Lately, a novel improved adaptive progressive censored strategy of Type-II was developed that can ensure that the experiment duration does not overextend a specific span. When a sample is formed using such censoring, three estimation issues of the model parameter and certain reliability metrics of the inverted Lindley lifetime distribution are taken into consideration. In addition to the traditional likelihood methodology, Bayesian and E-Bayesian methodologies with squared error loss are considered. The asymptotic distribution of frequentist estimates over the empirical Fisher information is employed to get the estimated confidence intervals for each parameter. A technical procedure called Monte-Carlo Markov-Chain is operated to provide the required Bayes and E-Bayes estimations as well as to construct their credible intervals. We deliver extensive empirical comparisons to explain the applicability and usefulness of the various suggested strategies. Lastly, two actual data collections gathered from the engineering and medical disciplines are analyzed to verify the offered model’s relevance and viability in the context of reality. The study findings suggest that, in order to get the required estimations, the E-Bayesian paradigm via the Metropolis-Hastings sampler is preferable in comparison to the other approaches.