Reliability growth models for hardware and software systems based on nonhomogeneous Poisson processes: A survey

We summarize the reliability growth models for hardware and software systems described by a stochastic process, where the underlying stochastic process is assumed to be a nonhomogeneous Poisson process (NHPP). The background of reliability growth modelling based on an NHPP is surveyed. The Duane model, which was first postulated as a reliability growth model and is commonly used, is first explained. Secondly, the Weibull growth and modified Weibull growth models for hardware systems and the exponential type growth and gamma type growth models for error detection for software systems are discussed. The parameter estimates can be obtained by maximum likelihood estimation. Finally, the goodness-of-fit tests based on chi-square, Cramér-von Mises and Kolmogorov-Smirnov statistics are presented for the reliability growth models based on an NHPP.