IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v167y2017icp95-104.html
   My bibliography  Save this article

A nonparametric Bayesian modeling approach for heterogeneous lifetime data with covariates

Author

Listed:
  • Li, Mingyang
  • Meng, Hongdao
  • Zhang, Qingpeng

Abstract

Lifetime data collected at product design and production stage or field operational stage often exhibit heterogeneity patterns, making the homogeneity assumption in conventional statistical lifetime models invalid. Mixture models are important modeling approaches that account for data heterogeneity. However, existing mixture models are constrained by assuming an known number of sub-populations. This paper proposes a new Bayesian statistical model to analyze heterogeneous lifetime data by assuming an unknown number of sub-populations. Each sub-population is characterized by an accelerated failure time model to quantify the effects of possible reliability impact factors. The proposed model allows simultaneous identification of the number of sub-populations and the model parameters of sub-populations. Convenient sampling strategies are further proposed to address the challenges of model estimation. Both numerical case study and real case study are provided to illustrate the proposed approach and demonstrate its validity.

Suggested Citation

  • Li, Mingyang & Meng, Hongdao & Zhang, Qingpeng, 2017. "A nonparametric Bayesian modeling approach for heterogeneous lifetime data with covariates," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 95-104.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:95-104
    DOI: 10.1016/j.ress.2017.05.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832017305987
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2017.05.029?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. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. Raed Kontar & Junbo Son & Shiyu Zhou & Chaitanya Sankavaram & Yilu Zhang & Xinyu Du, 2017. "Remaining useful life prediction based on the mixed effects model with mixture prior distribution," IISE Transactions, Taylor & Francis Journals, vol. 49(7), pages 682-697, July.
    3. Richard L Warr & David H Collins, 2014. "Bayesian nonparametric models for combining heterogeneous reliability data," Journal of Risk and Reliability, , vol. 228(2), pages 166-175, April.
    4. Anne B. Koehler & Emily S. Murphree, 1988. "A Comparison of the Akaike and Schwarz Criteria for Selecting Model Order," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(2), pages 187-195, June.
    5. Tao Yuan & Xiaoyan Zhu, 2012. "Reliability study of ultra-thin dielectric films with variable thickness levels," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 744-753.
    6. Mingyang Li & Jiali Han & Jian Liu, 2017. "Bayesian nonparametric modeling of heterogeneous time-to-event data with an unknown number of sub-populations," IISE Transactions, Taylor & Francis Journals, vol. 49(5), pages 481-492, May.
    7. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.
    8. Peter J. Green & Sylvia Richardson, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(2), pages 355-375, June.
    9. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    10. Li, Mingyang & Liu, Jian, 2016. "Bayesian hazard modeling based on lifetime data with latent heterogeneity," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 183-189.
    11. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    12. Castet, Jean-Francois & Saleh, Joseph H., 2010. "Single versus mixture Weibull distributions for nonparametric satellite reliability," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 295-300.
    13. Yisha Xiang & David Coit & Qianmei Feng, 2013. "Subpopulations experiencing stochastic degradation: reliability modeling, burn-in, and preventive replacement optimization," IISE Transactions, Taylor & Francis Journals, vol. 45(4), pages 391-408.
    14. Jiang, R. & Murthy, D.N.P., 2009. "Impact of quality variations on product reliability," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 490-496.
    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. Peña-Ramírez, Fernando A. & Guerra, Renata Rojas & Canterle, Diego Ramos & Cordeiro, Gauss M., 2020. "The logistic Nadarajah–Haghighi distribution and its associated regression model for reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Santos, Cristiano C. & Loschi, Rosangela H., 2020. "Semi-parametric Bayesian models for heterogeneous degradation data: An application to laser data," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    3. Zhou, Chongwen & Chinnam, Ratna Babu & Dalkiran, Evrim & Korostelev, Alexander, 2017. "Bayesian approach to hazard rate models for early detection of warranty and reliability problems using upstream supply chain information," International Journal of Production Economics, Elsevier, vol. 193(C), pages 316-331.
    4. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.
    5. Yang, Lechang & Wang, Pidong & Wang, Qiang & Bi, Sifeng & Peng, Rui & Behrensdorf, Jasper & Beer, Michael, 2021. "Reliability analysis of a complex system with hybrid structures and multi-level dependent life metrics," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    6. Kowal, Karol, 2022. "Lifetime reliability and availability simulation for the electrical system of HTTR coupled to the electricity-hydrogen cogeneration plant," Reliability Engineering and System Safety, Elsevier, vol. 223(C).

    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. Sylvia Frühwirth-Schnatter & Gertraud Malsiner-Walli, 2019. "From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 33-64, March.
    2. Im, Yunju & Tan, Aixin, 2021. "Bayesian subgroup analysis in regression using mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    3. Moya, Blake & Walker, Stephen G., 2024. "Full uncertainty analysis for Bayesian nonparametric mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    4. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    5. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    6. Lin, Kunsong & Chen, Yunxia & Xu, Dan, 2017. "Reliability assessment model considering heterogeneous population in a multiple stresses accelerated test," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 134-143.
    7. De Blasi, Pierpaolo & Martínez, Asael Fabian & Mena, Ramsés H. & Prünster, Igor, 2020. "On the inferential implications of decreasing weight structures in mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    8. C. Yau & O. Papaspiliopoulos & G. O. Roberts & C. Holmes, 2011. "Bayesian non‐parametric hidden Markov models with applications in genomics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 37-57, January.
    9. Santos, Cristiano C. & Loschi, Rosangela H., 2020. "Semi-parametric Bayesian models for heterogeneous degradation data: An application to laser data," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    10. Carlos Medel, 2017. "Forecasting Chilean inflation with the hybrid new keynesian Phillips curve: globalisation, combination, and accuracy," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 20(3), pages 004-050, December.
    11. Murthy, D.N.P. & Hagmark, P.-E. & Virtanen, S., 2009. "Product variety and reliability," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1601-1608.
    12. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    13. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    14. Zhang, Jian-Xun & Hu, Chang-Hua & He, Xiao & Si, Xiao-Sheng & Liu, Yang & Zhou, Dong-Hua, 2017. "Lifetime prognostics for deteriorating systems with time-varying random jumps," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 338-350.
    15. Aldo M. Garay & Francyelle L. Medina & Suelem Torres de Freitas & Víctor H. Lachos, 2024. "Bayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data," Statistical Papers, Springer, vol. 65(9), pages 5649-5690, December.
    16. Carlos A. Medel, 2015. "Probabilidad Clásica de Sobreajuste con Criterios de Información: Estimaciones con Series Macroeconómicas Chilenas," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 30(1), pages 57-72, Abril.
    17. N. T. Longford & Pierpaolo D'Urso, 2011. "Mixture models with an improper component," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2511-2521, January.
    18. Conti, Gabriella & Frühwirth-Schnatter, Sylvia & Heckman, James J. & Piatek, Rémi, 2014. "Bayesian exploratory factor analysis," Journal of Econometrics, Elsevier, vol. 183(1), pages 31-57.
    19. Zhengyi Zhou & David S. Matteson & Dawn B. Woodard & Shane G. Henderson & Athanasios C. Micheas, 2015. "A Spatio-Temporal Point Process Model for Ambulance Demand," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 6-15, March.
    20. Francisco Richter & Bart Haegeman & Rampal S. Etienne & Ernst C. Wit, 2020. "Introducing a general class of species diversification models for phylogenetic trees," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 261-274, August.

    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:167:y:2017:i:c:p:95-104. 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.