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The Stress-Strength Models for the Proportional Hazards Family and Proportional Reverse Hazards Family

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Statistical Quality Technologies

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

Abstract

The stress-strength model has been widely used for reliability design of systems. The reliability of the model is defined as the probability that the strength is larger than the stress. This chapter considers the stress-strength model when both the stress and the strength variables follow the two-parameter proportional hazards family or the proportional reverse hazards family. These two distribution families include many commonly-used distributions, such as the Weibull distribution, the Gompertz distribution, the Kumaraswamy distribution and the generalized exponential distribution, etc. Based on complete samples and record values, we derive the maximum likelihood estimation for the these stress-strength reliability. We also present the generalized confidence intervals for these stress-strength reliability. The simulation results show that the proposed generalized confidence intervals work well.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under the contract numbers 11871431, 11671303, and First Class Discipline of Zhejiang - A (Zhejiang Gongshang University—Statistics).

Author information

Authors and Affiliations

  1. Department of Statistics, Zhejiang Gongshang University, Hangzhou, China

    Bing Xing Wang & Xiaofei Wang

  2. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China

    Pei Hua Jiang

  3. School of Mathematics and Statistics, Huangshan University, Huangshan, China

    Xiaofei Wang

Authors
  1. Bing Xing Wang
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  2. Pei Hua Jiang
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  3. Xiaofei Wang
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Corresponding author

Correspondence to Bing Xing Wang .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of South Dakota, Vermillion, SD, USA

    Yuhlong Lio

  2. Department of Statistical Science, Southern Methodist University, Dallas, TX, USA

    Hon Keung Tony Ng

  3. Department of Statistics, Tamkang University, New Taipei, Taiwan

    Tzong-Ru Tsai

  4. Department of Statistics, University of Pretoria, Pretoria, South Africa

    Ding-Geng Chen

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Wang, B.X., Jiang, P.H., Wang, X. (2019). The Stress-Strength Models for the Proportional Hazards Family and Proportional Reverse Hazards Family. In: Lio, Y., Ng, H., Tsai, TR., Chen, DG. (eds) Statistical Quality Technologies. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-20709-0_12

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