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On testing whether burn-in is required under the long-run average cost

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  • Mohammadi, Faezeh
  • Izadi, Muhyiddin
  • Lai, Chin-Diew

Abstract

In this paper, we consider the testing problem whether burn-in is required based on the long-run average cost for a population with bathtub-shaped failure rate function. We propose a test based on kernel density estimation. We then apply our proposed test to two real data sets in the context of reliability.

Suggested Citation

  • Mohammadi, Faezeh & Izadi, Muhyiddin & Lai, Chin-Diew, 2016. "On testing whether burn-in is required under the long-run average cost," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 217-224.
  • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:217-224
    DOI: 10.1016/j.spl.2015.10.009
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    References listed on IDEAS

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    1. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    2. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    3. Ji Hwan Cha, 2011. "A Survey of Burn-in and Maintenance Models for Repairable Systems," Springer Series in Reliability Engineering, in: Lotfi Tadj & M.-Salah Ouali & Soumaya Yacout & Daoud Ait-Kadi (ed.), Replacement Models with Minimal Repair, pages 179-203, Springer.
    4. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    5. Mahmood Shafiee & Maxim Finkelstein & Ming Zuo, 2013. "Optimal burn-in and preventive maintenance warranty strategies with time-dependent maintenance costs," IISE Transactions, Taylor & Francis Journals, vol. 45(9), pages 1024-1033.
    6. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    7. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(2), pages 390-412, April.
    8. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    9. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
    10. Hirukawa, Masayuki & Sakudo, Mari, 2014. "Nonnegative bias reduction methods for density estimation using asymmetric kernels," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 112-123.
    11. 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.
    12. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    13. Kim, Kyungmee O. & Kuo, Way, 2009. "Optimal burn-in for maximizing reliability of repairable non-series systems," European Journal of Operational Research, Elsevier, vol. 193(1), pages 140-151, February.
    14. Mohamed-Salah Ouali & Lotfi Tadj & Soumaya Yacout & Daoud Ait-Kadi, 2011. "A Survey of Replacement Models with Minimal Repair," Springer Series in Reliability Engineering, in: Lotfi Tadj & M.-Salah Ouali & Soumaya Yacout & Daoud Ait-Kadi (ed.), Replacement Models with Minimal Repair, pages 3-100, Springer.
    15. Jie Mi, 1996. "Minimizing Some Cost Functions Related to Both Burn-In and Field Use," Operations Research, INFORMS, vol. 44(3), pages 497-500, June.
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