On simple calculation of the Fisher information in hybrid censoring schemes

A hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes. In this paper, we present two interesting results which are useful in deriving the Fisher information along with the expected censoring times and expected numbers of failures in hybrid and generalized hybrid censoring schemes. We first interpret the Type-II censoring scheme in terms of a Type-I censoring scheme so that the censoring time in hybrid censoring schemes can be regarded as a mixture of Type-I censoring times. We then exploit this mixture form to derive the Fisher information in hybrid censored schemes. We further establish an addition rule underlying Type-I and Type-II hybrid censoring schemes and derive the Fisher information in the case of generalized hybrid censoring schemes. Finally, we present an example to illustrate the results developed here.