Discrete Time-Space Stochastic Mathematical Modelling for Quantitative Description of Software Imperfect Fault-Debugging with Change-Point

Abstract

Statistics and stochastic-process theories, along with the mathematical modelling and the respective empirical evidence support, describe the software fault-debugging phenomenon. In software-reliability engineering literature, stochastic mathemat-ical models based on the non-homogeneous Poisson process (NHPP) are employed to measure and boost reliability too. Since reliability evolves on account of the running of computer test-run, NHPP type of discrete time-space models, or difference-equation, is superior to their continuous time-space counterparts. The majority of these models assume either a constant, monotonically increasing, or decreasing fault-debugging rate under an imperfect fault-debugging environment. However, in the most debugging scenario, a sudden change may occur to the fault-debugging rate due to an addition to, deletion from, or modification of the source code. Thus, the fault-debugging rate may not always be smooth and is subject to change at some point in time called change-point. Significantly few studies have addressed the problem of change-point in discrete-time modelling approach. The paper examines the combined effects of change-point and imperfect fault-debugging with the learning process on software-reliability growth phenomena based on the NHPP type of discrete time-space modelling approach. The performance of the proposed modelling approach is compared with other existing approaches on an actual software-reliability dataset cited in literature. The findings reveal that incorporating the effect of change-point in software-reliability growth modelling enhances the accuracy of software-reliability assessment because the stochastic character-istics of the software fault-debugging phenomenon alter at the change-point.