Estimation of fixed-accuracy confidence interval of the stress-strength reliability for inverse Pareto distribution using two-stage sampling technique
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 paramet...
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Published in | Sequential analysis Vol. 43; no. 1; pp. 79 - 102 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Taylor & Francis
02.01.2024
Taylor & Francis Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0747-4946 1532-4176 |
DOI: | 10.1080/07474946.2023.2288129 |