FAILURE ANALYSIS FOR AN AIRBAG INFLATOR BY PETRI NETS

Petri nets are useful for modelling a variety of asynchronous and concurrent systems, such as automated manufacturing, computer fault tolerant systems, and communication networks. This study employs an airbag inflator system as an example to demonstrate a Petri net approach to failure analysis. This paper uses Petri nets to study minimum cut sets finding, marking transfer, and dynamic behaviour of system failure. For Petri net models incorporating sensors, fault detection and higher-level fault avoidance is dealt with. Compared with fault trees that present only static logic relations between events, Petri nets indeed offer more capabilities in the scope of failure analysis. © 1997 John Wiley & Sons, Ltd.     

System Failure Analysis Through Counters of Petri Net Models

Petri nets are a powerful technique widely used in the modeling and analysis of complex manufacturing systems and processes. Due to their capability in modeling the dynamics of the systems, Petri nets have been combined with fault tree analysis techniques to determine the average rate of occurrence of system failures. Current methods in combining Petri nets with fault trees for system failure analysis compute the average rate of occurrence of system failures by tracking the markings of the Petri net models. The limitations of these methods are that tracking the markings of a Petri net represented by a reachability tree can be very complicated as the size of the system grows. Therefore, these methods offer less flexibility in analyzing sequential failures in the system. To overcome the limitations of the current methods in applying Petri nets for system failure assessment, this paper expands and extends the concept of counters used in Petri net simulation to perform the failure and reliability analysis of complex systems. The presented method allows the system failures to be modeled using general Petri nets with inhibitor arcs and loops, which employs fewer variables than existing marking‐based methods and substantially accelerates the computations. It can be applied to real system failure analysis where basic events can have different failure rates. Copyright © 2003 John Wiley & Sons, Ltd.     

Reliability modelling of repairable systems using Petri nets and fuzzy Lambda–Tau methodology

A methodology is developed which uses Petri nets instead of the fault tree methodology and solves for reliability indices utilising fuzzy Lambda–Tau method. Fuzzy set theory is used for representing the failure rate and repair time instead of the classical (crisp) set theory because fuzzy numbers allow expert opinions, linguistic variables, operating conditions, uncertainty and imprecision in reliability information to be incorporated into the system model. Petri nets are used because unlike the fault tree methodology, the use of Petri nets allows efficient simultaneous generation of minimal cut and path sets.     

应用Petri网改进基于故障树的诊断方法

故障树是表示故障发生和故障传播关系的一种逻辑模型,基于故障树诊断方法的广泛应用由于实际故障树分析过程的ＮＰ困难问题而受到妨碍。而Ｐｅｔｉｒ网是一种特殊的有向网,适合于描述故障的传播关系。本文提出了两种基于Ｐｅｔｒｉ网的改进方法,与下行法相比,用该方法寻找最小割集和最小路集能有效地节省上计算时间,提高推理速度和效率;最后还应用Ｐｉｔｒｉ网的状态方程分析方法提出了基于Ｐｅｔｒｉ网的故障监测和诊断方法。     

Analysis of sequential failures for assessment of reliability and safety of manufacturing systems

Assessment of reliability and safety of a manufacturing system with sequential failures is an important issue in industry, since the reliability and safety of the system depend not only on all failed states of system components, but also on the sequence of occurrences of those failures. Methods that are currently available in sequential failure analysis always start with given sequences of the failures in the system, which is not the case in real life situations; therefore, the sequences of the failures should be identified and the probability of their occurrence should be determined. In this paper, we represent a methodology that can be used for identifying the failure sequences and assessing the probability of their occurrence in a manufacturing system. The method employs Petri net modeling and reachability trees constructed based on the Petri nets. The methodology is demonstrated on an example of an automated machining and assembly system.     

Implementation of Petri nets using a field‐programmable gate array

Although Petri nets have various capabilities, the Petri net approach is done on paper. A field‐programmable gate array (FPGA) is implemented in this study so as to realize basic Petri net symbols, logic structures in Petri nets, and specific functions for Petri nets by logic circuits. As an example, a Petri net for an early failure detection and isolation arrangement (EFDIA) is implemented as an application‐specific integrated circuit (ASIC) on a Xilinx Demonstration Board. This ASIC is verified by three simulations dealing with three different failure scenarios of a system, and the ASIC functions identically to the EFDIA Petri net. Accordingly, not only the EFDIA Petri net but also any specific function Petri nets can be implemented by FPGA circuits. Copyright © 2000 John Wiley & Sons, Ltd.     

