Estimation of fixed-accuracy confidence interval of the stress–strength reliability for inverse Pareto distribution using two-stage sampling technique

Abstract

In recent years, several probability distributions have been introduced in the literature to analyze the data exhibiting an upside-down bathtub–shaped failure rate; an inverse Pareto distribution (IPD) is an appropriate choice among them. For stress–strength reliability models, estimation of parameters is an interesting area of research. In this article, we estimate the stress–strength reliability parameter $R=P(X>Y)$ (where X and Y are strength and stress variables, respectively) of the IPD, whereby we focus on the problem of fixed-accuracy confidence interval estimation of R. It is established that the proposed interval estimation problem cannot be solved with the help of any fixed sample technique. As a result, we propose a two-stage sequential sampling strategy (which reduces the sample size significantly) to solve the given estimation problem. We obtain the expressions of several exact operating characteristics associated with our two-stage sampling technique. We also establish that the proposed two-stage procedure enjoys interesting first-order asymptotic properties. The detailed simulation analyses support our theoretical findings, and two real data sets based on insurance claims reinforce the practical utility of the proposed technique.

Keywords:

• Asymptotic consistency
• asymptotic efficiency
• exact distributions
• fixed accuracy
• insurance claims
• interval estimation
• inverse Pareto distribution
• stress–strength reliability
• two-stage sampling

Subject Classifications:

• 62F12
• 62L12
• 62L15
• 62P05
• 62P30

ACKNOWLEDGMENTS

We thank the Editor-in-Chief Professor Nitis Mukhopadhyay, an Associate Editor, and two anonymous reviewers for meticulously reading the original manuscript. Their comments and suggestions led to this revised and significantly improved version.

DISCLOSURE

The authors have no conflict of interests to declare.