In this paper we motivate a random coefficient autoregressive process of order 1 for describing reliability growth or decay. We introduce several ramifications of this process, some of which reduce it to a Kalman Filter model. We illustrate the usefulness of our approach by applying these processes to some real life data on software failures. Finally, we make a pairwise comparison of the models in terms of the ratio of likelihoods of their predictive distributions, and identify the "best" model.