IDEAS home Printed from https://ideas.repec.org/a/bpj/jossai/v9y2021i5p533-548n5.html
   My bibliography  Save this article

Statistical Inference for a Simple Step Stress Model with Competing Risks Based on Generalized Type-I Hybrid Censoring

Author

Listed:
  • Mao Song

    (School of Economics and Management, Shanxi University, Taiyuan030006, China)

  • Liu Bin

    (School of Applied Science, Taiyuan University of Science and Technology, Taiyuan030024, China)

  • Shi Yimin

    (School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an710072, China)

Abstract

This paper investigates a simple step-stress accelerated lifetime test (SSALT) model for the inferential analysis of exponential competing risks data. A generalized type-I hybrid censoring scheme is employed to improve the efficiency and controllability of the test. Firstly, the MLEs for parameters are established based on the cumulative exposure model (CEM). Then the conditional moment generating function (MGF) for unknown parameters is set up using conditional expectation and multiple integral techniques. Thirdly, confidence intervals (CIs) are constructed by the exact MGF-based method, the approximate normality-based method, and the bias-corrected and accelerated (BCa) percentile bootstrap method. Finally, we present simulation studies and an illustrative example to compare the performances of different methods.

Suggested Citation

  • Mao Song & Liu Bin & Shi Yimin, 2021. "Statistical Inference for a Simple Step Stress Model with Competing Risks Based on Generalized Type-I Hybrid Censoring," Journal of Systems Science and Information, De Gruyter, vol. 9(5), pages 533-548, October.
    • Handle: RePEc:bpj:jossai:v:9:y:2021:i:5:p:533-548:n:5
    DOI: 10.21078/JSSI-2021-533-16
    as

    Download full text from publisher

    File URL: https://doi.org/10.21078/JSSI-2021-533-16
    Download Restriction: no
    File URL: https://libkey.io/10.21078/JSSI-2021-533-16?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. Chien-Tai Lin & Cheng-Chieh Chou & N. Balakrishnan, 2020. "Planning step-stress test plans under Type-I hybrid censoring for the log-location-scale distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 265-288, June.
    2. Park, Sangun & Balakrishnan, N., 2009. "On simple calculation of the Fisher information in hybrid censoring schemes," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1311-1319, May.
    3. B. Chandrasekar & A. Childs & N. Balakrishnan, 2004. "Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(7), pages 994-1004, October.
    4. Christian Kohl & Maria Kateri, 2019. "Bayesian analysis for step‐stress accelerated life testing under progressive interval censoring," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(2), pages 234-246, March.
    5. Ritwik Bhattacharya & Baidya Nath Saha & Graceila González Farías & Narayanaswamy Balakrishnan, 2020. "Multi-criteria-based optimal life-testing plans under hybrid censoring scheme," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 430-453, June.
    6. Xiaojun Zhu & N. Balakrishnan & Yiliang Zhou, 2020. "Exact Likelihood-Ratio Tests for a Simple Step-Stress Cumulative Exposure Model with Censored Exponential Data," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 497-509, June.
    7. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    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. Bhattacharya, Ritwik & Pradhan, Biswabrata & Dewanji, Anup, 2015. "Computation of optimum reliability acceptance sampling plans in presence of hybrid censoring," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 91-100.
    2. Suparna Basu & Sanjay K. Singh & Umesh Singh, 2019. "Estimation of Inverse Lindley Distribution Using Product of Spacings Function for Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1377-1394, December.
    3. Tanmay Sen & Yogesh Mani Tripathi & Ritwik Bhattacharya, 2018. "Statistical Inference and Optimum Life Testing Plans Under Type-II Hybrid Censoring Scheme," Annals of Data Science, Springer, vol. 5(4), pages 679-708, December.
    4. Xiaojun Zhu & N. Balakrishnan & Helton Saulo, 2019. "On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 759-778, October.
    5. Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    6. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2015. "Estimation for mixed exponential distributions under type-II progressively hybrid censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 85-96.
    7. Xiaojun Zhu & Narayanaswamy Balakrishnan & Hon-Yiu So, 2022. "Exact One- and Two-Sample Likelihood Ratio Tests based on Time-Constrained Life-Tests from Exponential Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2009-2028, September.
    8. Xun Xiao & Amitava Mukherjee & Min Xie, 2016. "Estimation procedures for grouped data – a comparative study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2110-2130, August.
    9. López-Fidalgo, J. & Rivas-López, M.J., 2014. "Optimal experimental designs for partial likelihood information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 859-867.
    10. Tzong-Ru Tsai & Yuhlong Lio & Wei-Chen Ting, 2021. "EM Algorithm for Mixture Distributions Model with Type-I Hybrid Censoring Scheme," Mathematics, MDPI, vol. 9(19), pages 1-18, October.
    11. Tanmay Sen & Ritwik Bhattacharya & Biswabrata Pradhan & Yogesh Mani Tripathi, 2020. "Determination of Bayesian optimal warranty length under Type-II unified hybrid censoring scheme," Papers 2004.08533, arXiv.org.
    12. Soumya Roy & Biswabrata Pradhan, 2023. "Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 208-232, May.
    13. Kapil Kumar & Shrawan Kumar & Renu Garg & Indrajeet Kumar, 2024. "Reliability estimation for inverse Pareto lifetime model based on unified hybrid censored data," 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. 15(6), pages 2473-2482, June.
    14. Jimut Bahan Chakrabarty & Shovan Chowdhury & Soumya Roy, 2019. "Optimum life test plan for products sold under warranty having Type-I generalizedhybrid censored Weibull distributed lifetimes," Working papers 302, Indian Institute of Management Kozhikode.
    15. Farha Sultana & Yogesh Mani Tripathi & Shuo-Jye Wu & Tanmay Sen, 2022. "Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 9(6), pages 1283-1307, December.
    16. Zhang, Fode & Shi, Yimin, 2016. "Geometry of exponential family with competing risks and censored data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 234-245.
    17. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    18. Julian Górny & Erhard Cramer, 2018. "Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 173-210, February.
    19. Narayanaswamy Balakrishnan & Ritwik Bhattacharya, 2022. "Revisiting Best Linear Unbiased Estimation of Location-Scale Parameters Based on Optimally Selected Order Statistics Using Compound Design," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1891-1915, September.
    20. Ruhul Ali Khan & Murari Mitra, 2021. "Estimation issues in the Exponential–Logarithmic model under hybrid censoring," Statistical Papers, Springer, vol. 62(1), pages 419-450, February.

    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:bpj:jossai:v:9:y:2021:i:5:p:533-548:n:5. 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 Golla (email available below). General contact details of provider: https://www.degruyter.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.