| Abstract: | This paper continues the study of the software reliability model of Fakhre-Zakeri & Slud (1995), an "exponential order statistic model" in the sense of Miller (1986) with general mixing distribution, imperfect debugging and large-sample asymptotics reflecting increase of the initial number of bugs with software size. The parameters of the model are θ (proportional to the initial number of bugs in the software), G (·, μ) (the mixing df, with finite dimensional unknown parameter μ, for the rates λ i with which the bugs in the software cause observable system failures), and p (the probability with which a detected bug is instantaneously replaced with another bug instead of being removed). Maximum likelihood estimation theory for (θ, p , μ) is applied to construct a likelihood-based score test for large sample data of the hypothesis of "perfect debugging" ( p = 0) vs "imperfect" ( p > 0) within the models studied. There are important models (including the Jelinski–Moranda) under which the score statistics with 1/√ n normalization are asymptotically degenerate. These statistics, illustrated on a software reliability data of Musa (1980), can serve nevertheless as important diagnostics for inadequacy of simple models |