Mode automata and their compilation into fault trees

In this article, we advocate the use of mode automata as a high level representation language for reliability studies. Mode automata are states/transitions based representations with the additional notion of flow. They can be seen as a generalization of both finite capacity Petri nets and block diagrams. They can be assembled into hierarchies by means of composition operations.The contribution of this article is twofold. First, we introduce mode automata and we discuss their relationship with other formalisms. Second, we propose an algorithm to compile mode automata into Boolean equations (fault trees). Such a compilation is of interest for two reasons. First, assessment tools for Boolean models are much more efficient than those for states/transitions models. Second, the automated generation of fault trees from higher level representations makes easier their maintenance through the life cycle of systems under study.     

A Petri Net Approach to Remote Diagnosis for Failures of Cardiac Pacemakers

This paper describes the application of Petri nets to remote diagnosis for failures of cardiac pacemakers. The operations, structures and basic control methods of the different types of cardiac pacemakers are first described. A combined synchronous pacemaker is modeled into a Petri net in this study. Twelve checkpoints are added into the modeled Petri net so as to construct a Petri net for failure diagnosis. A remote mode for failure diagnosis of implanted pacemakers is also designed by the Petri net approach. A low‐power transmitter transmits a checking‐code with 12 digits from the implanted pacemaker to the outside of the patient's body manually or automatically. By observing the markings of the checking code, the working status and the health condition of the pacemaker are clear at a glance. Applications of the Petri net method for failure diagnosis and control optimization are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Integration of process simulations in availability studies

The aim of this paper is to describe a method to integrate the results of process simulations in availability studies. It is shown that this can be achieved if two conditions are met: firstly, close co-operation between process experts and reliability engineers and secondly, a flexible modelling tool. Principles of the modelling method, the interpreted stochastic Petri nets, are provided. The way to use them to model plant availability is described, together with a computer code enabling calculations to be made. The aim of the plant availability study and how results of process simulations were integrated in the Petri net model is then explained. Results are discussed and conclusions given on the ability of interpreted stochastic Petri nets to model complex systems.     

Reliability analysis of discrete event dynamic systems with Petri nets

This paper deals with dynamic reliability of embedded systems. It presents a method for deriving feared scenarios (which might lead the system to a critical situation) in Petri nets. A classical way to obtain scenarios in Petri nets is to generate the reachability graph. However, for complex systems, it leads to the state space explosion. To avoid this problem, in our approach, Petri net reachability is translated into provability of linear logic sequents. Linear logic bases are introduced and used to formally define scenarios and minimality of scenarios. These definitions allow the method to produce only pertinent scenarios. The steps of the method are described and illustrated through a landing-gear system example.     

Automatic hazard analysis of batch operations with Petri nets

A systematic procedure has been proposed in this study to construct Petri nets for modeling the fault propagation behaviors in batch processes. An efficient algorithm has also been developed to enumerate all possible scenarios, which may lead to an undesirable consequence. This approach has been applied to a number of examples. The results show that it is more accurate and more comprehensive when compared with the conventional methods.     

Industrial systems maintenance modelling using Petri nets

This article presents a new algorithm that we have developed to find the minimal cut-sets of a coherent fault tree. The model presented is based on Petri nets. We also show that for a large fault tree, we are faced with the complexity problem. We suggest the use of place fusion as well as a methodology that can allow us to overcome this difficulty.     

基于随机Petri网的铜带拉弯矫直机可用度分析

为了合理确定铜带拉弯矫直机的校验周期,提高其生产效率,确保其矫直精度,根据某铜板带公司拉弯矫直机9个月的维修数据,对拉弯矫直机的失效模式进行随机Petri网建模,将系统失效模式转换成相应的随机Petri网;基于马尔科夫过程对随机Petri网进行瞬态概率求解,并得到该拉弯矫直机失效模式的稳态概率;利用或门对应的随机Petri网模型分析,计算不同校验周期下拉弯矫直机的可用度.综合考虑设备可用度和经济效益,确定了合理的校验周期,为拉弯矫直机的长周期运行提供了依据.     

