Interval estimators for reliability: the bivariate normal case

Abstract

This paper proposes procedures to provide confidence intervals (CIs) for reliability in stress–strength models, considering the particular case of a bivariate normal set-up. The suggested CIs are obtained by employing either asymptotic variances of maximum-likelihood estimators or a bootstrap procedure. The coverage and the accuracy of these intervals are empirically checked through a simulation study and compared with those of another proposal in the literature. An application to real data is provided.

Keywords:

• approximate estimators
• Monte Carlo simulations
• parametric bootstrap
• stress–strength models
• variance estimation

Acknowledgements

The author thanks the Editor and two anonymous referees for their helpful comments and suggestions and wishes to dedicate this work to the memory of his dear grandparents Lidia and Paolino.