Estimation the parameters of the life of the new XLindley distribution under accelerated adaptive type-II progressively hybrid censored data with applications

In this paper, a parameter and corresponding lifetime parameters of the New X-Lindley distribution (NX-LD) are estimated. Collecting complete lifetime data from a population using highly reliable items is costly and time-consuming. An adaptive Type-II progressively hybrid censoring scheme under a constant-stress accelerated life test (ALT) is used to balance the optimal test time and the number of failed items. Under the constant-stress ALT model, a variety of statistical methods are developed to estimate the parameters of the lifetime distribution. These methods include maximum-likelihood and Bayesian point estimates. Asymptotic maximum-likelihood, bootstrap confidence intervals, and equal two-sided credible intervals are also formulated. These methods aim to obtain efficient estimators for the distribution parameter, acceleration factor, and reliability and failure rate indices. The estimators are assessed in terms of mean squared error, coverage percentage, and interval length through a Monte Carlo simulation study. The usefulness of the accelerated adaptive censoring scheme is demonstrated with a real-life application in the field of engineering, the voltage and failure time data, as well as a simulated data example to illustrate its practicality.