Inference for the Lindley distribution under partially accelerated life tests with adaptive progressive hybrid censoring

The purpose of this research is to examine the statistical inference for the Lindley distribution using step-stress partially accelerated life testing (SS-PALT) and an adaptive Type I progressive hybrid censoring scheme (AT-I PHCS). To improve the analysis of lifetime observations, the suggested method combines adaptive censoring processes with acceleration mechanisms. Both maximum likelihood and Bayesian approaches are used to estimate the acceleration factor and unknown distribution parameters. The asymptotic properties of the maximum likelihood estimators are derived, upon which approximate confidence intervals are built. In the Bayesian context, estimation is performed under the squared error loss function, while posterior summaries and credible intervals are obtained using Markov chain Monte Carlo (MCMC) methods. An extensive simulation study is carried out to evaluate the performance of the suggested estimators across different censoring schemes and acceleration conditions. Additionally, optimal design considerations are taken into account to determine efficient sampling plans within the SS-PALT setting. The practical relevance of the developed methodology is demonstrated through an application to real data, confirming its effectiveness in fitting lifetime data collected from accelerated experiments. Overall, the findings indicate that the combination of adaptive censoring strategies with partially accelerated life testing can lead to improved estimation accuracy and greater experimental efficiency.