Probabilistic error propagation model for mechatronic systems

Abstract

This paper addresses a probabilistic approach to error propagation analysis of a mechatronic system. These types of systems require highly abstractive models for the proper mapping of the mutual interaction of heterogeneous system components such as software, hardware, and physical parts. A literature overview reveals a number of appropriate error propagation models that are based on Markovian representation of control flow. However, these models imply that data errors always propagate through the control flow. This assumption limits their application to systems, in which components can be triggered in arbitrary order with non-sequential data flow. A motivational example, discussed in this paper, shows that control and data flows must be considered separately for an accurate description of an error propagation process.For this reason, we introduce a new concept of error propagation analysis. The central idea is a synchronous examination of two directed graphs: a control flow graph and a data flow graph. The structures of these graphs can be derived systematically during system development. The knowledge about an operational profile and properties of individual system components allow the definition of additional parameters of the error propagation model. A discrete time Markov chain is applied for the modeling of faults activation, errors propagation, and errors detection during operation of the system. A state graph of this Markov chain can be generated automatically using the discussed dual-graph representation. A specific approach to computation of this Markov chain makes it possible to obtain the probabilities of erroneous and error-free system execution scenarios.This information plays a valuable role in development of dependable systems. For instance, it can help to define an effective testing strategy, to perform accurate reliability estimation, and to speed up error detection and fault localization processes. This paper contains a comprehensive description of a mathematical framework of the new dual-graph error propagation model and a Markov-based method for error propagation analysis.