A novel two-sample joint unified hybrid censoring scheme with the application of insulating fluid data

In life testing tests, various censoring schemes are employed, primarily Type-I and Type-II censoring schemes and their modified forms. In life testing experiments, most tests are based on a single sample. When conducting comparative life tests of products from different production lines within the same facility, a joint censoring scheme is quite useful. In this article, a novel joint unified hybrid censoring scheme has been proposed for two sample populations. Based on the assumption that the lifetime distributions of the two populations follow a Weibull distribution, we provide the maximum likelihood estimators of the unknown parameters. The asymptotic confidence intervals for the parameters have been constructed using the observed Fisher information matrix. Further, the Bayes estimates have been derived using informative gamma priors under symmetric and asymmetric loss functions. The Markov chain Monte Carlo method has been employed to obtain the Bayes estimates. The results indicated that the Bayes estimates outperform the other estimators in a very satisfactory manner. A comparison of expected test time is done with another censoring scheme, where the proposed joint censoring scheme performs well. Finally, a real-life data set has been analyzed to demonstrate the utility of the presented techniques in investigating such phenomena.