1 February 2015
This example explains how an Influence Diagram (ID) is used to select the best time for maintenance on a piece of equiptment.
Assume we are monitoring the health condition of a machine. Based on knowledge about the mean time between failures and a machine degradation indicator, we want to make an optimal decision on the time for maintenance of the machine. The time for maintenance decision depends on the health condition of the machine, which is observed through mean time between failures and the degradation indicator. Once we have made a decision on the maintenance (with some associated cost), the health condition of the machine depends on the condition of the machine before the decision and the decision. There is an utility associated with the machine health condition and the state of the indicators (i.e., mean time between failures and degradation).
The network in Figure 1 shows the graphical structure of an influence diagram. It has six chance nodes (ovals), one decision node (boxes) with the possible decision options and two utility nodes (diamonds) representing utility functions. The chance nodes of the influence diagram can be divided into two groups. One group describes the state of the machine before the decision and the other group describes the state of the machine after the decision on time for maintenance. The state of the machine after the maintenance decision is impacted by the state of the machine before the maintenance decision is made and the maintenance decision itself.
The dependence relations between nodes of the influence diagram are specified using arcs. An arc into a chance node represents a probabilistic dependence relation, i.e. the Machine Health Condition after variable depends probabilistically on the Machine Health Condition before variable and the Time for Maintenance decision. An arc into a decision node specifies that the state of the parent is known prior to making the decision, i.e., when making the decision on time for maintenance, we know the value of Mean time between failures before and Machine Degradation Indicator before. Finally, an arc into a utility node specifies that the corresponding utility function depends on the parent, i.e., the Cost depends on the decision.
The strengths of the dependence relations are defined using conditionality probability distributions in the case of chance nodes and utility functions in the case of utility nodes. With a specification of the strengths of the dependence relations, an optimal policy, i.e., a mapping from observations to decision options, can be identified. The model interface below, gives the user the opportunity to see the optimal decision option based on observations on Mean Time between failures before and Machine Degradation Indicator before. The interface shows the probability of selecting a specific decision option (under the identified strategy) and the associated expected utility (EU).
Below is a set of HUGIN widgets for interacting with the model (click on the probability bar to instantiate a node or remove evidence):
The expected utility is:
As an example, the optimal decision for maintenance is Next Day when observing that the Mean time between failures is Medium and the Machine degradatation indicator is Good.
For further details contact:
on the example: Michael Kempf at Michael-dot-Kempf-at-ipa-dot-fraunhofer-dot-de on IDs: Anders L Madsen at anders-at-hugin-dot-com
Kjærulff, U.B and Madsen, A.L. (2013): Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Second Edition. Springer.