Analysis of the debugging model based on probabilistic state transition

In general, software reliability test is an important task in software developing process. Meanwhile, it called perfect debugging which assumed that detecting a fault and fixing it, no introducing new faults, in turn, introducing new faults, called imperfect debugging. We all hope the testing process is perfect debugging and no new faults will be introduced. Therefore, it can shorten the testing time and decrease the testing costs. However, in practice, the software test is a complex, intractable process and can be divided into two categories, which are perfect debugging and imperfect debugging. Furthermore, most of testing processes are imperfect debugging. Then, what is relation between perfect debugging and imperfect debugging and what is impact to imperfect debugging transiting to perfect debugging? In this paper, we propose two state models based on probabilistic state transition to analyze the relation between perfect debugging and imperfect debugging and express debugging time and costs during imperfect debugging transiting to perfect debugging process in terms of the parameters in that model. Threshold conditions for perfect debugging process to be beneficial are also derived. Finally, using the numerical examples prove our assumptions and inference.