Modelling an Imperfect Debugging Phenomenon with Testing Effort zy * ** ** zyxwv P.K.Kapur , P.S.Grover and Said Younes *Department of Operational Research, University of Delhi, Delhi,110007, India **Department of Computer Science , University of Delhi, Delhi,110007, India Abstract zyxwvutsr In this paper, we develope a Software Reliability Growth Model (SRGM) based on Non Homogeneous zyxwvu Poisson Process (NHPP). The model describes the relationshb between the calendar time, testing effort consumption and error removal process under imperfect debugging environment. The role of learning (gaining experience) with theprogress of testingphase zyxwvut is taken into consideration by assuming that the imperfect debugging probability is dependent on the current software error content. The model has the inbuilt frexibildy of representing a wide range of growth curves. The model can be used to plan the amount of testing effort required to achieve a predetermined target in terms of errors removed in a given span of time. I- Introduction Computers are being widely used for a variety of applications in our daily 1ife.With rapid advancement in the technology, the cost of computer hardware has been steadily declinnig while on the contrary the cost of computer software is increasing. The production of computer software systems is seen to be the most prominent industry today. Therefore, it is of utmost importance to develope high quality software systems. The quality of the software system can be described in terms of Complexity, Maintainability, Portability and Reliability etc. The software reliability can easily quantify the quality of the software. It is defined as the probability that the system will workwithout failure for specified span of time under a given usage environment . The software failure is the departure of the software output from the system specification and is the manifestation of the software error which may have been introduced by the system analysers, designers, programmers and managers during different phases of software development cycle. In order to detect and remove the errors, the software is tested and its quality in terms of its reliability is measured by the removal of these errors. Several Software Reliability Growth Models (SRGMs) have been developed in the literature to monitor the error removal process and measure and predict the reliability of the software systems .During the testing ,it has been observed that the relationship between the testing time and the corresponding number of errors removed is either exponential or S-Shaped or the mix of the two. SRGMs due to Jelinski and Moranda [7] , Musa [12] ,Goel and Okumoto [4] are exponential in nature while several others due to Yamada et a1.[15], Ohba[l3], Bittanti et al. [2],Kapur and Garg [ 101 and Kapur et al. [ 11 ] describe the S-Shaped phenomenon.The S-Shapedness can he due to several reasons.Ohba [13] attributed it to thc mulual dependency between the software errors,Yamada et al. [lS] ascribed it to the time delay between the failure observation and the subsequent error removal while Bittanti et al. [2] accrued it to the increase of the removal rate as the testing progresses. Kapur et al. (111 ascribed it to the presence of different types of errors in a software system. However$ seems little effort has been made to develope SRGMs when the error removal phenonienon is imperfect . The concept of imperfect debugging was introduced by Goel [5] and Kapur and Garg [9]. Recently Zeephongsekul et al. [18] have summarised some of these in their review paper. Due to the complexity of the software systems and the incomplete understanding of the software requirements/ specifications, the testing team may not be able to remove the errors perfectly and the original error is replaced by another error. The new error may generate new failures when this part of the software system is traversed during the testing. The iiiultiple removal of the errors slows down the error removal process and gives rise to S-Shaped growth curve.The software reliability is also related to the resourccs spent in terms of CPU hours,man power and the number of executed test cases (Musa et al. [12]). Yamada zyx ct al.[ 161 proposed an exponential SRGM which describes the 1071-9458/94 $4.00 zyxwvutsrqpon 0 1994 IEEE 178