Applications of Bayesian networks and Petri nets in safety, reliability, and risk assessments: A review

This paper formally establishes a hierarchy, among the most commonly used types of dependability models, according to their modeling power. Among the combinatorial (non-state-space) model types, we show that fault trees with repeated events are the most powerful in terms of kinds of dependencies among various system components that can be modeled. Reliability graphs are less powerful than fault trees with repeated events but more powerful than reliability block diagrams and fault trees without repeated events. By virtue of the constructive nature of our proofs, we provide algorithms for converting from one model type to another. Among the Markov (state-space) model types, we consider continuous-time Markov chains, generalized stochastic Petri nets, Markov reward models, and stochastic reward nets. These are more powerful than combinatorial-model types in that they can capture dependencies such as a shared repair facility between system components. However, they are analytically tractable only under certain distributional assumptions such as exponential failure- and repair-time distributions. They are also subject to an exponentially large state space. The equivalence among various Markov-model types is briefly discussed. >

Power-hierarchy of dependability-model types

Purpose – To help the maintenance managers/decision makers to select a suitable maintenance strategy for the components/parts associated with the system.Design/methodology/approach – An approach based on fuzzy linguistic modeling is used to select the most effective and efficient maintenance strategy. Three input parameters, i.e. historical data (I1), present data (I2) and competence of data (I3) related to failures of a component (gears), were taken to judge the effectiveness of the nature of maintenance strategies. These parameters are represented as members of a fuzzy set, combined by matching them against (if‐then) rules in rule base, evaluated in fuzzy inference system (Mamdani, min‐max type) and then defuzzified to assess the capability or effectiveness of maintenance strategy.Findings – The results show how the fuzzy logic approach translates vague, ambiguous, qualitative and imprecise information into numerical/quantitative terms, which helps to identify the most informative and efficient maintena...

FLM to select suitable maintenance strategy in process industries using MISO model

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

Preventive maintenance (PM) is an effective approach for reliability enhancement. Time-based and condition-based maintenance are two major approaches for PM. In contrast, condition-based maintenance can be a better and more cost-effective type of maintenance than time-based maintenance. However, irrespective of the approach adopted for PM, whether a failure can be detected early or even predicted is the key point. This paper presents a failure prediction method for PM by state estimation using the Kalman filter. To improve preventive maintenance, this study uses a hybrid Petri-net modeling method coupled with fault-tree analysis and Kalman filtering to perform failure prediction and processing. A Petri net arrangement, viz, early failure detection and isolation arrangement (EFDIA), is used; it facilitates alarm, early failure detection, fault isolation, event count, system-state description, and automatic shutdown or regulation. These functions are very useful for health-monitoring and preventive-maintenance of a system. This study implements EFDIA to an application-specific integrated circuit on a Xilinx Demonstration Board. A condition-monitoring system of a thermal power plant is used as an example to demonstrate the proposed scheme. Linking the Kalman filter to the EFDIA Petri net, a condition-based failure prediction and processing scheme has been completed for preventive maintenance. This paper presents a failure prediction and processing scheme for PM via the thermal power-plant example, by using a hybrid Petri net modeling method endowed with fault-tree analysis and Kalman filtering. The FPN (Petri net dealing with system failure) has to be constructed beforehand. The next step is to obtain control charts for all fault places in the FPN in order to prescribe thresholds and increment times for every step in Kalman prediction. Afterwards, the system model of each place in the FPN must be derived to perform Kalman filtering. With these prerequisites, this method can be applied to any system. The proposed Petri net approach not only can achieve early failure detection and isolation for fault diagnosis but also facilitates event count, system state description, and automatic shutdown or regulation. These capabilities are very useful for health monitoring and PM of a system. Since the triggering signal of S/sub i/ place of the EFDIA in Section IV (S/sub i/ is a place for the Kalman-predicted indicator value of the sensing signal for the Petri net dealing with system failure) indicates that subsystem #i performance is going to reach the prescribed failure threshold, the signal can be provided via the Kalman filtering method in Section III. Linking the Kalman filter to the EFDIA Petri net, a condition-based failure prediction and processing scheme has been completed for preventive maintenance.

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A condition-based failure-prediction and processing-scheme for preventive maintenance

The use of Petri nets to represent fault trees is discussed. Using reachability and other analytic properties of Petri nets, a more general and useful method to study the dynamic behavior of the model at various levels of abstraction is examined. The problems of fault-detection and propagation are discussed. For simplicity, only coherent fault trees are considered. However, the representation and analysis techniques are general and can be used for noncoherent fault trees. >

J.W. Atwood

Papers

The use of Petri nets to analyze coherent fault trees