A study of stress-strength reliability using a generalization of power transformed half-logistic distribution

Abstract

A new probability model obtained by generalizing the power transformed half logistic distribution is introduced by transforming the type II beta distribution. The basic properties of the distribution are studied and observed that the distribution can be used for modeling heavy tailed data. Further the expression for stress strength reliability of a single component system with strength following the proposed model and different cases for stress are obtained. Different methods of estimation of parameters – method of moments, quantile estimation, and maximum likelihood estimation are also explained. The usefulness of the model is also studied by applying it to a real-life data set.

Keywords:

• Half-logistic distribution
• generalized hypergeometric function
• stress-strength reliability
• maximum likelihood estimation

Acknowledgment

The authors are thankful to Dr A. M. Mathai for his useful insights. The first author is also thankful to Dr T. M. Jacob for his support. The authors are also thankful to the reviewers for their constructive comments and suggestions, which certainly improved the quality and presentation of the paper.