5 March 2014. This example is based on (Nielsen & Sørensen, 2009) and (Lauritzen & Nilsson, 2001)
Limid-memory influence diagrams (LIMIDs) are compact and intuitive graphical models for supporting decision making under uncertainty. A LIMID can be used as a knowledge integration tool to represent information from diverse sources combined with an encoding of decision alternatives for the decision making and a specification of the usefulness of decision alternatives (i.e., usually cost and reward functions). As such it can be used to identify (locally optimal) policies for decisions and posterior probability distributions for events and decisions under the strategy encoded by the policies.
Assume we have a piece of equipment used in some kind of production for a specified time frame. As time proceeds the equipment may or may not show signs of deterioration. If the equipment has deteriorated, then we would like to repair it. There is a cost associated with repair and there is a cost if the equipment has deteriorated at the end of the time frame. At three well defined points in time, we need to inspect the equipment and based on the results of the inspection we make a decision to repair the equipment (or not). The challenge is to identify a policy for each decision point. That is, when to repair and not to repair as a function of the result of each inspection. In the example we assume that only the most recent inspection result is avaiable for each repair decision, e.g., at the second repair decision we do not recall the inspecition result for the first decision.
The figure on the left shows the structure of a LIMID that can be used to support reasoning and decision making about this problem. The oval nodes represent chance variables, the boxes represent decisions while the diamonds represent cost functions. The directed edges going into chance nodes describe probabilistic dependence relations, directed edges going into decision nodes specifies the information available at the decision and directed edges into utility nodes represent functionality dependencies.
Below is a set of HUGIN widgets for interacting with the model (click on the probability bar to instantiate a node or remove evidence):
Assume, for instance, that the first inspection shows no signs of deterioration (and the decision maker therefore does not perform a repair) while the second inspection shows signs of low deterioration making a repair the best decision. Assuming you decide to repair at the second inspection, the repair decision at the third decision will depend on the result of the inspection. Notice how the failure cost changes as the model is used to reflect the new knowledge about the decision problem.
For further details contact: 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.
Nielsen, J. J. and Sørensen, J. D. (2009): Bayesian Nnetworks as a decision tool for O&M of offshore wind turbines
Lauritzen, S. L. and Nilsson, D. (2001), Representing and solving decision problems with limited information. Management Science, 47, 1238 - 1251.