Probabilistic error propagation model for mechatronic systems Andrey Morozov ⇑ , Klaus Janschek Institute of Automation, Technische Universität Dresden, 01062 Dresden, Germany article info Article history: Received 5 November 2013 Accepted 15 September 2014 Available online xxxx Keywords: Control flow graph Data flow graph Error propagation analysis Discrete time Markov chain Dependability UML 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 interac- tion 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 repre- sentation 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 synchro- nous 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. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction The research results presented in this article belong to a rather young scientific domain – system dependability. By this reason, in various papers devoted to error propagation analysis, different terms can describe similar entities. In this article, the term ‘‘error’’ is used in a general context that fits for the engineering domain. This paper adheres to the definition proposed by Laprie [1]. A brief overview of the dependability research domain helps to distinguish the term ‘‘error’’ from other similar terms. Dependability is the ability of a system to deliver a service that can be justifiably trusted. The service, delivered by a system, is its behavior as it is perceived by its user. Laprie describes dependability from three points of view: the attributes of depend- ability, the means by which dependability is attained, and the threats to dependability. We are focused on the threats: Fault is a defect in the system that can be activated and cause an error. Error is an incorrect internal state of the system, or a discrepancy between the intended behavior of a system and its actual behavior. Failure is an instance in time when the system displays behavior that is contrary to its specification. Activation of a fault leads to the occurrence of an error. The invalid internal system state, generated by an error, may lead to another error or to a failure. Failures are defined according to the system boundary. If an error propagates outside the system, a failure is said to occur. http://dx.doi.org/10.1016/j.mechatronics.2014.09.005 0957-4158/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +49 351 46332202; fax: + 49 351 46337039. E-mail address: andrey.morozov@tu-dresden.de (A. Morozov). Mechatronics xxx (2014) xxx–xxx Contents lists available at ScienceDirect Mechatronics journal homepage: www.elsevier.com/locate/mechatronics Please cite this article in press as: Morozov A, Janschek K. Probabilistic error propagation model for mechatronic systems. Mechatronics (2014), http:// dx.doi.org/10.1016/j.mechatronics.2014.09.005