BAYESIAN INFERENCE FOR THE POWER LAW PROCESS

SHAUL K. BAR-LEV, IDIT LAVI AND BENJAMIN REISER

Department of Statistics, University of Haifa, Haifa 31999, Israel

(Received December 17, 1990; revised November 8, 1991)

Abstract. The power law process has been used to model reliability growth, software reliability and the failure times of repairable systems. This article reviews and further develops Bayesian inference for such a process. The Bayesian approach provides a unified methodology for dealing with both time and failure truncated data. As well as looking at the posterior densities of the parameters of the power law process, inference for the expected number of failures and the probability of no failures in some given time interval is discussed. Aspects of the prediction problem are examined. The results are illustrated with two data examples.

Key words and phrases: Power law process, Bayesian inference, prediction, repairable system.