yang & Diyin Tang & Jing Dai, 2018. "An Optimal Burn-In Policy for Cellular Phone Lithium-Ion Batteries Using a Feature Selection Strategy and Relevance Vector Machine," Energies, MDPI, vol. 11(11), pages 1-19, November.
    5. Zhi-Sheng Ye & Loon-Ching Tang & Min Xie, 2014. "Bi-objective burn-in modeling and optimization," Annals of Operations Research, Springer, vol. 212(1), pages 201-214, January.
    6. Bebbington, Mark & Lai, Chin-Diew & Wellington, Morgan & Zitikis, RiÄ ardas, 2012. "The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 37-44.

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