In this paper, we investigate a system composed of mixtures of one-shot units with nonhomogeneous and time-dependent characteristics. We propose analytical expressions to predict system reliability metrics and consider a physics-statistics-based lifetime model to demonstrate the units' failure mechanism as well as its failure process uncertainty. We design a sequence of optimum accelerated non-destructive testing (NDT) plans to predict the reliability metrics of the system and show that a well-designed sequential accelerated NDTs is an effective approach to shorten the test duration with negligible consequence on system reliability metrics.