A Markovian model for reliability and other performance measures

Several studies have been undertaken in recent years to investigate the software failure phenomenon, with the objective of developing analytical models for quantitative assessment of software performance. Most of these studies assume that the times between software failures follow an exponential distribution with a failure rate that depends on the number of errors in the system (see, for example, Jelinski and Moranda,5 Littlewood and Verra1l6 and Shoomanll). A key assumption made in most of these studies is that the errors are removed with certainty when detected. However, as pointed out in Miyamot07 and Thayer et al.,l2 errors are not always corrected when detected. The existing models do not provide a solution for such situations. In this paper we develop a Markovian model, which we call an Imperfect Debugging Model (IDM), for studying software failures when ermrs are not removed/corrected with certainty, i.e., for the case of imperfect debugging. Also, expressions are derived for the following probabilistic performance measures: