A common practice in reliability studies is to model the failure process of systems with a single distribution. This thesis investigates this practice for modeling the failure distribution of systems subject to a finite number of independent failure mechanisms experiencing age acceleration. The models of systems during component age acceleration and the models of the residual lives of systems surviving component age acceleration are investigated. The fit of a single distribution to represent the failure time distribution of such systems is investigated for both modeling environments. More importantly, the assumption of time scale compression, and the resulting effect of parameter stability in the single Weibull and lognormal distribution models, is investigated for systems experiencing both differential component age acceleration and uniform component age acceleration.

The analysis in this thesis shows that single distribution models are biased when modeling systems with non-identical components. Also, parameter stability in the single distribution models does not occur when the components experience differential age acceleration. The bias in the models leads systems with uniform age acceleration to experience parameter instability because of data dependency due to the bias.