Fitting the log-linear rate to Poisson processes

Abstract

Given a sample of repairable systems, the author models its failure behavior. Each system is assumed to be an independent realization of a nonhomogeneous Poisson process with underlying log-linear intensity function. The author finds the maximum-likelihood estimates of the unknown parameters, presenting the likelihood function and its derivatives. Accurate starting values are obtained through a graphical method for the case of an increasing intensity. Finally, a set of real data is borrowed from R.E. Barlow and B. Davis (1978) to illustrate the techniques.<>