Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case

Abstract

In this article, we propose some procedures to get confidence intervals for the reliability in stress-strength models. The confidence intervals are obtained either through a parametric bootstrap procedure or using asymptotic results, and are applied to the particular context of two independent normal random variables. The performance of these estimators and other known approximate estimators are empirically checked through a simulation study which considers several scenarios.

Keywords:

• Asymptotically normal
• Independent normal
• Monte Carlo simulations
• Parametric bootstrap
• Stress-strength
• Variance estimation

Mathematics Subject Classification:

• 62F12
• 62F25
• 62F40
• 62N05

Acknowledgments

The author would like to thank the referees for their helpful comments and suggestions.

The author wishes to dedicate this article to the cherished memory of his mother and to his father.