Beyond the identification of reliability for system with binary subsystems

Consider a stochastic system composed of multiple subsystems, each subsystem with binary outputs. Based on the test data from both the subsystems and the full system, the goal is to estimate the parameters of the whole system. Beyond the interest of full system mean parameter, this paper studies the identification of the system parameters under a more general setting, where the full system can follow an exponential family distribution with more than one unknown parameter. Using the maximum likelihood estimation technique, we derive the general formula of the score vector and the Fisher information matrix. It is also shown that under some conditions, the full system maximum likelihood estimators converge to the true parameter value as long as the total sample size goes to infinity.