Software Belief Reliability Growth Model Based on Uncertain Differential Equation

Software reliability plays an important role in modern society. To evaluate software reliability, software reliability growth models (SRGMs) investigate the number of software faults in the testing phase. Obviously, testing progresses are inevitably influenced by dynamic indeterministic fluctuations such as the testing effort expenditure, testing efficiency and skill, testing method, and strategy. To model these dynamic fluctuations, several probability theory-based SRGMs are proposed. However, probability theory is suitable for dealing with aleatory uncertainty, but fails to deal with epistemic uncertainty widely existing in software faults. Therefore, this article considers software reliability from a new perspective under the framework of uncertainty theory, which is a new mathematical system different from probability theory, and proposes a software belief reliability growth model (SBRGM) based on uncertain differential equations for the first time. Based on this SBRGM, properties of essential software reliability metrics are investigated under belief reliability theory, which is a brand-new reliability theory. Parameter estimations for unknown parameters in SBRGM are presented. Furthermore, some numerical examples and real data analyses illustrate our methodology in detail, and show that it performs better than several famous probability-based SRGMs in terms of fitting ability and prediction ability. Finally, an optimal software release policy is discussed.

I. Introduction

Nowadays, computer-based systems have penetrated into all aspects of our daily life, which greatly improves our productivity and promotes the development of society, but also makes our life heavily dependent on them. The successful operation of a computer system largely depends on the fault-free of its software system. Therefore, software reliability [1]–[3] has become one of the concerns of modern society. As one of the main tools to study software reliability, software reliability growth model (SRGM) quantitatively evaluates and analyzes software reliability and other reliability metrics by modeling the number of software faults in the testing phase, so as to implement software quality control and improve the software development process.