Design of Generalized Hybrid Censoring Schemes with an Application to Likelihood Prediction: Accepted January 2026

A general approach to the design of hybrid censoring schemes is proposed. It is shown that the hybrid censoring schemes discussed in the literature fit into this scheme. Assuming generalized order statistics as the underlying sample, a representation of the joint density of hybrid censored generalized order statistics is obtained which yields a simple expression for the predictive likelihood function. As an application of the approach, we consider maximum likelihood prediction and maximum observed likelihood prediction. The results are illustrated for exponential and Weibull distributed lifetimes as well as for order statistics, record data/minimal repair data, progressively Type-II censored data, and generalized order statistics, respectively.