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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2476584, 13 pages
Research Article

Software Reliability Growth Model with Partial Differential Equation for Various Debugging Processes

School of Computer Science and Engineering, Beihang University, Beijing 100191, China

Received 19 September 2015; Revised 8 December 2015; Accepted 20 December 2015

Academic Editor: Jean-Christophe Ponsart

Copyright © 2016 Jiajun Xu and Shuzhen Yao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Most Software Reliability Growth Models (SRGMs) based on the Nonhomogeneous Poisson Process (NHPP) generally assume perfect or imperfect debugging. However, environmental factors introduce great uncertainty for SRGMs in the development and testing phase. We propose a novel NHPP model based on partial differential equation (PDE), to quantify the uncertainties associated with perfect or imperfect debugging process. We represent the environmental uncertainties collectively as a noise of arbitrary correlation. Under the new stochastic framework, one could compute the full statistical information of the debugging process, for example, its probabilistic density function (PDF). Through a number of comparisons with historical data and existing methods, such as the classic NHPP model, the proposed model exhibits a closer fitting to observation. In addition to conventional focus on the mean value of fault detection, the newly derived full statistical information could further help software developers make decisions on system maintenance and risk assessment.