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.

The aim of this study is to investigate different methods of estimating the stress-strength reliability parameter, $\theta =P(Y<X)$, when the strength (X) and the stress (Y) are independent random variables taken from the inverse Weibull distribution (IWD), with the same shape parameter and different scale parameters. Based on Adaptive Type-II Hybrid progressive censored samples, we employ classical and Bayesian approaches. In the classical approach, we use the maximum likelihood estimator (MLE), the approximate maximum likelihood estimator (AMLE), and the least squares estimator (LSE). In contrast, the Bayesian approach utilizes symmetric and asymmetric loss functions. Due to the absence of explicit forms for Bayes estimators, we propose using Lindley's approximation method for computing the Bayes estimators. We compare these estimators using extensive simulations and two criteria: the bias and the mean square error (MSE). Finally, two real-life data examples are provided for illustrations.

Accelerated failure time (AFT) models have intensive applications in many research areas, including but not limited to behavioral, chronic (e.g., cancer), and infectious diseases (e.g., HIV) research. In this paper, we investigate the performance of the AFT models when Progressive Type-II censoring schemes are performed. We demonstrate the usefulness of using these schemes. We discuss their testing procedure power, $Bias$, and $MSE$ of the hazard ratio estimates compared to the same sample size of the uncensored data. Theoretically, we derive the models, the $MLE$ scores, and the Fisher information matrix. A comparison between these estimators is provided by using extensive simulation. A real-life data example is provided to illustrate our proposed estimators.