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