Simple exact methods to find confidence intervals for bivariate normal stress-strength reliability

Gboyega David Adepoju; Md Mahadi Hasan; Kalimuthu Krishnamoorthy

Simple exact methods to find confidence intervals for bivariate normal stress-strength reliability

Gboyega David Adepoju
, Md Mahadi Hasan
, Kalimuthu Krishnamoorthy

Research output: Contribution to journal › Article › peer-review

Abstract

We first show that the problems of estimating stress-strength reliability in a bivariate normal distribution and estimating coefficient of variation for a normal distribution are equivalent. On the basis of this result, we propose a simple exact method of computing confidence intervals (CIs) for the reliability
R=P(X1>X2), where the random vector (X1,X2) has a bivariate normal distribution. A simple closed-form approximate CI for R, which are as good as the exact one, is also proposed.

Original language	American English
Pages (from-to)	389-397
Journal	Communications in Statistics Case Studies and Data Analysis and Applications
State	Published - Jul 2025
Externally published	Yes

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Keywords

coverage probability
exact CI
fiducial inference
tolerance limits
precision

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https://doi.org/10.1080/23737484.2025.2531897

Cite this

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title = "Simple exact methods to find confidence intervals for bivariate normal stress-strength reliability",

abstract = "We first show that the problems of estimating stress-strength reliability in a bivariate normal distribution and estimating coefficient of variation for a normal distribution are equivalent. On the basis of this result, we propose a simple exact method of computing confidence intervals (CIs) for the reliability R=P(X1>X2), where the random vector (X1,X2) has a bivariate normal distribution. A simple closed-form approximate CI for R, which are as good as the exact one, is also proposed.",

keywords = "coverage probability, exact CI, fiducial inference, tolerance limits, precision",

author = "Adepoju, \{Gboyega David\} and Hasan, \{Md Mahadi\} and Kalimuthu Krishnamoorthy",

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journal = "Communications in Statistics Case Studies and Data Analysis and Applications",

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T1 - Simple exact methods to find confidence intervals for bivariate normal stress-strength reliability

AU - Adepoju, Gboyega David

AU - Hasan, Md Mahadi

AU - Krishnamoorthy, Kalimuthu

PY - 2025/7

Y1 - 2025/7

N2 - We first show that the problems of estimating stress-strength reliability in a bivariate normal distribution and estimating coefficient of variation for a normal distribution are equivalent. On the basis of this result, we propose a simple exact method of computing confidence intervals (CIs) for the reliability R=P(X1>X2), where the random vector (X1,X2) has a bivariate normal distribution. A simple closed-form approximate CI for R, which are as good as the exact one, is also proposed.

AB - We first show that the problems of estimating stress-strength reliability in a bivariate normal distribution and estimating coefficient of variation for a normal distribution are equivalent. On the basis of this result, we propose a simple exact method of computing confidence intervals (CIs) for the reliability R=P(X1>X2), where the random vector (X1,X2) has a bivariate normal distribution. A simple closed-form approximate CI for R, which are as good as the exact one, is also proposed.

KW - coverage probability

KW - exact CI

KW - fiducial inference

KW - tolerance limits

KW - precision

M3 - Article

SP - 389

EP - 397

JO - Communications in Statistics Case Studies and Data Analysis and Applications

JF - Communications in Statistics Case Studies and Data Analysis and Applications

ER -

Simple exact methods to find confidence intervals for bivariate normal stress-strength reliability

Abstract

Funding

Keywords

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