An estimation of software reliability models based on EM algorithm
Hiroyuki Okamura, Yasuhiro Watanabe, Tadashi Dohi, Shunji Osaki · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 2003
Abstract In this paper, a new estimation method is proposed for the model parameters of a software reliability model based on the EM (Expectation‐Maximization) principle. The debugging of the software including finite faults can be described by a generalized order statistics model. The generalized order statistics model is expressed by a nonhomogeneous Poisson process (NHPP) and the maximum likelihood method can usually be used for estimation of model parameters. However, since in this method the simultaneous logarithmic likelihood equation is numerically solved, it is not always effective from the viewpoints of algorithm stability and computation effort. The EM algorithm proposed here is a simple iteration method, which consists of several updating equations. The algorithm can accurately and stably obtain the maximum likelihood estimates. In this paper, specific EM algorithms are also derived for the cases where the occurrence of a software failure follows the exponential distribution, second‐order Erlang distribution, Rayleigh distribution, Pareto distribution, and log normal distribution. Further, by using real data, the EM algorithm is compared with the method based on the simultaneous logarithmic likelihood equation in terms of the stability of the solution. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(6): 29–37, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecjc.10058