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

Abstract

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.

Adaptive Type-II Hybrid Progressive Censoring Samples for Statistical Inference of Comparative Inverse Weibull Distributions

“…The data and the corresponding joint sample are presented in Table 5. The problem of fitting the data with respect to IWD was discussed by Alslman and Amal [29]. The estimate PDF of two data points is described in Figures 3 and 4, see [29] Hence, we considered the IWD as a good fit for both data samples.…”

“…The problem of fitting the data with respect to IWD was discussed by Alslman and Amal [29]. The estimate PDF of two data points is described in Figures 3 and 4, see [29] Hence, we considered the IWD as a good fit for both data samples. From the joint sample, we generated the joint adaptive type-II PHCS under censoring scheme τ = 10 and R ={1, 1, 1, 2, 1, 0, 0, 2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0}.…”

Weibull analysis of ceramics and related materials: A review

“…The symmetry settings are not fulfilled for the maximum likelihood (ML) estimate of the three-parameter Weibull distribution since the backing of the PDF rests on the unidentified parameter once the threshold parameter is not known. The ML estimators may not be available at that point, and even if they are, they may not have the standard asymptotic properties [ [216] , [217] , [218] , [219] , [220] , [221] ]. Arising from this, several different procedures have been sought after in the literature.…”

A New Cubic Transmuted Inverse Weibull Distribution: Theory and Applications

“…Recently some researchers have also conducted some other research using the IW distribution. These include Alslman and Helu (2022)…”