Bayesian and Classical Estimation of Stress-Strength Reliability for Inverse Weibull Lifetime Models

Bi, Qixuan; Gui, Wenhao

doi:10.3390/a10020071

Cited by 16 publications

(7 citation statements)

References 19 publications

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“…For an illustration of how the proposed methods will work two real data sets are analyzed. The first and second data sets, see Surles and Padgett [45], Kundu and Gupta [46], and Bi and Gui [35], are:…”

Section: Real Data Applicationmentioning

confidence: 99%

“…Extensive work has been done on the IWD; see, for example, Keller et al [26], Calabria, and Pulcini [27][28][29][30] provide an interpretation of the IWD in the context of the load strength relationship for a component. Maswadah [31,32] has fitted IWD to the flood data reported in Dumonceaux and Antle [33], for more details see, e.g., Murthy et al [34] and Bi and Gui [35]. IWD is a very flexible distribution model that approaches different distributions when its shape parameter varies.…”

Section: Introductionmentioning

confidence: 99%

“…The utility of the IWD for modeling reliability data was further discussed by researching the failure of mechanical components subject to degradation, see Keller et al [26]. The ability of IWD to model failure rates is quite common in reliability and biological studies, see Bi and Gui [35] and Li and Hao [39]. In the field of engineering sciences, several lifetime distributions are used to study stress-strength reliability models, and these models are frequently used to estimate the system reliability R, see Yadav et al [40].…”

Section: Introductionmentioning

confidence: 99%

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Reliability Estimation in Multicomponent Stress-Strength Based on Inverse Weibull Distribution

Shawky

Khan

2022

Processes

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The present study focuses on the multi-component stress-strength (MCSS) model based on inverse Weibull distribution (IWD). Both stress and strength are assumed to follow IWD with a common shape parameter. In such a system, reliability is obtained by the maximum likelihood (ML) method. The results are extracted using Monte Carlo simulation for comparing the performance of the reliability component Rs,k using different sample sizes and different combinations of the parameters (s,k). The procedure is further illustrated through a real data set to show how the proposed technique may be employed to study the strength and stress of multicomponent model.

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Section: Real Data Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reliability Estimation in Multicomponent Stress-Strength Based on Inverse Weibull Distribution

Shawky

Khan

2022

Processes

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“…Bi and Gui (2017) for the maximum likelihood estimator of R for inverse Weibull distribution under simple random sampling. Now, for getting the maximum likelihood estimator of R for inverse Weibull distribution under ranked set sampling, let X and Y be two independent strength and stress random variables that follow inverse Weibull distribution i.e.…”

Section: Point Estimator Of R=pfalse[ymentioning

confidence: 99%

Ranked set sampling on estimation of P[Y<X] for inverse Weibull distribution and its applications

Hassan

2021

IJQRM

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PurposeDistribution. The purpose of this study is to obtain the modified maximum likelihood estimator of stress–strength model using the ranked set sampling, to obtain the asymptotic and bootstrap confidence interval of P[Y < X], to compare the performance of author’s estimates with the estimates under simple random sampling and to apply author’s estimates on head and neck cancer.Design/methodology/approachThe maximum likelihood estimator of R = P[Y < X], where X and Y are two independent inverse Weibull random variables common shape parameter that affect the shape of the distribution, and different scale parameters that have an effect on the distribution dispersion are given under ranked set sampling. Together with the asymptotic and bootstrap confidence interval, Monte Carlo simulation shows that this estimator performs better than the estimator under simple random sampling. Also, the asymptotic and bootstrap confidence interval under ranked set sampling is better than these interval estimators under simple random sampling. The application to head and neck cancer disease data shows that the estimator of R = P[Y < X] that shows the treatment with radiotherapy is more efficient than the treatment with a combined radiotherapy and chemotherapy under ranked set sampling that is better than these estimators under simple random sampling.FindingsThe ranked set sampling is more effective than the simple random sampling for the inference of stress-strength model based on inverse Weibull distribution.Originality/valueThis study sheds light on the author’s estimates on head and neck cancer.

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“…Originally introduced by Birnbaum [1], the stress-strength model has since garnered significant interest from researchers in the field of reliability statistics. Bi et al [2] studied the R estimation problem of the inverse Weibull distribution of the stress intensity. Hamad et al [3] utilized maximum likelihood estimation and the least squares method to estimate R in Lomax distributed models.…”

Section: Introductionmentioning

confidence: 99%

Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme

Dong,

Gui

2024

Mathematics

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This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter (R) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R. The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry.

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Bayesian and Classical Estimation of Stress-Strength Reliability for Inverse Weibull Lifetime Models

Cited by 16 publications

References 19 publications

Reliability Estimation in Multicomponent Stress-Strength Based on Inverse Weibull Distribution

Reliability Estimation in Multicomponent Stress-Strength Based on Inverse Weibull Distribution

Ranked set sampling on estimation of P[Y<X] for inverse Weibull distribution and its applications

Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme

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