Imperfect Debugging Software Belief Reliability Growth Model Based on Uncertain Differential Equation

Due to the increased dependency of the modern system on software-based system, software reliability has become the primary concern during the software development. To track and measure the software reliability, various software reliability growth models under the framework of probability theory have been proposed. Note that software failures involve lots of epistemic uncertainty, which cannot be depicted well by the probability theory, and debugging processes are usually imperfect due to the complexity and incomplete understanding of software systems. This article deduces an imperfect debugging software belief reliability growth model using the uncertain differential equation under the framework of uncertainty theory, and investigates properties of essential software belief reliability metrics, namely belief reliability, belief reliable time, and mean time between failures based on the belief reliability theory. Estimations for unknown parameters in this model are derived. Real data analyses validate our model and show that it performs better than previous models from the perspective of the sum of square error. A theoretical analysis for these results is presented.