Expected values of the number of failures for two populations under joint Type-II progressive censoring

The model in which joint Type-II progressive censoring is implemented on two samples from different populations in a combined manner is considered and the probabilities of failures are discussed. This model may have relevance for practical applications, when an experimenter need to know the expected values of the number of failures for each population. This knowledge plays an important role in the selection of appropriate sampling plans and the construction of efficient estimators for parameters. The formula allowing numerical computation of the expected value of the number of failures for each of the two populations is given. Also, a detailed numerical study of this expected value is carried out for different parametric families of distributions.