Estimation of parameters of component lifetime distribution in a coherent system

We deal with estimation of parameters of lifetime distribution of components which form a coherent system. It is assumed that the system lifetime and the number of failed components up to the moment of the system failure, including the component which fails at the system failure epoch, are observed for each system.We apply the theory of optimal estimating functions and obtain optimal estimators of the parameters assuming that component lifetime has exponential and Weibull distribution. We apply Fisher’s conditionality principle and obtain properties of estimators of the system based on the conditional distribution of the system life-time, given the number of failed components in the system. Exact conditional distributions of the estimators as well as conditional consistency and asymptotic normality have been discussed for both the models. We also compare the proposed estimators with some of the existing estimators.