The problem of optimizing accelerated production testing is a pressing one in most electronic manufacturing facilities. Yet, practical models are scarce in the literature, especially for testing high volumes of electronic circuit packs in failure-accelerating environments. In this paper, we develop both a log-linear and linear model, based initially on the Weibull distribution. The models developed are suitable for modeling accelerated production testing data from a temperature-cycled environment. The model is "piecewise" in that the failures in each discrete "piece" of the temperature cycle are modeled as if the testing was in parallel rather than sequential mode. An extra covariate is introduced to indicate age at the start of each piece. The failures in a piece then depend on the stress in the piece itself and the time elapsed to the start of the piece. This last dependence captures the influence of reliability growth and has the result of providing an alternative linear model to the log-linear one. The paper demonstrates a simpler use of Poisson regression. An application, using actual production data, is described. Uses of the Loglogistic, Logistic, Lognormal and Normal distributions are also illustrated.