Abstract - Software companies are coming with multiple add-ons to survive in the pure competitive environment. Each succeeding up-gradation offers some performance enhancement and distinguishing itself from the past release. If the size of the software system is large, the number of faults detected during the testing phase becomes large, and the number of faults, which are removed through each debugging, becomes small compared to 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 propose a multi-release software reliability growth model based on ^ ' Ito s type of differential equation. The model categorizes Faults in two categories: simple and hard with respect to time which they take for isolation and removal after their observation. The model developed is validated on real data set. Keywords - Add-ons, Software Reliability Growth Models (SRGM), Up-Gradation. I. INTRODUCTION A Software Reliability growth model (SRGM) is a tool of Software Reliability Engineering (SRE), which can be used to evaluate the software quantatively, develop test status, schedule status and monitor the changes in reliability performance. In the last two decades several Software Reliability models have been developed in the literature to estimate the fault content, failure rate and fault removal rate per fault in software and to predict the reliability of the software at time of the release. It has also been observed that the relationship between the testing time and the corresponding number of faults removed is either exponential or S-shaped or a mix of the two[1,2,5,9,11]. In the present study we have assumed that the software includes different types of faults (simple and hard) and each fault requires different strategies to be removed. Obha[5] refined the Goel-Okumoto model by assuming that the fault detection/removal rate increases with time and that there are two types of faults in the software. SRGM proposed by Bittanti et al [1] and Kapur and Garg [9] have similar forms as that of Obha[5] but are developed under different set of assumptions.Bittanti et al [1] proposed an SRGM exploiting the fault removal rate during the initial and final time epochs of testing, whereas Kapur and Garg [9,10] describe a fault revoval phenomenon, where they assume that during a removal process of a fault some of the additional faults might be removed without these faults causing any failure. These models can describe both exponential and S-shaped growth curves and therefore are termed as flexible models [5,9]. In the development of computer operations systems, a number of faults are detected and removed during the long testing period, and the system is then released to the market. However, the users then find number of faults, and the software company then releases an upgraded version of the software. Thus, in this case the number of faults that remain in the system can be considered to be a stochastic process with continuous state space [7]. Yamada et al [12] proposed a simple software Reliability model to describe the fault detection process during the testing phase by applying Stochastic Differential Equations (SDE) and obtain several software reliability measures using the probability distributions on Stochastic Process. Lee et al [13] used SDEs to represent a per-fault detection rate that incorporates an irregular fluctuation instead of NHPP, and consider a per-fault detection rate that depends on time t. In this paper we will use SDEs to represent fault detection rate that incorporates an irregular fluctuations. The rest of the paper is organized as follows: Sec II describes about Multiple Release phenomenon, Sec III and IV deals with the assumptions and notations used in the paper. Sec V describes SDE based Modeling framework for various Releases. In Sec VI, we have given the estimations and Results followed by Conclusion and References in Sec VII and VIII respectively. II. MULTIPLE-RELEASES OF SOFTWARE The major strategy to survive in the competitive era is multiple add-ons/up-gradation of the software system; because timely and positive up-gradation of the software system attracts the users which in-return increases the market size. On the other hand the developers are very active to review and evaluate the existing system i.e. when the system is in operational phase or via reported bugs from the user’s end. Hence, the main aim of the software developing firm is to gain maximum portion of the customer size with positive feedback. With each add- ons/up-gradation developer/company bring some special feature or new functionality into software. Adding some A Stochastic Formulation of Successive Software Releases with Faults Severity Ompal Singh, P.K Kapur, Adarsh Anand Department of Operational Research, University of Delhi,Delhi,India (drompalsingh@yahoo.co.in , pkkapur1@gmail.com , adarsh.anand86@gmail.com ) 978-1-4577-0739-1/11/$26.00 ©2011 IEEE 136