Diagnosting with Object Oriented Bayesian Networks.
28 March 2014. This example is based on (Sayed and Lohse, 2013).
Object Oriented Bayesian Networks (OOBNs) are Bayesian Belief networks (BBNs) extended Objects. Objects encapsulate details of a particular section of a BBN. Objects will usually be a part of the BBN which is logically grouped together and separated from other parts of the model. Objects are connected to the rest of the model using input and output nodes while nodes that are neither input nor output variables are not visible to the rest of the model. OOBNs thus imply reusability, encapsulation and abstraction to BBNs which simplify the construction of complex BBNs.
In the following example we show how to diagnose the HAS 200 with OOBNs. For this example it suffices to know that the HAS 200 is a modular multi-station educational assebly system that constitutes three production stations and quality check stations. The final product is boxes filled with three kinds of beans. The system handles each box by moving it from station to station which fills it with each their type of beans. After visiting each station the box is analyzed by measuring its weight and the height of the beans inside the box. If the box has passed all three checks it will be packed and prepared for shipping.
If the box however does not pass one of the quality checks it would be nice to be able to assess the cause of failure. There are three possible causes of a failure. Either the Box is faulty or a handling or measurement error has occurred at one of the three stations.
The OOBN model shown in Figure 2 allows to diagnose such cases. It consists of a global node labelled 'Box' and three objects labelled 'Station1', 'Station2' and 'Station3' respectively. The 'Box' node is connected to the 'Box' input node at each station. It has two states representing whether the box was ok or if it was faulty (labelled 'OK' and 'NOK'). The input nodes at the station are 'Box' and 'PreviousHeight' while the output nodes are 'Handling', 'Feed', 'Height' and 'Measure'. Note that only the input and output nodes are visible at the system wide level which is shown in Figure 2. Figure 3 shows the "internals" of each station. At this level it is possible to see how the nodes are connected and additional elements, namely a node labelled 'Spillage' and an object labelled 'station_measure_1', are visible.
Below the figures is a set of HUGIN widgets for interacting with the model. You can enter observations of 'Weight' and 'Height' at each of the stations by clicking on the green belief bars. Insert, for instance, the observation that at Station 3 the weight was OK, while the Height was not ok (NOK) and notice how the probability of a Handling error at Station 3 has increased to 72.66%. Then change the findings to a situation where at Station 3 the Weight was not ok (NOK) while the Height was OK. Notice how the probabilitie change, in particular the probability that the Box was not ok (NOK) increased to 32.28%.
Global Root Cause
| Box: |
Station 1
Root Causes
| Feed: | |
| Handling: |
Observations
Weight:
Height:
Station 2
Root Causes
| Feed: | |
| Handling: |
Observations
Weight:
Height:
Station 3
Root Causes
| Feed: | |
| Handling: |
Observations
Weight:
Height:
Contact information
For further details contact: Anders L Madsen at anders-at-hugin-dot-com
References
Kjærulff, U.B and Madsen, A.L. (2013) Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Second Edition. Springer.
Sayed, M. S., Lohse, N. (2013) Distributed Bayesian diagnosis for modular assembly systems- A case study. Journal of Manufacturing Systems, 32 (3), 480-488.