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Estimation and testing procedures for the reliability characteristics of Kumaraswamy-G distributions based on the progressively first failure censored samples

Author

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  • Ajit Chaturvedi

    (University of Delhi)

  • Renu Garg

    (University of Delhi)

  • Shubham Saini

    (University of Delhi)

Abstract

This paper deals with the classical estimation of the mission time reliability $$R(t)=P(X>t)$$ R ( t ) = P ( X > t ) and stress–strength reliability $$\delta =P(X>Y)$$ δ = P ( X > Y ) for Kumaraswamy-G distributions using progressively first failure censored data. It is assumed that the stress and strength variables follow independent Kumaraswamy-G distributions. The uniformly minimum variance unbiased and maximum likelihood estimators of the parameters, reliability functions R(t) and $$\delta$$ δ are developed. The asymptotic confidence intervals and hypothesis testing for the parameters and $$\delta$$ δ are obtained. A simulation study to evaluate the performance of the developed estimators is performed. Finally, a couple of real data examples is analyzed for illustrative purposes.

Suggested Citation

  • Ajit Chaturvedi & Renu Garg & Shubham Saini, 2022. "Estimation and testing procedures for the reliability characteristics of Kumaraswamy-G distributions based on the progressively first failure censored samples," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 494-517, June.
    • Handle: RePEc:spr:opsear:v:59:y:2022:i:2:d:10.1007_s12597-021-00523-7
    DOI: 10.1007/s12597-021-00523-7
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    References listed on IDEAS

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    1. Ajit Chaturvedi & Narendra Kumar & Kapil Kumar, 2018. "Statistical Inference for the Reliability Functions of a Family of Lifetime Distributions based on Progressive Type II Right Censoring," Statistica, Department of Statistics, University of Bologna, vol. 78(1), pages 81-101.
    2. D. K. Al-Mutairi & M. E. Ghitany & Debasis Kundu, 2015. "Inferences on Stress-Strength Reliability from Weighted Lindley Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(19), pages 4096-4113, October.
    3. Y. L. Lio & Tzong-Ru Tsai, 2012. "Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 309-322, April.
    4. Wu, Shuo-Jye & Kus, Coskun, 2009. "On estimation based on progressive first-failure-censored sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3659-3670, August.
    5. Syamsundar, A. & Naikan, V.N.A. & Wu, Shaomin, 2020. "Alternative scales in reliability models for a repairable system," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
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    Cited by:

    1. Ashish Kumar Shukla & Sakshi Soni & Kapil Kumar, 2023. "An inferential analysis for the Weibull-G family of distributions under progressively censored data," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1488-1524, September.

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