In survival, reliability and medical studies, it is natural to have experience with several situations pertaining to testing, cost or money constraints where the removal of units prior to failure is preplanned. In this context, we consider the inference problem including estimation and prediction for power Lindley distribution under the progressively type-II censored sample data. For the estimation purposes and other reliability characteristics maximum likelihood and Bayes approaches for estimating the model parameters are considered in this paper. Confidence intervals of the parameters and the corresponding average lengths and coverage probabilities are developed based on maximum likelihood and Bayes techniques. The Gibbs and Metropolis samplers are used to predict the life lengths of the removed units in multiple stages of the progressively censored sample. Monte Carlo simulations are performed to compare different methods and one real data set is analyzed for illustrative purposes.
