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A Criterion for Burn-in that Balances Mean Residual Life and Residual Variance

Author

Listed:
  • Henry W. Block

    (Department of Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

  • Thomas H. Savits

    (Department of Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260)

  • Harshinder Singh

    (Department of Statistics, West Virginia University, Morgantown, West Virginia 26506-6330, and Department of Statistics, Panjab University, Chandigarh 160014, India)

Abstract

Optimum burn-in times have been determined for a variety of criteria such as mean residual life and conditional survival. In this paper we consider a residual coefficient of variation that balances mean residual life with residual variance. To study this quantity, we develop a general result concerning the preservation ofbathtub distributions. Using this result, we give a condition so that the residual coefficient of variation is bathtub-shaped. Furthermore, we show that it attains its optimum value at a time that occurs after the mean residual life function attains its optimum value, but not necessarily before the change point of the failure rate function.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:2:p:290-296
    DOI: 10.1287/opre.50.2.290.435
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    References listed on IDEAS

    as
    1. Prem S. Puri & Harshinder Singh, 1986. "Optimum Replacement of a System Subject to Shocks: A Mathematical Lemma," Operations Research, INFORMS, vol. 34(5), pages 782-789, October.
    2. Robert L. Launer, 1984. "Inequalities for NBUE and NWUE Life Distributions," Operations Research, INFORMS, vol. 32(3), pages 660-667, June.
    3. Ebrahimi, Nader & Kirmani, S. N. U. A., 1996. "Some results on ordering of survival functions through uncertainty," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 167-176, August.
    4. 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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    Cited by:

    1. Ji Cha & Maxim S. Finkelstein, 2009. "Stochastically ordered subpopulations and optimal burn-in procedure," MPIDR Working Papers WP-2009-030, Max Planck Institute for Demographic Research, Rostock, Germany.
    2. Cha, Ji Hwan & Finkelstein, Maxim, 2010. "Burn-in by environmental shocks for two ordered subpopulations," European Journal of Operational Research, Elsevier, vol. 206(1), pages 111-117, October.
    3. M. Khorashadizadeh & A. Roknabadi & G. Borzadaran, 2013. "Variance residual life function based on double truncation," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 175-188, September.
    4. 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.
    5. Ji Hwan Cha, 2006. "A stochastic model for burn‐in procedures in accelerated environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 226-234, April.
    6. Cha, Ji Hwan & Pulcini, Gianpaolo, 2016. "Optimal burn-in procedure for mixed populations based on the device degradation process history," European Journal of Operational Research, Elsevier, vol. 251(3), pages 988-998.
    7. Kim, Kyungmee O., 2011. "Burn-in considering yield loss and reliability gain for integrated circuits," European Journal of Operational Research, Elsevier, vol. 212(2), pages 337-344, July.
    8. Mark Bebbington & Chin-Diew Lai & Ričardas Zitikis, 2010. "Life expectancy of a bathtub shaped failure distribution," Statistical Papers, Springer, vol. 51(3), pages 599-612, September.
    9. Ji Hwan Cha & Sangyeol Lee & Jie Mi, 2004. "Bounding the optimal burn‐in time for a system with two types of failure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1090-1101, December.

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