Closed-Form Solution for System Availability Distribution

Highly reliable systems with long mission time, that can tolerate no down time, have motivated the study of system reliability. The emergence of fault-tolerant computing systems, where small down times may be tolerable, and preventive and corrective maintenance permitted, motivates a revisit to measures like mean availability. Vendors of computer systems are being required to specify the level of availability that will be met by their systems over a finite time interval, and pay a penalty for non-compliance. Since no closed-form solution has been reported in the literature, numerical approaches have often been used to compute systems availability over a finite time, even for simple Markov models. We report a Laplace transform solution for the distribution of availability over a finite interval, for a semi-Markov model. The transform of the distribution is analytically inverted to obtain a closed-form solution for the corresponding Markov model.