Non-Homogeneous Autoregressive Processes for Tracking (Software) Reliability Growth, and Their Bayesian Analysis
Nozer D. Singpurwalla, Refik Soyer · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1992
SUMMARY We motivate a non-homogeneous autoregressive process as a model for reliability growth and consider two formulations, both Bayesian, which alleviate a limitation that least squares estimators for such processes of order greater than 1 exist only when repeated measurements of the time series are available. In one formulation, the prior assumption involves exchangeability of coefficients, whereas in the other an autoregressive structure is imposed on them. Both formulations enable us to cast the resulting processes in state space form for which the Kalman filter algorithm can be used. The first formulation involves an adaptation of standard techniques whereas the second results in a new methodology for adaptive filtering which is facilitated by an approximation due to Lindley. The procedures are demonstrated via a consideration of some data on software failures.