A Dependability Measure for Degradable Computing Systems

Report, 1992

This paper deals with the problem of finding a comprehensive dependability measure or figure of merit for computing systems. Dependability is a term used for a general description of a systems trustworthiness in non-quantitative terms. It is commonly described by a number of aspects, like reliability, availability, safety and security. Quantitative measures are conveniently used for e.g. reliability and availability, but are rare for security. However, it is felt that a more general measure of a system’s dependability would be of great interest and could be used for system evaluations, design trade-offs etc. In order to achieve this, we adopt a generalized view that facilitates a recompilation of the dependability aspects into fewer and more general qualities. Key issues for the generalization are the concepts of degradability and service. A degraded service is the result of the discontinuation of one or several subservices, yielding a system that operates on a reduced service level. A vectorized measure based on Markov processes is suggested, and mathematical definitions are given. The measure describes the expected time a system will be operating at a certain service level, and also the probability that this level be reached. By means of applying the concept of reward rate to each service level, an even more simplified figure of merit can be calculated. Normally, when making reliability calculations, an assumption of exponential failure rates for system components is made. Sometimes this assumption is not realistic and we outline how phase-type distributions can be used to cope with this situation. Finally, two different schemes for the calculation of the measure is given. First, a hierarchical procedure feasible for small systems and calculations by hand is presented. Second, a general procedure based on matrix calculus is given. This procedure is suitable for complicated systems. It is also general in the sense that it may be used for measures extended to repairable systems.