Towards a calculus of systems dependability

Abstract

This paper presents a calculus that enables a designer of an embedded, real-time system to reason about and calculate whether a given requirement will hold with a sufficiently high probability for given failure probabilities of components used in the design of the system. The main idea is: - to specify requirements and design in DC (Duration Calculus, an extension of real-time, interval logic); - to define satisfaction probabilities for formulas in this calculus; - to establish a basic probabilistic calculus, PC, with rules that support calculation of the satisfaction probability for a composite formula from probabilities of its constituents; - to develop a collection of theorems expressing specific important PC formulas in terms of the probability matrices used in classical reliability engineering. These theorems are oriented towards systematic numerical calculations. This ensures that reasoning about probabilities is consistent with requirements and design decisions. We thus avoid introducing separate models for requirements and dependability analysis. The system model is a finite automaton with fixed transition probabilities. This defines discrete Markov processes as basis for the calculus.