This analysis derives likelihood functions using uncensored and censored data for lifetime distributions, indicating potential maximum likelihood estimators.
In this paper general formulas for the likelihood function have been 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, 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.
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Leahu et al. (2025) studied this question.
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