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

• Published in: Sequential analysis Vol. 43; no. 1; pp. 79 - 102
• Main Authors: Joshi, Neeraj, Bapat, Sudeep R., Sengupta, Raghu Nandan
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.01.2024; Taylor & Francis Ltd
• Subjects: Accuracy; Asymptotic consistency; asymptotic efficiency; Asymptotic methods; Asymptotic properties; Confidence intervals; exact distributions; Failure rates; fixed accuracy; insurance claims; interval estimation; inverse Pareto distribution; Parameters; Reliability analysis; Sampling methods; Sampling techniques; Sequential sampling; Statistical analysis; stress-strength reliability; two-stage sampling
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2023.2288129

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.