IDEAS home Printed from https://ideas.repec.org/p/dem/wpaper/wp-2009-030.html
   My bibliography  Save this paper

Stochastically ordered subpopulations and optimal burn-in procedure

Author

Listed:
  • Ji Cha
  • Maxim S. Finkelstein

    (Max Planck Institute for Demographic Research, Rostock, Germany)

Abstract

Burn-in is a widely used engineering method which is adopted to eliminate defective items before they are shipped to customers or put into the field operation. In the studies of burn-in, the assumption of bathtub shaped failure rate function is usually employed and optimal burn-in procedures are investigated. In this paper, however, we assume that the population is composed of two ordered subpopulations and optimal burn-in procedures are studied in this context. Two types of risks are defined and an optimal burn-in procedure, which minimizes the weighted risks is studied. The joint optimal solutions for the optimal burn-in procedure, which minimizes the mean number of repairs during the field operation, are also investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:dem:wpaper:wp-2009-030
    DOI: 10.4054/MPIDR-WP-2009-030
    as

    Download full text from publisher

    File URL: https://www.demogr.mpg.de/papers/working/wp-2009-030.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4054/MPIDR-WP-2009-030?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. E. Arjas & I. Norros, 1989. "Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 355-361, May.
    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.
    3. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, July.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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.
    4. 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.
    5. 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.
    6. J H Cha & M Finkelstein, 2012. "Burn-in via shocks for avoiding large risks," Journal of Risk and Reliability, , vol. 226(3), pages 318-326, June.
    7. Cha, Ji Hwan & Finkelstein, Maxim, 2015. "Environmental stress screening modelling, analysis and optimization," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 149-155.
    8. Cha, Ji Hwan & Finkelstein, Maxim, 2013. "The failure rate dynamics in heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 120-128.
    9. 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.
    10. 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.
    11. Gregory Levitin & Maxim Finkelstein, 2018. "Optimal Mission Abort Policy for Systems Operating in a Random Environment," Risk Analysis, John Wiley & Sons, vol. 38(4), pages 795-803, April.
    12. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort policy optimization for series systems with overlapping primary and rescue subsystems operating in a random environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    13. Ji Hwan Cha & Maxim Finkelstein, 2019. "New failure and minimal repair processes for repairable systems in a random environment," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 522-536, May.
    14. Maxim S. Finkelstein, 2008. "On systems with shared resources and optimal switching strategies," MPIDR Working Papers WP-2008-025, Max Planck Institute for Demographic Research, Rostock, Germany.
    15. Laniado Rodas, Henry, 2013. "Allocation policies of redundancies in two-parallel-series and two-series-parallel systems," DES - Working Papers. Statistics and Econometrics. WS ws132622, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2018. "Constructing a Markov process for modelling a reliability system under multiple failures and replacements," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 34-47.
    17. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    18. Levitin, Gregory & Finkelstein, Maxim, 2018. "Optimal mission abort policy for systems in a random environment with variable shock rate," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 11-17.
    19. Omid Shojaee & Majid Asadi & Maxim Finkelstein, 2021. "On Some Properties of $$\alpha $$ α -Mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1213-1240, November.
    20. Navarro, Jorge & Arriaza, Antonio & Suárez-Llorens, Alfonso, 2019. "Minimal repair of failed components in coherent systems," European Journal of Operational Research, Elsevier, vol. 279(3), pages 951-964.

    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:dem:wpaper:wp-2009-030. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Wilhelm (email available below). General contact details of provider: https://www.demogr.mpg.de/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.