Quantitative evaluation of Pandora Temporal Fault Trees via Petri Nets

© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Using classical combinatorial fault trees, analysts are able to assess the effects of combinations of failures on system behaviour but are unable to capture sequence dependent dynamic behaviour. Pandora introduces temporal gates and temporal laws to fault trees to allow sequence-dependent dynamic analysis of events. Pandora can be easily integrated in model-based design and analysis techniques; however, the combinatorial quantification techniques used to solve classical fault trees cannot be applied to temporal fault trees. Temporal fault trees capture state and therefore require a state space solution for quantification of probability. In this paper, we identify Petri Nets as a possible framework for quantifying temporal trees. We describe how Pandora fault trees can be mapped to Petri Nets for dynamic dependability analysis and demonstrate the process on a fault tolerant fuel distribution system model

Analysis of Probabilistic Basic Parallel Processes

Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates other processes according to a probability distribution. We study the decidability and complexity of fundamental qualitative problems over probabilistic BPPs -- in particular reachability with probability 1 of different classes of target sets (e.g. upward-closed sets). Our results concern both the Markov-chain model, where processes are scheduled randomly, and the MDP model, where processes are picked by a scheduler.Comment: This is the technical report for a FoSSaCS'14 pape

Impact of Improving Machines’ Availability Using Stochastic Petri Nets on the Overall Equipment Effectiveness

The objective of this chapter is to demonstrate the robustness of stochastic petri nets in the field of maintenance for the improvement of machine availability. We aim to present the modeling of the maintenance function in a production site with stochastic Petri nets by using two performance indicators: the mean time between failures (MTBF: the time between two successive failures) and the mean time to repair (MTTR: average time to repair) to improve the equipment performance. The determination of the distribution law is essential for each statistical study and provides a powerful and reliable model for the evaluation of the equipment performance. After determining these laws we switched to modeling Petri nets, we proposed the establishment of an effective preventive maintenance plan which aims at increasing the reliability, thus reducing the probability of failures. Consequently, we increase the machines’ availability and then the overall equipment effectiveness

Bayesian network semantics for Petri nets

Recent work by the authors equips Petri occurrence nets (PN) with probability distributions which fully replace nondeterminism. To avoid the so-called confusion problem, the construction imposes additional causal dependencies which restrict choices within certain subnets called structural branching cells (s-cells). Bayesian nets (BN) are usually structured as partial orders where nodes define conditional probability distributions. In the paper, we unify the two structures in terms of Symmetric Monoidal Categories (SMC), so that we can apply to PN ordinary analysis techniques developed for BN. Interestingly, it turns out that PN which cannot be SMC-decomposed are exactly s-cells. This result confirms the importance for Petri nets of both SMC and s-cells.Fil: Bruni, Roberto. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Montanari, Ugo. Università degli Studi di Pisa; Itali

Mechatronic system reliability evaluation using petri networks and PHI2 method

In this paper, we propose an approach allowing us to study the performance of a mechatronic system using Petri Nets in which we use particularly the PH12 method for the evaluation of failure probability of a mechanical component. The Petri Nets are used to describe the process of sequential dynamics of a system. Deterministic stochastic Petri networks have been implemented to introduce random phenomena following the laws of distribution. After the functional and dysfunctional modeling of a mechatronic system using Petri Nets, it is necessary to associate times to different transitions of the network. It is necessary to take into account a physical modeling in order to determine functional times of different components which are associated with functional transitions. Regarding dysfunctional transitions, the laws of probability are assigned depending on the knowledge concerning the reliability of different types of components: the exponential law for electronic devices, the Jelinski-Moranda model for software, etc. For the mechanical components, we use the PH12 method for the evaluation of the time variant failure probability

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

The derivation of performance expressions for communication protocols from timed Petri net models

Petri Net models have been extended in a variety of ways and have been used to prove the correctness and evaluate the performance of communication protocols. Several extensions have been proposed to model time. This work uses a form of Timed Petri Nets and presents a technique for symbolically deriving expressions which describe system performance. Unlike past work on performance evaluation of Petri Nets which assumes a priori knowledge of specific time delays, the technique presented here applies to a wide range of time delays so long as the delays satisfy a set of timing constraints. The technique is demonstrated using a simple communication protocol