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

Computer implementation of Mason\u27s rule and software development of stochastic petri nets

A symbolic performance analysis approach for discrete event systems can be formulated based on the integration of Petri nets and Moment Generating Function concepts [1-3]. The key steps in the method include modeling a system with arbitrary stochastic Petri nets (ASPN), generation of state machine Petri nets with transfer functions, derivation of equivalent transfer functions, and symbolic derivation of transfer functions to obtain the performance measures. Since Mason\u27s rule can be used to effectively derive the closed-form transfer function, its computer implementation plays a very important role in automating the above procedure. This thesis develops the computer implementation of Mason\u27s rule (CIMR). The algorithms and their complexity analysis are also given. Examples are used to illustrate CIMR method\u27s application for performance evaluation of ASPN and linear control systems. Finally, suggestions for future software development of ASPN are made

Decomposition-based analysis of queueing networks

Model-based numerical analysis is an important branch of the model-based performance evaluation. Especially state-oriented formalisms and methods based on Markovian processes, like stochastic Petri nets and Markov chains, have been successfully adopted because they are mathematically well understood and allow the intuitive modeling of many processes of the real world. However, these methods are sensitive to the well-known phenomenon called state space explosion. One way to handle this problem is the decomposition approach.\ud In this thesis, we present a decomposition framework for the analysis of a fairly general class of open and closed queueing networks. The decomposition is done at queueing station level, i.e., the queueing stations are independently analyzed. During the analysis, traffic descriptors are exchanged between the stations, representing the streams of jobs flowing between them. Networks with feedback are analyzed using a fixed-point iteration

Structural characterization of decomposition in rate-insensitive stochastic Petri nets

This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al.~as $S\Pi^2$ nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of $T$-invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its $T$-invariants