More and more software systems have been developed to provide great flexibility to customers, but they also introduce great uncertainty to software development. The fault detection rate (FDR) within the fault detection process shows an irregular fluctuation and is usually modeled as a white noise. White noise is Markovian, but Non-Markov is the rule while Markov is the exception. In many cases the white noise idealization is insufficient, as real fluctuations are always correlated noise (non-Markovian noise). This study proposes a novel model to quantify the uncertainties associated with the debugging process. Based on the Non-homogeneous Poisson process (NHPP) model for software fault detection process, the environmental uncertainties are considered collectively as a noise of arbitrary distribution and correlation structure. Through a number of comparisons with existing methods, the new model exhibits a closer fitting to observation data. In addition to focusing on the mean value of detected-fault number, this work provides a formula to compute its cumulative density function (CDF) and probabilistic density function (PDF), thus encapsulating full statistical information of the debugging process.