Stochastic Differential Equation Based SRGM for Errors of Different Severity With Testing-Effort

Abstract

Models that describe the failure phenomenon and consequent enhancement in reliability due to fault removal are termed as Software Reliability Growth Models (SRGM). 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. Several continuous-state space SRGM based on stochastic differential equations of c Ito type to assess software reliability for large scale software systems have been proposed in the literature so far. However these continuous-state space SRGM have seldom taken the effect of testing-effort into consideration. The resources, such as manpower used for fault detection/removal, number of executed test-cases and CPU hours spent in executing software under test, are well-known as one of the most important factors related to the software reliability growth process. Some of the existing SRGM define errors of different severity. Severity of a failure or fault is the impact it has on the operation of a software-based system. Different faults may require different amount of testing efforts and testing strategy for their removal from the software. The aim of this paper is to determine the type of faults and their proportion present in the software. We have also assumed that learning of removal team grows as testing progresses due to experience and have incorporated the logistic removal rate during modeling of different types of faults with testing-effort by applying a mathematical technique of stochastic differential equations of c Ito type. Finally, a goodness-of-fit comparison between proposed models and existing continuous-state space SRGM using stochastic differential equations has been conducted.

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