The software rejuvenation is a proactive fault management technique for operational software systems which age due to the error conditions that accrue with time and/or load, and is important for high assurance systems design. In this paper, fine-grained shock models are developed to determine the optimal rejuvenation policies which maximize the system availability. We introduce three kinds of rejuvenation schemes and calculate the optimal software rejuvenation schedules maximizing the system availability for respective schemes. The stochastic models with three rejuvenation policies are extentions of Bobbio et al. (1998, 2001) and represent the failure phenomenon due to the exhaustion of the software resources caused by the memory leak, the fragmentation, etc. Numerical examples are devoted to compare three control schemes quantitatively.

Software certification is a notoriously difficult problem. From software reliability engineering perspective, certification process must provide evidence that the program meets or exceeds the required level of reliability. When certifying the reliability of a high assurance system very few, if any, failures are observed by testing. In statistical estimation theory the probability of an event is estimated by determining the proportion of the times it occurs in a fixed number of trials. In absence of failures, the number of required certification tests becomes impractically large. We suggest that subjective reliability estimation from the development lifecycle, based on observed behavior or the reflection of one's belief in the system quality, be included in certification. In statistical terms, we hypothesize that a system failure occurs with the hypothesized probability. Presumed reliability needs to be corroborated by statistical testing during the reliability certification phase. As evidence relevant to the hypothesis increases, we change the degree of belief in the hypothesis. Depending on the corroboration evidence, the system is either certified or rejected. The advantage of the proposed theory is an economically acceptable number of required system certification tests, even for high assurance systems so far considered impossible to certify.

Software rejuvenation is a proactive fault management technique that has been extensively studied in the recent literature. In this paper, we focus on an example for a telecommunication billing application considered in Huang et al. (1995) and develop the discrete-time stochastic models to estimate the optimal software rejuvenation schedule. More precisely, two software availability models with rejuvenation are formulated via the discrete semi-Markov processes, and the optimal software rejuvenation schedules which maximize the steady-state availabilities are derived analytically. Further, we develop statistically non-parametric algorithms to estimate the optimal software rejuvenation schedules, provided that the complete sample data of failure times are given. Then, a new statistical device, called the discrete total time on test statistics, is introduced. Finally, we examine asymptotic properties for the statistical estimation algorithms proposed in this paper through a simulation experiment.