Applications of Marshall–Olkin Fréchet Distribution

Abstract

In this article, we consider the applications of Marshall–Olkin Fréchet distribution. The reliability of a system when both stress and strength follows the new distribution is discussed and related characteristics are computed for simulated data. The model is applied to a real data set on failure times of air-conditioning systems in jet planes and reliability is estimated. We also develop acceptance sampling plan for the acceptance of a lot whose lifetime follows this distribution. Four different autoregressive time series models of order 1 are developed with minification structure as well as max-min structure having these stationary marginal distributions. Some properties of the models are also established.

Keywords:

• Acceptance sampling plan
• Auto regressive models
• Marshall–Olkin Fréchet distribution
• Max-min process
• Stress-strength analysis
• Time series modeling

Mathematics Subject Classification:

• Primary 60E05
• Secondary 62P99

Acknowledgments

The authors would like to thank the reviewers for their valuable comments which helped to improve the article significantly. The first two authors acknowledge the financial support from U.G.C, Govt. of India towards this research. The research of the third author was supported by Grant of MNTR 174013.