Multi up-gradation software reliability growth model with learning effect and severity of faults using SDE

Abstract

In recent years, the dependence on a computer system has become large in our social life. Therefore, it becomes more important for software developers to produce highly reliable software systems. Due to timely demand and competitive nature of the market of software product, firms are frequently launching their upgraded versions of the base software. Many software reliability growth model have been developed by software developers and managers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous-state space. In this paper, we derive a stochastic differential equation of $i\hat{t}o$ type based multi-up-gradation model with severity of faults and effect of learning. Moreover, we discuss the identification of the faults left in the software when it is in operational phase during the testing of the new code i.e. developed while adding new features to the existing software. We examine the case where there exists two types of faults in the software; simple and hard and during testing the simple faults are removed by exponential rate whereas hard faults are removed by Yamada with learning effect function. Results are supplemented by a numerical example.