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Stress–strength reliability models on power-Muth distribution

Author

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  • Prashant Kumar Sonker

    (Banaras Hindu University)

  • Mukesh Kumar

    (Banaras Hindu University)

  • Agni Saroj

    (Banaras Hindu University)

Abstract

The power Muth distribution (PM), was first introduced by Jodra et al. (Math Model Anal 22(2):186–201, 2017) with great applicability in reliability theory. In this paper, we studied parameter estimation of PM distribution to know the changes in the behaviour of distribution by varying their parameters. Also, the reliability estimation, the stress–strength reliability (SSR) and the multi-component stress–strength reliability (MSSR) estimation are carried out. For the stress–strength model, the component strength and the stress applied to it, both are independent random variables and follow similar PM distribution. SSR describes the probability that the component strength is greater than the stress applied to it. While the MSSR works based on s-out-of-k ( $$1\le s \le k$$ 1 ≤ s ≤ k ) model which is described as the probability that at least s-out-of-k components’ strength are greater than the stress applied on it. Reliability behaviour is the major objective of this paper. For the estimation of parameters, we are inclined towards the maximum likelihood and maximum product spacing method of estimation. Based on their mean square error we compared these two. In the multi-component reliability model, the suitable trend is observed based on the number of components’ strengths exceeding the stresses applied to them. The effect of shape and scale parameters of PM distribution on various reliability models is observed. All the above statistical performances are carried out via the Monte Carlo simulation process. Real data applicability of the distribution is applied to the stress rupture life of Kevlar pressure vessel data on different used reliability models.

Suggested Citation

  • Prashant Kumar Sonker & Mukesh Kumar & Agni Saroj, 2023. "Stress–strength reliability models on power-Muth distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 173-195, March.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:1:d:10.1007_s13198-022-01832-w
    DOI: 10.1007/s13198-022-01832-w
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    References listed on IDEAS

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    1. G. Srinivasa Rao & Muhammad Aslam & Debasis Kundu, 2015. "Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 4953-4961, December.
    2. Tanmay Kayal & Yogesh Mani Tripathi & Sanku Dey & Shuo-Jye Wu, 2020. "On estimating the reliability in a multicomponent stress-strength model based on Chen distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2429-2447, May.
    3. 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.
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    5. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
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