The likelihood function based on uncensored/censored statistical data for Min-PSD(Max-PSD) and Max-PSD(Min-PSD) as lifetime distributions in network reliability

Abstract

In our paper general formulas for the likelihood function are derived in the case when uncensored/censored statistical data refer to the lifetime of serial-parallel and parallel-serial type networks when the lifetimes of the system units are independent, identically distributed random variables and the number of subsystems and the number of units in each subsystem are random variables with power series type distribution. The formulas can be applied to obtain maximum likelihood estimators for the parameters of the lifetime distribution of the mentioned networks. The results are illustrated by examples of concrete probabilistic models.