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

Shawky, Ahmed; Khan, Khushnoor

doi:10.3390/pr10020226

Cited by 10 publications

(4 citation statements)

References 36 publications

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“…T , then X follows the IWD with PDF, cumulative distribution function (CDF), and HF given by Eqs 3, 4 and 5 respectively. Many studies have considered the IWD under progressive censoring, see for example [5] estimated the unknown parameters of the three-parameter IWD and as a result obtained a theorem on the existence of the least squares estimates, [6] considered statistical inferences about the unknown parameters of the IWD based on progressively type-II censoring using the maximum likelihood, least squares estimators, and the approximate maximum likelihood estimators as well as the Bayes estimators using Lindley's approximation method and symmetric and asymmetric loss functions, and for recent references, see [7][8][9].…”

Section: Plos Onementioning

confidence: 99%

Estimation of the stress-strength reliability for the inverse Weibull distribution under adaptive type-II progressive hybrid censoring

Alslman

Helu

2022

PLoS ONE

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In this article, we compare the maximum likelihood estimate (MLE) and the maximum product of spacing estimate (MPSE) of a stress-strength reliability model, θ = P(Y < X), under adaptive progressive type-II progressive hybrid censoring, when X and Y are independent random variables taken from the inverse Weibull distribution (IWD) with the same shape parameter and different scale parameters. The performance of both estimators is compared, through a comprehensive computer simulation based on two criteria, namely bias and mean squared error (MSE). To demonstrate the effectiveness of our proposed methods, we used two examples of real-life data based on Breakdown Times of an Insulated Fluid by (Nelson, 2003) and Head and Neck Cancer Data by (Efron, 1988). It is concluded that the MPSE method outperformed the MLE method in terms of bias and MSE values.

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Section: Plos Onementioning

confidence: 99%

Estimation of the stress-strength reliability for the inverse Weibull distribution under adaptive type-II progressive hybrid censoring

Alslman

Helu

2022

PLoS ONE

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“…The work by Rao et al [16] was based on complete random samples from Burr XII distributions. The work by Shawky and Khan [17] was based on random samples from inverse Weibull distributions. The work by Lio et al [18] was based on type II sample of strength and complete random sample of stress Burr XII distributions.…”

Section: Introductionmentioning

confidence: 99%

The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution

Lio,

Chen,

Tsai

et al. 2024

AppliedMath

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The reliability of the multicomponent stress–strength system was investigated under the two-parameter Burr X distribution model. Based on the structure of the system, the type II censored sample of strength and random sample of stress were obtained for the study. The maximum likelihood estimators were established by utilizing the type II censored Burr X distributed strength and complete random stress data sets collected from the multicomponent system. Two related approximate confidence intervals were achieved by utilizing the delta method under the asymptotic normal distribution theory and parametric bootstrap procedure. Meanwhile, point and confidence interval estimators based on alternative generalized pivotal quantities were derived. Furthermore, a likelihood ratio test to infer the equality of both scalar parameters is provided. Finally, a practical example is provided for illustration.

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“…Jana and Bera [15] discussed multicomponent stress-strength reliability based on IW distribution. Shawky and Khan [16] obtained reliability estimation in multicomponent stress-strength based on IW distribution. Okasha and Nassar [17] studied the product of spacing estimation of entropy for IW distribution under progressive type-II censored data.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy vs. Traditional Reliability Model for Inverse Weibull Distribution

Hussam

Sabry

El‐Raouf

et al. 2023

Axioms

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In this paper, fuzzy stress strengths RF=P(Y≺X) and traditional stress strengths R=P(Y<X) are considered and compared when X and Y are independently inverse Weibull random variables. When axiomatic fuzzy set theory is taken into account in the stress–strength inference, it enables the generation of more precise studies on the underlying systems. We discuss estimating both conventional and fuzzy models of stress strength utilizing a maximum product of spacing, maximum likelihood, and Bayesian approaches. Simulations based on the Markov Chain Monte Carlo method are used to produce various estimators of conventional and fuzzy dependability of stress strength for the inverse Weibull model. To generate both conventional and fuzzy models of dependability, we use the Metropolis–Hastings method while performing Bayesian estimation. In conclusion, we will examine a scenario taken from actual life and apply a real-world data application to validate the accuracy of the provided estimators.

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

Cited by 10 publications

References 36 publications

Estimation of the stress-strength reliability for the inverse Weibull distribution under adaptive type-II progressive hybrid censoring

Estimation of the stress-strength reliability for the inverse Weibull distribution under adaptive type-II progressive hybrid censoring

The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution

Fuzzy vs. Traditional Reliability Model for Inverse Weibull Distribution

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