Reliability Estimation under Normal Operating Conditions for Progressively Type-II XLindley Censored Data

Abstract

This paper assumes constant-stress accelerated life tests when the lifespan of the test units follows the XLindley distribution. In addition to the maximum likelihood estimation, the Bayesian estimation of the model parameters is acquired based on progressively Type-II censored samples. The point and interval estimations of the model parameters and some reliability indices under normal operating conditions at mission time are derived using both estimation methods. Using the Markov chain Monte Carlo algorithm, the Bayes estimates are calculated using the squared error loss function. Simulating the performances of the different estimation methods is performed to illustrate the proposed methodology. As an example of how the proposed methods can be applied, we look at two real-life accelerated life test cases. According to the numerical outcomes and based on some criteria, including the root of the mean square error and interval length, we can conclude that the Bayesian estimation method based on the Markov chain Monte Carlo procedure performs better than the classical methods in evaluating the XLindley parameters and some of its reliability measures when a constant-stress accelerated life test is applied with progressively Type-II censoring.

Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings

“…Their study illustrated that datasets from chemical engineering could be effectively modeled using the XL distribution instead of traditional distributions such as gamma and Weibull distributions. Additionally, Alotaibi et al [36] delved into the estimation of constant-stress accelerated life tests (CSALT) for XL distribution based on progressive.…”

Data analysis with applications in physics and engineering using XLindley model with improved adaptive Type-II progressively censored samples

“…Alotaibi et al [2] stated the superiority of the XL distribution over some lifetime models, including Lindley, Weibull and gamma distributions. Alotaibi et al [3] considered the reliability estimation of the XL model in the case of progressively censored samples. See also the work of Nassar et al [4] .…”