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Inference for One-Shot Devices with Dependent k -Out-of- M Structured Components under Gamma Frailty

Author

Listed:
  • Man-Ho Ling

    (Department of Mathematics and Information Technology, The Education University of Hong Kong, Tai Po, Hong Kong, China
    These authors contributed equally to this work.)

  • Narayanaswamy Balakrishnan

    (Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
    These authors contributed equally to this work.)

  • Chenxi Yu

    (Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
    These authors contributed equally to this work.)

  • Hon Yiu So

    (Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
    These authors contributed equally to this work.)

Abstract

A device that performs its intended function only once is referred to as a one-shot device. Actual lifetimes of such kind of devices under test cannot be observed, and they are either left-censored or right-censored. In addition, one-shot devices often consist of multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. In this paper, we develop an efficient expectation–maximization algorithm for determining the maximum likelihood estimates of model parameters, on the basis of one-shot device test data with multiple failure modes under a constant-stress accelerated life-test, with the dependent components having exponential lifetime distributions under gamma frailty that facilitates an easily understandable interpretation. The maximum likelihood estimate and confidence intervals for the mean lifetime of k -out-of- M structured one-shot device under normal operating conditions are also discussed. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations. Three examples including Class-H failure modes data, mice data from ED01 experiment, and simulated data with four failure modes are used to illustrate the proposed inferential methods.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3032-:d:688563
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    References listed on IDEAS

    as
    1. Ling, Xiaoliang & Wei, Yinzhao & Si, Shubin, 2019. "Reliability optimization of k-out-of-n system with random selection of allocative components," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 186-193.
    2. Cheng, Yao & Elsayed, Elsayed A., 2017. "Reliability modeling of mixtures of one-shot units under thermal cyclic stresses," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 58-66.
    3. David D. Hanagal & Arvind Pandey, 2016. "Gamma shared frailty model based on reversed hazard rate," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(7), pages 2071-2088, April.
    4. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    5. Cheng, Yao & Elsayed, Elsayed A., 2018. "Reliability modeling and optimization of operational use of one-shot units," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 27-36.
    6. Newby, Martin, 2008. "Monitoring and maintenance of spares and one shot devices," Reliability Engineering and System Safety, Elsevier, vol. 93(4), pages 588-594.
    7. Sheng-Tsaing Tseng & Nan-Jung Hsu & Yi-Chiao Lin, 2016. "Joint modeling of laboratory and field data with application to warranty prediction for highly reliable products," IISE Transactions, Taylor & Francis Journals, vol. 48(8), pages 710-719, August.
    8. Balakrishnan, N. & Ling, M.H., 2014. "Gamma lifetimes and one-shot device testing analysis," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 54-64.
    9. Jane C. Lindsey & Louise M. Ryan, 1993. "A Three‐State Multiplicative Model for Rodent Tumorigenicity Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(2), pages 283-300, June.
    10. Coit, David W. & Chatwattanasiri, Nida & Wattanapongsakorn, Naruemon & Konak, Abdullah, 2015. "Dynamic k-out-of-n system reliability with component partnership," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 82-92.
    11. Bocchetti, D. & Giorgio, M. & Guida, M. & Pulcini, G., 2009. "A competing risk model for the reliability of cylinder liners in marine Diesel engines," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1299-1307.
    12. 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.
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