IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v76y2018i2d10.1007_s40300-018-0141-7.html
   My bibliography  Save this article

A Bayesian approach to estimate the failure time distribution of a log-logistic degradation model

Author

Listed:
  • Aymen Rawashdeh

    (Yarmouk University)

  • Mohammed Hassan Al-Haj Ebrahem

    (Yarmouk University)

  • Ayat Momani

    (Yarmouk University)

Abstract

This paper presents a Bayesian approach, using differential evolution Markov chain method, to estimate the parameters of the failure time distribution and its percentiles based on grouped and non-grouped degradation data. The observed failure times are modeled by linear degradation path model with random degradation rates follow log-logistic distribution. Two Monte Carlo simulation studies are conducted. The first one is devoted to assess the performance of the proposed method with respect to the mean squared error (MSE) for different values of the scale and shape parameters of the degradation model using small, moderate and large sample sizes. The proposed method performs better when applied to non-grouped data compared with grouped data. The second simulation study is conducted to compare the proposed log-logistic model with a Weibull degradation model. More importantly, the log-logistic model outperforms the Weibull model. The proposed methods are demonstrated by modeling real life times of laser devices.

Suggested Citation

  • Aymen Rawashdeh & Mohammed Hassan Al-Haj Ebrahem & Ayat Momani, 2018. "A Bayesian approach to estimate the failure time distribution of a log-logistic degradation model," METRON, Springer;Sapienza Università di Roma, vol. 76(2), pages 155-176, August.
  • Handle: RePEc:spr:metron:v:76:y:2018:i:2:d:10.1007_s40300-018-0141-7
    DOI: 10.1007/s40300-018-0141-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40300-018-0141-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s40300-018-0141-7?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. David D. Hanagal & Richa Sharma, 2015. "Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(7), pages 1351-1380, April.
    2. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    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. Buddhavarapu, Prasad & Bansal, Prateek & Prozzi, Jorge A., 2021. "A new spatial count data model with time-varying parameters," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 566-586.
    2. Mumtaz, Haroon & Theodoridis, Konstantinos, 2017. "Common and country specific economic uncertainty," Journal of International Economics, Elsevier, vol. 105(C), pages 205-216.
    3. Jesse Elliott & Zemin Bai & Shu-Ching Hsieh & Shannon E Kelly & Li Chen & Becky Skidmore & Said Yousef & Carine Zheng & David J Stewart & George A Wells, 2020. "ALK inhibitors for non-small cell lung cancer: A systematic review and network meta-analysis," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-18, February.
    4. Christina Leuker & Thorsten Pachur & Ralph Hertwig & Timothy J. Pleskac, 2019. "Do people exploit risk–reward structures to simplify information processing in risky choice?," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 5(1), pages 76-94, August.
    5. Francois Olivier & Laval Guillaume, 2011. "Deviance Information Criteria for Model Selection in Approximate Bayesian Computation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-25, July.
    6. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    7. Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2023. "Large Time‐Varying Volatility Models for Hourly Electricity Prices," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 545-573, June.
    8. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    9. Alessandri, Piergiorgio & Mumtaz, Haroon, 2019. "Financial regimes and uncertainty shocks," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 31-46.
    10. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    11. Svetlana V. Tishkovskaya & Paul G. Blackwell, 2021. "Bayesian estimation of heterogeneous environments from animal movement data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(6), September.
    12. David Macro & Jeroen Weesie, 2016. "Inequalities between Others Do Matter: Evidence from Multiplayer Dictator Games," Games, MDPI, vol. 7(2), pages 1-23, April.
    13. Tautenhahn, Susanne & Heilmeier, Hermann & Jung, Martin & Kahl, Anja & Kattge, Jens & Moffat, Antje & Wirth, Christian, 2012. "Beyond distance-invariant survival in inverse recruitment modeling: A case study in Siberian Pinus sylvestris forests," Ecological Modelling, Elsevier, vol. 233(C), pages 90-103.
    14. Julian P. T. Higgins & Simon G. Thompson & David J. Spiegelhalter, 2009. "A re‐evaluation of random‐effects meta‐analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 137-159, January.
    15. Simon Mak & Derek Bingham & Yi Lu, 2016. "A regional compound Poisson process for hurricane and tropical storm damage," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 677-703, November.
    16. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    17. Huang, Zhaodong & Chien, Steven & Zhu, Wei & Zheng, Pengjun, 2022. "Scheduling wheel inspection for sustainable urban rail transit operation: A Bayesian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    18. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.
    19. Leonardo Oliveira Martins & Hirohisa Kishino, 2010. "Distribution of distances between topologies and its effect on detection of phylogenetic recombination," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 145-159, February.
    20. Tamal Ghosh & Malay Ghosh & Jerry J. Maples & Xueying Tang, 2022. "Multivariate Global-Local Priors for Small Area Estimation," Stats, MDPI, vol. 5(3), pages 1-16, July.

    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:spr:metron:v:76:y:2018:i:2:d:10.1007_s40300-018-0141-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.