A transient interval reliability analysis for software rejuvenation models with phase expansion

The phenomenon of software aging refers to the continuing degradation of software system performance with the operation time and is usually caused by the aging-related bugs such as the memory leak and the accumulation of round-off errors. Software rejuvenation acts as one of the proactive fault management techniques against the software aging. In this paper, we evaluate the interval reliability for two basic stochastic models with periodic software rejuvenation by Garg et al. (1995) and Suzuki et al. (2002a, b). The interval reliability is one of the most generalized dependability measures that involve commonly used reliability function and steady-state availability as the special cases, and is helpful for the system design during a fixed mission period. From the mathematical point of view, the interval reliability for the software rejuvenation models leads to the transient analysis. We focus on the phase expansion approach for solving the transient solutions for the basic software rejuvenation models. The phase expansion is an approximate technique that replaces arbitrary probability distributions by the phase-type (PH) distributions. Benefiting from the phase expansion, we can numerically derive the transient interval reliability for two software rejuvenation models. In numerical examples, we discuss the accuracy of the phase expansion and also reveal quantitative properties of the interval reliability measures.