Reliability inference for stress-strength model based on inverted exponential Rayleigh distribution under progressive Type-II censored data

Abstract

In this paper, stress-strength model is studied for an inverted exponential Rayleigh distribution (IERD) when the latent failure times are progressively Type-II censored. When both strength and stress random variables follow common IERD scale parameters, the maximum likelihood estimate of stress-strength reliability (SSR) is established and the associated approximate confidence interval is also constructed using the asymptotic distribution theory and delta method. By constructing pivotal quantities, another alternative generalized estimates for SSR are also proposed for comparison. Moreover, when there are arbitrary strength and stress parameters, likelihood and generalized pivotal based estimates are also presented. In addition, testing problem is gave for comparing the equality of different strength and stress parameters. Finally, simulation study and a real data example are provided for illustration.

Keywords:

• Delta method
• Generalized inference
• Inverted exponential Rayleigh distribution
• Maximum likelihood estimation
• Stress-strength model

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• Primary 62F10
• 62F15
• Secondary 62E15

Acknowledgments

The authors would like to thank the editor and the referees for their insightful comments that have led to a substantial improvement to an earlier version of the paper.

Additional information

Funding

This work of Liang Wang was supported by National Natural Science Foundation of China (No. 12061091), the Yunnan Fundamental Research Projects in Year of 2021 and the China Postdoctoral Science Foundation (No. 2019M650260). Yogesh Mani Tripathi gratefully acknowledges the partial financial support for this research work under a grant EMR/2016/001401 Science and Engineering Research Board, India.