Estimation of stress-strength reliability for multicomponent system with a generalized inverted exponential distribution

Abstract

Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results.

Keywords:

• Bootstrap confidence interval
• generalized inverted exponential distribution
• generalized pivotal quantity
• likelihood ratio test
• maximum likelihood estimation
• multicomponent stress-strength model

Acknowledgments

The author wishes to our thank the Associate Editor and two referees for their valuable suggestions which led to the improvement of the paper.

Additional information

Funding

This work of Liang Wang was supported by the National Natural Science Foundation of China (No. 12061091) and the Yunnan Fundamental Research Projects (No. 202101AT070103). This work of Song Mao was supported by Ministry of Education of Humanities and Social Science project (18YJC910009).