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Importance Measures are indicators of the risk significance of the components of a system. They are widely used in various applications of Probabilistic Safety Analyses, off-line and on-line, in decision making for preventive and corrective purposes, as well as to rank components according to their contribution to the global risk. They are primarily defined for the case the support model is a coherent fault tree and failures of components are described by basic events of this fault tree. In this article, we study their extension to complex components, i.e. components whose failures are modeled by a gate rather than just a basic event. Although quite natural, such an extension has not received much attention in the literature. We show that it raises a number of problems. The Birnbaum Importance Measure and the notion of Critical States concentrate these difficulties. We present alternative solutions for the extension of these notions. We discuss their respective advantages and drawbacks. This article gives a new point of view on the mathematical foundations of Importance Measures and helps us to clarify their physical meaning. [ABSTRACT FROM AUTHOR]

The control of risks generated by modern industrial facilities could not be guaranteed without the use of safety instrumented systems (SIS). The failure of SIS to achieve their assigned functions could result in huge consequences with respect to both (i) the safety of the monitored system (relating to the SIS safety integrity) as well as (ii) its production availability due to false trips (relating to the SIS operational integrity). Furthermore, these two aspects are usually antagonistic. Therefore, the assurance of this double performance comes first by a thoughtful design of SIS. In that case, the aim of this paper is twofold. First, it focuses on the establishment of generic analytical formulations allowing the assessment of the SIS performance regarding safety integrity and operational integrity. Second, it deals with SIS architecture design optimization. The optimization problem is firstly addressed by a preliminary search for a balance between the above two quantities relying on the analysis of the structure of KooN architectures. Then, a more general and suitable approach based on genetic algorithms is proposed, where several performance indicators and the costs of purchase and maintenance are expected to be considered simultaneously. This general approach is illustrated through an application example. [ABSTRACT FROM AUTHOR]

Abstract: For more than 30 years, the Petri nets (PNs) have proven to be very powerful for safety/dependability modeling and calculations. The number of publications is increasing and a standard is even going to be issued soon. Nevertheless, the dissemination is slow and the PNs are not yet commonly used by reliability engineers. As a matter of fact, the current PNs are often intricate and difficult to understand even if, in reality, they model simple systems. This is discouraging both for the PN designers and the PN readers and this is certainly one of the causes impeding the dissemination of this approach. Hopefully, some simple additional graphical rules can be easily implemented to undertake the PN modeling of large industrial systems while keeping the readability and the understandability all along the building process. The aim of this publication is to deal with the graphical aspects of Petri nets and it proposes first some very simple tricks and guidelines to structure and improve the drawing of standard PNs. It explains how the introduction of predicates and assertions allows developing modules (i.e., generic sub-PNs) in order to build the PNs in a modular way. Then it shows how reliability block diagrams (respectively flow diagrams) may be used as guidelines to build large PNs by using the above modules. It describes the RBD driven PNs which are very effective to model safety systems (e.g. safety instrumented systems) and explains how to extend them to the flow diagram (FD) driven PNs which allow to undertake simplified production availability modeling and calculations. [Copyright &y& Elsevier]

This paper combines universal moment generating function technique with stochastic Petri nets to solve the redundancy optimization problem for multi-state systems under repair policies. Redundant elements are included in order to achieve a desirable level of production availability. The elements of the system are characterized by their cost, performance and availability. These elements are chosen from a list of products available on the market. The number of repair teams is less than the number of reparable elements, and a repair policy specifies the maintenance priorities between the system elements. A heuristic is proposed to determine the minimal cost system configuration under availability constraints. This heuristic, first applies universal moment generating function technique to evaluate the system availability, assuming unlimited maintenance resources. Once a preliminary solution is found by the optimization algorithm, stochastic Petri nets are used to model different repair policies, and to find the best system configuration (architecture and number of repairmen) in terms of global performance (availability and cost). This combined procedure is applied to a reference example. [Copyright &y& Elsevier]

Presents a linear time algorithm to detect modules of a fault tree that is derived from the Tarjan algorithm to find strongly connected components of a graph. Description of a module of a fault tree; Use of modules to reduce the computational cost of basic operations of fault trees; Detection of modules of trees with several hundred gates and events within few milliseconds on a personal computer.

Abstract: The safety and reliability analysis of any system necessarily requires first to model its behavior or its failure logic, and second to assess its performance by using the previously chosen model. Among these performance indicators there is the failure frequency. In spite of its interest, it is not very often used, except in the standards devoted to the so-called functional safety, in which its genuine nature is not always made explicit. A sound method dedicated to the modeling and computing of the failure frequency of periodically tested systems is proposed in this paper. This type of systems comprises components with an availability curve which is discontinuous at deterministic instants. These discontinuities induce, in turn and at the same instants, frequency discontinuities. The impact of the latter on the overall value of the failure frequency is important, but largely unknown and therefore not taken into account in the safety and reliability area, in spite of the fact that it generally induces optimistic estimation, if no compensatory action is planned. The presented method is based on the notion of “critical state” and the use of advanced fault tree models (FT). The results obtained from these models are checked by using Monte Carlo simulation technique supported by equivalent Petri nets models (PN). [Copyright &y& Elsevier]

Abstract: This paper is keeping with the topic of two papers which treated dynamic reliability problems and were presented in previous conferences. Its aim is to confirm the potentialities of a method which combines the high modeling ability of the piecewise deterministic processes and the great computing power inherent to the Monte Carlo simulation. This method is now applied to a simplified but realistic offshore oil production system which is a hybrid system combining continuous-time and discrete-time dynamics. The results thus obtained have been compared with those given by an ad hoc Petri net model for comparison and validation purposes. [Copyright &y& Elsevier]