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Optimal sequential Bayesian analysis for degradation tests

Author

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  • Silvia Rodríguez-Narciso

    (Universidad Autónoma de Aguascalientes)

  • J. Andrés Christen

    (Centro de Investigación en Matemáticas)

Abstract

Degradation tests are especially difficult to conduct for items with high reliability. Test costs, caused mainly by prolonged item duration and item destruction costs, establish the necessity of sequential degradation test designs. We propose a methodology that sequentially selects the optimal observation times to measure the degradation, using a convenient rule that maximizes the inference precision and minimizes test costs. In particular our objective is to estimate a quantile of the time to failure distribution, where the degradation process is modelled as a linear model using Bayesian inference. The proposed sequential analysis is based on an index that measures the expected discrepancy between the estimated quantile and its corresponding prediction, using Monte Carlo methods. The procedure was successfully implemented for simulated and real data.

Suggested Citation

  • Silvia Rodríguez-Narciso & J. Andrés Christen, 2016. "Optimal sequential Bayesian analysis for degradation tests," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 405-428, July.
    • Handle: RePEc:spr:lifeda:v:22:y:2016:i:3:d:10.1007_s10985-015-9339-7
    DOI: 10.1007/s10985-015-9339-7
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    References listed on IDEAS

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    1. Leamer, Edward E, 1973. "Multicollinearity: A Bayesian Interpretation," The Review of Economics and Statistics, MIT Press, vol. 55(3), pages 371-380, August.
    2. Santanu Chakraborty & Nagi Gebraeel & Mark Lawley & Hong Wan, 2009. "Residual-life estimation for components with non-symmetric priors," IISE Transactions, Taylor & Francis Journals, vol. 41(4), pages 372-387.
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    Cited by:

    1. Ensiyeh Nezakati & Mostafa Razmkhah & Firoozeh Haghighi, 2019. "Reliability analysis of a k-out-of-n:F system under a linear degradation model with calibrations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 537-552, June.
    2. Saberzadeh, Zahra & Razmkhah, Mostafa, 2022. "Reliability of degrading complex systems with two dependent components per element," Reliability Engineering and System Safety, Elsevier, vol. 222(C).

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