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Estimation of multicomponent system reliability for inverse Weibull distribution using survival signature

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  • Nabakumar Jana

    (Indian Institute of Technology (ISM) Dhanbad)

  • Samadrita Bera

    (Indian Institute of Technology (ISM) Dhanbad)

Abstract

The problem of estimating multicomponent stress-strength reliability $$R_{k,n}$$ R k , n for two-parameter inverse Weibull distributions under progressive type-II censoring is considered. We derive maximum likelihood estimator, Bayes estimator and generalised confidence interval of $$R_{k,n}$$ R k , n when all parameters are unknown. We study the reliability of stress-strength system with multiple types of components using signature-based approach. When different types of random stresses are acting on a compound system, we derive MLE, maximum spacing estimator of multi-state reliability. Using generalized pivotal quantity, the generalized confidence interval and percentile bootstrap intervals of the reliability are derived. Under a common stress subjected to the system, we also derive the estimators of the reliability parameter. Different point estimators and generalized, bootstrap confidence intervals of the reliability are developed. Risk comparison of the classical and Bayes estimators is carried out using Monte-Carlo simulation. Application of the proposed estimators is shown using real-life data sets.

Suggested Citation

  • Nabakumar Jana & Samadrita Bera, 2024. "Estimation of multicomponent system reliability for inverse Weibull distribution using survival signature," Statistical Papers, Springer, vol. 65(8), pages 5077-5108, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01588-4
    DOI: 10.1007/s00362-024-01588-4
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    References listed on IDEAS

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    1. Nabakumar Jana & Somesh Kumar & Kashinath Chatterjee, 2016. "Bayes estimation for exponential distributions with common location parameter and applications to multi-state reliability models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2697-2712, November.
    2. M. S. Kotb & M. Z. Raqab, 2021. "Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution," Statistical Papers, Springer, vol. 62(6), pages 2763-2797, December.
    3. Subhash Kochar & Hari Mukerjee & Francisco J. Samaniego, 1999. "The “signature” of a coherent system and its application to comparisons among systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 507-523, August.
    4. Jana, Nabakumar & Bera, Samadrita, 2022. "Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 95-119.
    5. Keming Yu & Bing Wang & Valentin Patilea, 2013. "New estimating equation approaches with application in lifetime data analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 589-615, June.
    6. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, April.
    7. Louis J. M. Aslett & Frank P. A. Coolen & Simon P. Wilson, 2015. "Bayesian Inference for Reliability of Systems and Networks Using the Survival Signature," Risk Analysis, John Wiley & Sons, vol. 35(9), pages 1640-1651, September.
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