ESTIMATING THE PARAMETERS OF A NONHOMOGENEOUS POISSON-PROCESS MODEL FOR SOFTWARE-RELIABILITY

A stochastic model (G-O) for the software failure phenomenon based on a nonhomogeneous Poisson process (NHPP) was suggested by Goel & Okumoto (1979). This model has been widely used but some important work remains undone on estimating the parameters. We present a necessary & sufficient condition for the likelihood estimates to be finite, positive, and unique; and we suggest a modification of the G-O model. The performance measures and parametric inferences of the new model are discussed. The results of the new model are applied to real software failure data and compared with G-O and Jelinski-Moranda models. For the G-O model, the solution of the non-linear maximum likelihood (ML) equation has been investigated and a necessary & sufficient condition for the ML estimators to be finite is given. With positive probability, there is no solution for ML equations inside the parameter space. For our modified G-O model (HD/G-O), several quantitative measures for software performance are developed. ML equations have been investigated and a sufficient condition for the ML estimators to be finite is given. Although, like the G-O model, the HD/G-O model suffers from the problem of improper probability density function (pdf), it is superior to the G-O model because: 1) it is more flexible; 2) it assigns less weight at infinity in the pdf of the time to failure; and 3) the sufficient condition for the existence of finite solution of ML equations is the same as the necessary & sufficient condition for the G-O model - implying that the probability of MLE being finite and positive is higher for the HD/G-O model. We have also investigated and found that even when c = 1 with positive probability there is no finite positive solution for ML equations.