In this paper, we present a general technique for construction of the empirical Bayes (EB) methods considering accelerated life tests with m of the stress levels. Estimates of prior density based on orthogonal expansions are proposed for the conditional density. We obtain the EB estimators of the parameters of the inverse power model, and the parameters of the Weibull distribution. This is a first part of a two-part series on the empirical Bayes approach of estimation using accelerated data. The theory and application are described briefly here, and step-by-step procedures for a method for EB estimation of the parameters of the Weibull distribution and the reliability function in the coming Part.