Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 8593612, 11 pages

http://dx.doi.org/10.1155/2016/8593612

## Failure Propagation Modeling and Analysis via System Interfaces

^{1}State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China^{2}School of Computer Science, University of Oklahoma, Norman, OK 73019, USA^{3}Institute of Railway Research, University of Huddersfield, Huddersfield HD1 3DH, UK

Received 12 January 2016; Revised 30 March 2016; Accepted 5 April 2016

Academic Editor: Egidijus R. Vaidogas

Copyright © 2016 Lin Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Safety-critical systems must be shown to be acceptably safe to deploy and use in their operational environment. One of the key concerns of developing safety-critical systems is to understand how the system behaves in the presence of failures, regardless of whether that failure is triggered by the external environment or caused by internal errors. Safety assessment at the early stages of system development involves analysis of potential failures and their consequences. Increasingly, for complex systems, model-based safety assessment is becoming more widely used. In this paper we propose an approach for safety analysis based on system interface models. By extending interaction models on the system interface level with failure modes as well as relevant portions of the physical system to be controlled, automated support could be provided for much of the failure analysis. We focus on fault modeling and on how to compute minimal cut sets. Particularly, we explore state space reconstruction strategy and bounded searching technique to reduce the number of states that need to be analyzed, which remarkably improves the efficiency of cut sets searching algorithm.

#### 1. Introduction

Our society is relying more and more on the safety of a number of computer-based systems, for example, the control system of managing air traffic or operating a nuclear power plant. These systems are usually called safety-critical systems, which are a class of engineered systems that may pose catastrophic risks to its operators, the public, and the environment. The development of these systems demands a rigorous process of system engineering to ensure that safety risks of the system, even if some of its components fail, are mitigated to an acceptable level. System safety analysis techniques are well established and are used extensively during the design of safety-critical systems.

The size, scale, heterogeneity, and distributed nature of current (and likely future) systems make them difficult to verify and to analyze, particularly for nonfunctional properties including availability, performance, and security, as well as safety. Due to the manual, informal, and error-prone nature of the traditional safety analysis process, the use of models and automatic analysis techniques as an aid to support safety-related activities in the development process has attracted increasing interest. Model-based safety analysis (MBSA), where the analysis is carried out on formal system models that take into account system behaviors in the presence of faults, has been proposed to address some of the issues specific to safety assessment. Recent work in this area has demonstrated some advantages of this methodology over traditional approaches, for example, the capability of automatic generation of safety artifacts, and shown that it is a promising way to reduce costs while further improving efficiency and quality of safety analysis process.

The existing approaches to MBSA, for example, ESACS/ISAAC [1, 2], AltaRica [3–5], Failure Propagation and Transformation Notation (FPTN) [6, 7], Hierarchically Performed Hazard Origin and Propagation Studies (HiP-HOPS) [8], and the AADL with its error annex [9], can be classified into two groups: (a) failure logic based or (b) system states based. Original MBSA techniques, such as FPTN and HiP-HOPS, have sought to unify classical safety analysis methods such as Fault Tree Analysis (FTA) and Failure Modes and Effects Analysis (FMEA) and to provide a formalism for capturing a single authoritative safety model of the system. These approaches emphasized the model of failure propagation logic. The second group of MBSA approaches addresses the analysis of the transition of system states [10–12], in order to identify the routes that a system transits from a safe state to a hazardous state. Since these search-based techniques normally require exhaustive enumeration of all reachable states, they do not fully exploit the advantage of the internal structure of the state space and domain knowledge of safety analysis.

Safety is clearly an emergent property of a system that can only be determined in the context of the whole. As an emergent property, safety arises only when the system components interact with each other in an environment. Such property is controlled or enforced by a set of constraints related to behaviors of system components. Accidents often result from interactions among components that violate these constraints. In general, the term interaction is conceptually simple; it is a kind of action that occurs as two or more objects have an effect upon one another. In practice, interactions among the components dramatically increase the complexity of the overall system. It is intuitively obvious that growing interaction complexity poses a great challenge to engineer safety of the system. In some cases, although hazard identification and safety assessment had been undertaken for system components, the hazards could be missed apparently at least in part because they arise out of the complex and indirect interactions in a complex system, especially when the components of the system are independently developed or operated. The new challenge to MBSA due to the complexity of a system is that it is very hard to analyze all possible dysfunctional interactions in the system so that its hazardous states which reflect the effects of dysfunctional interactions and inadequate enforcement of safety constraints can be identified.

Using interface models to capture these interactions would offer twofold benefits. Interface information could be abstracted from the existing system design models conveniently. This is helpful to the tight integration of the systems and safety engineering processes. Furthermore, interface models are often more abstract and contain much less corresponding implementation details, which help to combat the state space explosion problem in the following automatic analysis.

In this paper, we propose an approach of model-based safety analysis which utilizes extended interface automata [13] to model the nominal behaviors as well as fault behaviors of the system. To avoid the exploration of the entire reachability set, we present a structural analysis strategy, which takes into account the inner structure of state space. This has made possible development of efficient algorithms for the purpose of safety analysis. By applying state space reduction and heuristic search, a much smaller reachable space needs to be explored and thus the efficiency of proposed minimal cut sets algorithm has been improved.

The rest of the paper is organized as follows. In Section 2, we introduce interface automaton as a formal model for safety analysis. In Section 3, we show how to use domain knowledge for efficient state space reduction and minimal cut sets generation. Section 4 mainly demonstrates our approach on a small yet realistic safety-related example where minimal cut sets are generated and analyzed. Conclusions and outlooks for future work are presented in Section 5.

#### 2. Interfaces and Fault Modeling

##### 2.1. Definitions and Notation

Interface automata give a formal and abstract description of the interactions between components and the environment. This formalism captures the temporal aspects of component interfaces, including input assumptions and output guarantees, in terms of actions and the order in which they occur in automata. Input assumptions describe the possible behaviors of the component’s external environment, while output guarantees describe the possible behaviors of the component itself.

*Definition 1 (interface automata). *An interface automaton is defined as a tuple , where(i) is a finite set of states,(ii) is a set of initial states,(iii), , and are mutually disjoint sets of input, output, and internal actions; one denotes by the set of all actions,(iv) is a transition relation.

A trace on interface automaton is an alternating sequence consisting of states and actions, such as , where and ( and ). If an action (resp., , ), then is called an input (resp., output, internal) transition. We denote by (resp., , ) the set of input (resp., output, internal) transitions. An action is enabled at a state if there is a transition for some . We denote by , , and the subsets of input, output, and internal actions that are enabled at the state .

We illustrate the basic features of interface automata by applying them to the modeling of a railroad crossing control system. Figure 1 depicts the interfaces of three components modeling the train, controller, and gate, respectively. Two sensors are used to detect the approach and exit of the train. The state changes of the controller stand for handshaking with the train (via the actions* Approach* and* Exit*) and the gate (via the actions* Lower* and* Raise* by which the controller commands the gate to close or to open). When everything is ready, a signal* Enter* is sent to authorize the entrance of the train.