Analysis of generalized type-II progressively hybrid Lindley-exponential data and its modeling in physics, engineering, and management

The life test is guaranteed to end at a predetermined time using a novel type-II generalized progressively hybrid censoring method that is investigated when the test participants’ lifetime model has a two-parameter Lindley-exponential (LndE) distribution. The LndE characteristics are estimated using Bayes and maximum likelihood inference techniques when the suggested censored data are present. By employing the normal approximation of each unknown quantity, the estimated confidence intervals are also constructed. Additionally, independent gamma density priors are used to generate the Bayesian estimators under symmetrical (squared error) loss. Since the likelihood function is formulated in a difficult manner, the Bayes estimators and their corresponding greatest posterior density intervals cannot be computed theoretically, but they may be evaluated using Markov-chain Monte Carlo algorithms. The most progressive design is then determined by applying four optimality criteria. Using Monte Carlo comparisons, the efficiency of the proposed estimating processes is evaluated, and some suggestions are made. In the end, the usefulness of the suggested methods that may be applied in practical situations is demonstrated by analyzing three distinct applications: physics, engineering, and management. When the experimenter’s primary concern is the test’s duration, the numerical findings revealed that the sampling strategy is adaptable and incredibly successful in finishing the experiment in a variety of realistic scenarios.