This article gives the detailed mathematical results on the hypergeometric distribution software reliability model (HGDSRM) proposed by Tohma et al. [IEEE Trans. Software Eng. (1989, 1991)]. In the above papers, Tohma et al. developed the HGDSRM as a discrete-time stochastic model and derived a recursive formula for the mean cumulative number of software faults detected up to the i-th (>0) test instance in test-ing phase. Since their model is based on only the mean value of the cumulative number of faults, it is impossible to estimate not only the software reliability but also the other probabilistic dependability measures.

In this article, we introduce the concept of cumulative trial processes, and describe the dynamic behavior of the HGDSRM exactly. In particular, we derive the probability mass function of the number of software faults detected newly at the i-th test instance and its mean as well as the software reliability defined as the probability that no faults are detected up to an arbi-trary time. In numerical examples with real software failure data, we compare several HGDSRMs with different model parameters in terms of least squared sum and show that the mathematical results obtained here are very useful to assess the software reliability with the HGDSRM.