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We present a new random effect reliability model in which observations are the classical dichotomous data (Go or No Go) corresponding with a set of continuous auxiliary measurement. In this model, the lifetime of each individual is considered a latent variable. Given the latent part, the dichotomous response is either 0 or 1 depending on if it fails or not at the measuring time, and the continuous part can be regarded as observations of a underlying possible degradation candidate of which descending process is a function of the lifetime. When the failure of products is defined as the time at which the continuous measurement reaches a threshold, these two parts can be linked easily, and the complete likelihood (assume lifetime were also observed) can be obtained. Because of the difficulty of integrating out latent variables in the complete data likelihood, the EM-algorithm is used to carry out the MLE. The Monte Carlo methods and important sampling techniques are used to deal with the problems in E-step. When there are more than one auxiliary measurements, we propose a criterion, CCP (correct classification probability), to select a better measurement as a degradation measurement. The performances of parameters estimators and CCP are investigated in a simulation study. In the end, this procedure is applied to an electro-explosive devices (EED) example.