State estimation of discrete event systems for RUL prediction issue

This paper concerns Remaining Useful Life (RUL) estimation of discrete event systems. For that purpose, physics-based models with partially observed stochastic Petri nets are used to represent the system and its sensors. The advantage of the proposed modelling approach is to provide a realistic representation of the system, including the interaction between the normal behaviours and the failure processes. From the proposed modelling and collected measurements, timed trajectories, which are consistent with the observations, are obtained. Based on the event dates, our approach consists in evaluating the probabilities of the consistent behaviours using probabilistic models. State estimation is obtained as a consequence. The most probable future degradations, from the current state, are then considered and a method for fault prognosis is presented. Finally, the prognosis result is used to estimate the RUL as a time interval. A case study is proposed to show the applicability of the proposed method.     

Petri-net based applications for supply chain management: an overview

Supply networks are discrete event dynamic systems consisting of suppliers, manufacturers, distributors, and customers. It is a difficult and challenging task to model such a complex system. Recently, characterised as being capable of model parallelism and synchronisation, Petri nets (PNs) have attracted great attention for modelling and studying a supply network. Since each type of Petri net has its unique properties to model specific applications, this paper reviews and classifies Petri net applications for supply chain management (SCM). According to the decision problems facing SCM, we have the Petri net applications classified into three areas: competitive strategy, firm focused tactics, and operational efficiency. Categorising the Petri net applications will provide a guideline to industry practitioners and research academics to choose the appropriate Petri net for the problem. In addition, the paper attempts to offer future directions in applying the Petri net to SCM including: (1) modelling with uncertainty elements; (2) addressing the scalability issue of Petri nets; (3) integrating Petri nets with other tools; and (4) extending Petri nets to emerging applications.     

Decomposition of Petri nets and Lagrangian relaxation for solving routing problems for AGVs

In this paper, we propose a Lagrangian relaxation method for solving routing problems for multiple AGVs by decomposition of timed Petri nets. The AGV routing problem is represented by an optimal transition firing sequence problem for timed Petri nets. The timed Petri net is decomposed into several subnets in which the subproblem for each subnet can be easily solved by Dijkstra's algorithm. We show that each subproblem generated by each subnet is polynomially solvable. The optimality of the solution can be evaluated by the duality gap derived by the Lagrangian relaxation method. The performance of the proposed method is compared with a conventional optimisation algorithm with the penalty function method. The effectiveness of the proposed method is demonstrated.     

A transformation from a Boolean equation control specification to a Petri net

In this article we present an algorithm to transform a set(s) of Boolean equations into a Petri net(s). Boolean logic provides a mathematical basis for switching control and many other areas. In the case of programmable logic controllers used for the sequential control in manufacturing applications, Boolean equations are fundamental both in programming and in understanding their operation. A major difficulty with Boolean equations is the lack of any type of mathematical theory for the analysis of the systems that are being represented by these equations. Petri nets, on the other hand, possess a mathematical framework to analyze the properties of the system being modeled. Furthermore, Petri nets have been proved to be appropriate models for sequential control. The popularity as well as the generality of Boolean logic, on one hand, and the modeling and analytical capabilities of Petri nets, on the other hand, are the major motivations for this research.     

Analysis and synthesis of the behaviour of complex programmable electronic systems in conditions of failure

This paper introduces a new method for safety analysis which modifies, automates and integrates a number of classical safety analysis techniques to address some of the problems currently encountered in complex safety assessments. The method enables the analysis of a complex programmable electronic system from the functional level through to low levels of its hardware and software implementation. In the course of the assessment, the method integrates design and safety analysis and harmonises hardware safety analysis with the hazard analysis of software architectures. It also introduces an algorithm for the synthesis of fault trees, which mechanises and simplifies a large and traditionally problematic part of the assessment, the development of fault trees. In this paper, we present the method and discuss its application on a prototypical distributed brake-by-wire system for cars. We argue that the method can help us rationalise and simplify an inherently creative and difficult task and therefore gain a consistent and meaningful picture of how a complex programmable system behaves in conditions of failure.