IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v123y2014icp99-103.html
   My bibliography  Save this article

Some notes on unobserved parameters (frailties) in reliability modeling

Author

Listed:
  • Cha, Ji Hwan
  • Finkelstein, Maxim

Abstract

Unobserved random quantities (frailties) often appear in various reliability problems especially when dealing with the failure rates of items from heterogeneous populations. As the failure rate is a conditional characteristic, the distributions of these random quantities, similar to Bayesian approaches, are updated in accordance with the corresponding survival information. At some instances, apart from a statistical meaning, frailties can have also useful interpretations describing the underlying lifetime model. We discuss and clarify these issues in reliability context and present and analyze several meaningful examples. We consider the proportional hazards model with a random factor; the stress–strength model, where the unobserved strength of a system can be viewed as frailty; a parallel system with a random number of components and, finally, the first passage time problem for the Wiener process with random parameters.

Suggested Citation

  • Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.
    • Handle: RePEc:eee:reensy:v:123:y:2014:i:c:p:99-103
    DOI: 10.1016/j.ress.2013.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832013002925
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2013.10.008?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Missov, Trifon I. & Finkelstein, Maxim, 2011. "Admissible mixing distributions for a general class of mixture survival models with known asymptotics," Theoretical Population Biology, Elsevier, vol. 80(1), pages 64-70.
    2. 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.
    3. 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.
    4. Anatoli Yashin & Ivan Iachine & Alexander Begun, 2000. "Mortality modeling: A review," Mathematical Population Studies, Taylor & Francis Journals, vol. 8(4), pages 305-332.
    5. 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.
    6. Finkelstein, Maxim, 2012. "On ordered subpopulations and population mortality at advanced ages," Theoretical Population Biology, Elsevier, vol. 81(4), pages 292-299.
    7. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    8. Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    9. Jiang, Xiaomo & Yuan, Yong & Liu, Xian, 2013. "Bayesian inference method for stochastic damage accumulation modeling," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 126-138.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Almeida, Marco Pollo & Paixão, Rafael S. & Ramos, Pedro L. & Tomazella, Vera & Louzada, Francisco & Ehlers, Ricardo S., 2020. "Bayesian non-parametric frailty model for dependent competing risks in a repairable systems framework," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Zeynab Allahkarami & Ahmad Reza Sayadi & Behzad Ghodrati, 2021. "Identifying the mixed effects of unobserved and observed risk factors on the reliability of mining hauling system," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(2), pages 281-289, April.
    3. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Optimal mission abort policy for partially repairable heterogeneous systems," European Journal of Operational Research, Elsevier, vol. 271(3), pages 818-825.
    4. Hao Zeng & Xuxue Sun & Kuo Wang & Yuxin Wen & Wujun Si & Mingyang Li, 2024. "A Bayesian Approach for Lifetime Modeling and Prediction with Multi-Type Group-Shared Missing Covariates," Mathematics, MDPI, vol. 12(5), pages 1-23, February.
    5. Rezgar Zaki & Abbas Barabadi & Javad Barabady & Ali Nouri Qarahasanlou, 2022. "Observed and unobserved heterogeneity in failure data analysis," Journal of Risk and Reliability, , vol. 236(1), pages 194-207, February.
    6. Barui, Sandip & Mitra, Debanjan & Balakrishnan, Narayanaswamy, 2024. "Flexible modelling of a bivariate degradation process with a shared frailty and an application to fatigue crack data," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    7. M. Kayid & S. Izadkhah & Ming J. Zuo, 2017. "Some results on the relative ordering of two frailty models," Statistical Papers, Springer, vol. 58(2), pages 287-301, June.
    8. Rezgar Zaki & Abbas Barabadi & Ali Nouri Qarahasanlou & A. H. S. Garmabaki, 2019. "A mixture frailty model for maintainability analysis of mechanical components: a case study," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(6), pages 1646-1653, December.
    9. Asfaw, Zeytu Gashaw & Lindqvist, Bo Henry, 2015. "Unobserved heterogeneity in the power law nonhomogeneous Poisson process," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 59-65.
    10. Awat Ghomghaleh & Reza Khaloukakaie & Mohammad Ataei & Abbas Barabadi & Ali Nouri Qarahasanlou & Omeid Rahmani & Amin Beiranvand Pour, 2020. "Prediction of remaining useful life (RUL) of Komatsu excavator under reliability analysis in the Weibull-frailty model," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-16, July.
    11. Gregory Levitin & Maxim Finkelstein, 2017. "A new stress–strength model for systems subject to stochastic shocks," Journal of Risk and Reliability, , vol. 231(2), pages 172-179, April.
    12. Hooti, Fatemeh & Ahmadi, Jafar & Longobardi, Maria, 2020. "Optimal extended warranty length with limited number of repairs in the warranty period," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    13. Slimacek, Vaclav & Lindqvist, Bo Henry, 2016. "Nonhomogeneous Poisson process with nonparametric frailty," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 14-23.
    14. Ramesh Gupta, 2016. "Properties of additive frailty model in survival analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 1-17, January.
    15. J. Jarrahiferiz & M. Kayid & S. Izadkhah, 2019. "Stochastic properties of a weighted frailty model," Statistical Papers, Springer, vol. 60(1), pages 53-72, February.

    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 & Finkelstein, Maxim, 2016. "Justifying the Gompertz curve of mortality via the generalized Polya process of shocks," Theoretical Population Biology, Elsevier, vol. 109(C), pages 54-62.
    2. Hal Caswell, 2014. "A matrix approach to the statistics of longevity in heterogeneous frailty models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(19), pages 553-592.
    3. Maxim S. Finkelstein, 2011. "On ordered subpopulations and population mortality at advanced ages," MPIDR Working Papers WP-2011-022, Max Planck Institute for Demographic Research, Rostock, Germany.
    4. Francisco Germán Badía & Hyunju Lee, 2020. "On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 355-375, April.
    5. Finkelstein, Maxim, 2012. "On ordered subpopulations and population mortality at advanced ages," Theoretical Population Biology, Elsevier, vol. 81(4), pages 292-299.
    6. Nil Kamal Hazra & Maxim Finkelstein, 2018. "On stochastic comparisons of finite mixtures for some semiparametric families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 988-1006, December.
    7. Finkelstein, Maxim, 2013. "On some comparisons of lifetimes for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 300-304.
    8. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 505-516, June.
    9. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2021. "Optimal warranty policy with inspection for heterogeneous, stochastically degrading items," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1142-1152.
    10. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal mission duration for systems subject to shocks and internal failures," Journal of Risk and Reliability, , vol. 232(1), pages 82-91, February.
    11. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "On some properties of shock processes in a ‘natural’ scale," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 104-110.
    12. James W. Vaupel & Trifon Missov, 2014. "Unobserved population heterogeneity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(22), pages 659-686.
    13. 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).
    14. Hui Zheng, 2014. "Aging in the Context of Cohort Evolution and Mortality Selection," Demography, Springer;Population Association of America (PAA), vol. 51(4), pages 1295-1317, August.
    15. 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.
    16. 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.
    17. Lee, Hyunju & Cha, Ji Hwan, 2014. "On construction of general classes of bivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 151-159.
    18. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    19. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Mission abort policy balancing the uncompleted mission penalty and system loss risk," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 194-201.
    20. M S Finkelstein, 2008. "Reliability modelling for biological ageing," Journal of Risk and Reliability, , vol. 222(1), pages 1-6, March.

    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:eee:reensy:v:123:y:2014:i:c:p:99-103. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.