Estimation ofP(Y&lt;X) for Weibull Distribution Under Progressive Type-II Censoring

Valiollahi, Reza; Asgharzadeh, A.; Raqab, Mohammad Z.

doi:10.1080/03610926.2011.650265

Cited by 42 publications

(11 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many authors investigated the estimation of R = P(Y < X) when X and Y are independent Weibull random variables, see for example [3,7,[16][17][18], and see the references cited therein. These studies considered the maximum likelihood as a frequentist method as well as the Bayesian estimation method.…”

Section: Introductionmentioning

confidence: 99%

On estimation procedures of stress-strength reliability for Weibull distribution with application

2020

View full text Add to dashboard Cite

For the first time, ten frequentist estimation methods are considered on stress-strength reliability R = P(Y < X) when X and Y are two independent Weibull distributions with the same shape parameter. The start point to estimate the parameter R is the maximum likelihood method. Other than the maximum likelihood method, a nine frequentist estimation methods are used to estimate R, namely: least square, weighted least square, percentile, maximum product of spacing, minimum spacing absolute distance, minimum spacing absolute-log distance, method of Cramé r-von Mises, Anderson-Darling and Right-tail Anderson-Darling. We also consider two parametric bootstrap confidence intervals of R. We compare the efficiency of the different proposed estimators by conducting an extensive Mont Carlo simulation study. The performance and the finite sample properties of the different estimators are compared in terms of relative biases and relative mean squared errors. The Mont Carlo simulation study revels that the percentile and maximum product of spacing methods are highly competitive with the other methods for small and large sample sizes. To show the applicability and the importance of the proposed estimators, we analyze one real data set.

show abstract

Section: Introductionmentioning

confidence: 99%

On estimation procedures of stress-strength reliability for Weibull distribution with application

2020

View full text Add to dashboard Cite

show abstract

“…Abdel-Hamid and Al-Hussaini [3] provided a progressive stress-accelerated life test model based on a progressive Type-II sample from a Weibull distribution through graphical and maximum likelihood methods of estimations. Valiollahi et al [4] studied the estimation of the stress strength reliability that represents the system stress less than its strength when the system stress and its strength are independent Weibull random variables under the progressive Type-II censoring scheme. However, these approaches suffer a disadvantage in that the shape parameter must be numerically estimated, despite its importance.…”

Section: Introductionmentioning

confidence: 99%

New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme

2020

View full text Add to dashboard Cite

This paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood estimator counterpart. To resolve serious rounding errors for the exact mean and variance of the pivotal quantity, two different types of Taylor series expansion are applied, and the resulting performance is enhanced in terms of the mean square error and bias obtained through the Monte Carlo simulation. Finally, an actual application example, including a simple goodness-of-fit analysis of the actual test data based on the pivotal quantity, proves the feasibility and applicability of the proposed approach.

show abstract

“…It is worth mentioning that some of the studies have been carried out about the estimation of stress-strength reliability for some distributions under progressively type II censoring. For example, the estimation of R in exponential distributions under censored data has been investigated by Saraoglua et al [41], and the stress-strength reliability of Weibull and inverse Weibull distributions has been studied under progressively censored data by Valiollahi et al [49] and Yadav et al [52], respectively. In another study carried out by Shoaee and Khorram [43], the estimation of the stress-strength reliability R = P(Y < X) was considered based on progressively type II censored samples when X and Y were two independent twoparameter bathtub-shaped lifetime distributions.…”

Section: Introductionmentioning

confidence: 99%

Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data

Rostamian

Nematollahi

2019

Math Sci

View full text Add to dashboard Cite

The stress-strength parameter R = P(Y < X) , as a reliability parameter, is considered in different statistical distributions. In the present paper, the stress-strength reliability is estimated based on progressively type II censored samples, in which X and Y are two independent random variables with inverse Gaussian distributions. The maximum likelihood estimate of R via expectation-maximization algorithm and the Bayes estimate of R are obtained. Furthermore, we obtain the bootstrap confidence intervals, HPD credible interval and confidence intervals based on generalized pivotal quantity for R. Additionally, the performance of point estimators and confidence intervals are evaluated by a simulation study. Finally, the proposed methods are conducted on a set of real data for illustrative purposes.

show abstract

Estimation ofP(Y<X) for Weibull Distribution Under Progressive Type-II Censoring

Cited by 42 publications

References 26 publications

On estimation procedures of stress-strength reliability for Weibull distribution with application

On estimation procedures of stress-strength reliability for Weibull distribution with application

New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme

Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data

Contact Info

Product

Resources

About