Estimations in a Constant‐Stress Partially Accelerated Life Test for Generalized Rayleigh Distribution under Type‐II Hybrid Censoring Scheme

Abstract

The constant-stress partially accelerated life test (CSPALT) model with Type-II hybrid censoring scheme (Type-II HCS) is the subject of our research. Units have a lifetime that follows the generalized Rayleigh distribution. Bayesian and E-Bayesian estimates are derived by applying two of the loss functions, mainly the squared error loss (SEL) and LINEX loss functions. Bayesian and E-Bayesian estimates are obtained using Markov chain Monte Carlo (MCMC) methods. To prove the applicability and the importance of the subject, a test for real data will be provided. To evaluate the distribution’s effectiveness, we utilized a variety of datasets and proposed several kinds of censoring. Finally, all results are compared in order to determine the effectiveness of the proposed methods. All major findings are concluded in the conclusion section.

Reliability analysis of bathtub-shaped distribution using empirical Bayesian and E-Bayesian estimations under progressive Type-II censoring

“…By substituting l =À ln R t e t u À1 into the function (8), the variable substitution method is applied to the function (8) to obtain the posterior pdf of R t as…”

“…Based on the variable substitution method, we substitute l = h t ut uÀ1 e t u into function (8), then obtain the posterior density function of h t as…”

“…The hyperparameters a 1 and b 1 are unknown constants in (8), so the Bayesian estimates of l, named by lBE cannot be estimated directly. Then the maximum likelihood method is used to estimate the hyperparameters.…”

“…7 Under the LINEX and squared error loss (SEL) functions, the constant stress partially accelerated life test was proposed with Type-II hybrid censored data, and the Bayesian estimates and E-Bayesian estimates of generalized Rayleigh distribution were derived. 8 The theoretical properties of the empirical Bayesian and E-Bayesian estimates were constructed under the asymmetric loss functions in a Lomax distribution. 9 More research of empirical Bayesian estimation can be found.…”

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

“…Shen et al [10] applied the generalized Rayleigh distribution to real-life scenarios, using its heavy-tailed property for Reddit ads and breast cancer datasets, and compared it with other generalized Rayleigh distributions. Rabie et al [11] studied the lifetime analysis of devices following the generalized Rayleigh distribution under a type-II mixed censored scheme, obtaining Bayes estimates and E-Bayes estimates using a squared error loss function and linear loss function. It can be seen that the generalized Rayleigh distribution not only helps to expand the scope of application of the Rayleigh distribution and improve the accuracy and reliability of data analysis, but also provides theoretical support for the modeling and prediction of practical problems.…”