Estimation of stress-strength reliability from unit-Burr Ⅲ distribution under records data

Yarong Yu; Liang Wang; Sanku Dey; Jia Liu; Yarong Yu; Liang Wang; Sanku Dey; Jia Liu

doi:10.3934/mbe.2023550

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12360-12379. doi: 10.3934/mbe.2023550

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Estimation of stress-strength reliability from unit-Burr Ⅲ distribution under records data

1.
School of Mathematics, Yunnan Normal University, Kunming, China
2.
Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India

Academic Editor: Piao Chen

Received: 27 March 2023 Revised: 24 April 2023 Accepted: 09 May 2023 Published: 22 May 2023

This paper explores estimation of stress-strength reliability based on upper record values. When the strength and stress variables follow unit-Burr Ⅲ distributions, a generalized inferential approach is proposed for estimating stress-strength reliability (SSR). Under the common strength and stress parameter case, two types of pivotal quantities are constructed respectively, and then the generalized point and interval estimates for SSR are proposed in consequence, where the associated Monte-Carlo sampling approach is provided for computation. In addition, when strength and stress variables feature unequal model parameters, different generalized point and confidence interval estimates are also established in this regard. Extensive simulation studies are conducted to examine the behavior of proposed methods. Finally, a real-life data example is presented for illustration.
- stress-strength model,
- Unit-Burr Ⅲ distribution,
- pivotal quantities,
- upper records data,
- generalized estimation
Citation: Yarong Yu, Liang Wang, Sanku Dey, Jia Liu. Estimation of stress-strength reliability from unit-Burr Ⅲ distribution under records data[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12360-12379. doi: 10.3934/mbe.2023550

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Abstract

This paper explores estimation of stress-strength reliability based on upper record values. When the strength and stress variables follow unit-Burr Ⅲ distributions, a generalized inferential approach is proposed for estimating stress-strength reliability (SSR). Under the common strength and stress parameter case, two types of pivotal quantities are constructed respectively, and then the generalized point and interval estimates for SSR are proposed in consequence, where the associated Monte-Carlo sampling approach is provided for computation. In addition, when strength and stress variables feature unequal model parameters, different generalized point and confidence interval estimates are also established in this regard. Extensive simulation studies are conducted to examine the behavior of proposed methods. Finally, a real-life data example is presented for illustration.

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