Discrete time software reliability modeling with periodic debugging schedule

In many situations, multiple copies of a software are tested in parallel with different test cases as input, and the detected errors from a particular round of testing are debugged together. In this article, we discuss a discrete time model of software reliability for such a scenario of periodic debugging. We propose likelihood based inference of the model parameters, including the initial number of errors, under the assumption that all errors are equally likely to be detected. The proposed method is used to estimate the reliability of the software. We establish asymptotic normality of the estimated model parameters. The performance of the proposed method is evaluated through a simulation study and its use is illustrated through the analysis of a dataset obtained from testing of a real-time flight control software. We also consider a more general model, in which different errors have different probabilities of detection.