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Copula models for one-shot device testing data with correlated failure modes

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  • M. H. Ling
  • P. S. Chan
  • H. K. T. Ng
  • N. Balakrishnan

Abstract

Copula models have become one of the most popular tools, especially in finance and insurance, for modeling multivariate distributions in the past few decades, and they have recently received increasing attention for data analysis in reliability engineering and survival analysis. This paper considers two Archimedean copula models — the Gumbel-Hougaard copula and Frank copula — for analyzing one-shot device data with two correlated failure modes, which are collected from constant-stress accelerated life tests. A one-shot device is a unit that cannot be used again after a test, e.g., munitions, rockets, and automobile airbags. Only either left- or right-censored data are collected instead of the actual lifetimes of the devices under test. With the aid of Kendall’s tau correlation coefficient, initial values of the dependence parameter for the copula models are presented to determine maximum likelihood estimates of model parameters through a numerical approach. Furthermore, the proposed model can be used to examine whether the correlation between times to failure modes changes over stress levels. Real data from a survival experiment are also re-analyzed to illustrate the proposed methods.

Suggested Citation

  • M. H. Ling & P. S. Chan & H. K. T. Ng & N. Balakrishnan, 2021. "Copula models for one-shot device testing data with correlated failure modes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(16), pages 3875-3888, August.
  • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:16:p:3875-3888
    DOI: 10.1080/03610926.2020.1725827
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    Cited by:

    1. Man-Ho Ling, 2022. "Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models," Mathematics, MDPI, vol. 10(5), pages 1-13, March.
    2. Deepak Prajapati & Man Ho Ling & Ping Shing Chan & Debasis Kundu, 2023. "Misspecification of copula for one-shot devices under constant stress accelerated life-tests," Journal of Risk and Reliability, , vol. 237(4), pages 725-740, August.
    3. Xiang, Shihu & Yang, Jun, 2023. "A novel adaptive deployment method for the single-target tracking of mobile wireless sensor networks," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    4. Man-Ho Ling & Narayanaswamy Balakrishnan & Chenxi Yu & Hon Yiu So, 2021. "Inference for One-Shot Devices with Dependent k -Out-of- M Structured Components under Gamma Frailty," Mathematics, MDPI, vol. 9(23), pages 1-24, November.
    5. Zhu, Xiaojun & Balakrishnan, N., 2022. "One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications," Reliability Engineering and System Safety, Elsevier, vol. 221(C).

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