Support for Diagnosis: Cost of Observation
From DSL
GeNIe allows for entering the cost of observing the value of the current node. The cost of performing a test can be expressed on some scale, e.g., time in minutes. This scale must be used for all costs encoded in the model. The cost can be a combination of three different types of costs: simple costs, conditional costs, and group costs. Each of these different types of cost effect the test ranking in a special way. This is a diagnostic feature of GeNIe, hence Enable Diagnosis option in Network Menu must be checked before you can use this feature, as shown below:
GeNIe uses two factors in evaluating the value of an observation. One is the observation's effectiveness in determining whether a given defect is likely. The other is the cost of performing the test. The cost of performing the test will affect the ranking by the following formula:
ValueOfObservation = CrossEntropy(test) - alpha * cost
where alpha, also known as "entropy to cost ratio," is a user-defined constant that brings the measures of informativeness to a common scale. The formula essentially weights costs and a measure of informativeness (CrossEntropy) linearly with a weighting factor alpha.
After computing the ValueOfObservation for each unobserved test in the model, GeNIe sorts the test according to the decreasing value. Zero cost associated with a test means that there is no cost associated with observation. The effect will be the the test will be ranked only by a measure of informativeness. Simple and conditional costs are for Ranked and Observable nodes. Group costs, on the other hand, are for Ranked nodes set at Unobservable and Auxiliary nodes.
The value of alpha is set in the Diagnostic window by moving the slider in the upper-right hand side of the window. The upper bound of alpha can be modified by typing the new value in the small edit box to the right of the slider.
Simple costs
Simple cost is used when the cost of observing a node is independent of whether other nodes are observed or not. Simple cost is also known as the cost associated with actually performing the test. For example, a simple cost could be the cost of performing a simple test. This cost is set in the Node Properties sheet under the Observation cost tab. Simple costs can also be entered in the Spreadsheet window.
GeNIe models that include observation costs define two overlapping networks. The first is a regular Bayesian network described elsewhere in this document. This network represents the structure of the problem along with uncertainties, encoded by means of probabilities. The second network, is the cost network, can be easily recognized by the fact that all arcs in it are colored red, This network represents the conditional cost structure.
The user can switch between the two networks by using the Show Cost Arcs button [ 
] on the Diagnosis toolbar.
The following changes will occur when the Cost Graph view is invoked:
- . The normal arcs [Dark Blue colored] will disappear between the nodes and the cost arcs [ Red colored ] will appear between the nodes. If the cost arcs are not visible then they are not yet defined.
- . The Arc button [
] changes into a Cost Arc button [ 
].
- . The Cost Arc menu item appears in the Tool Menu.
Connections between nodes can be drawn by means of a corresponding red Cost Arc ( 
) and black normal Arc ( 
) buttons.
Conditional costs
Conditional cost is the cost associated with performing the test where the actual cost for a test node will depend on the state of its parent nodes. For example, if a component is broken and for it to be fixed another component has to be removed, the cost will then be dependent upon both of the components. The cost of measuring some parameter of a locomotive engine depends on whether the locomotive is in the shop or in the field. It may be much lower when the locomotive is in the shop.
GeNIe models that include observation costs define two overlapping networks. The first is a regular Bayesian network described elsewhere in this document. This network represents the structure of the problem along with uncertainties, encoded by means of probabilities. The second network, is the cost network, can be easily recognized by the fact that all arcs in it are colored red, This network represents the conditional cost structure.
Shown below is a cost network for the inspection of the engine of a car:
The node Engine has normal arcs connecting it to the other nodes, but since this is a Cost Graph View they are not displayed. The node Engine Cover has a simple observation cost of 10.
The cost of inspection of the nodes Oil Ruler, Spark Plugs and Battery is dependent upon the status of the Engine Cover.
For e.g. for the Oil Ruler, if the Engine cover is on, then the inspection cannot be done, if the engine cover is off, then the cost of using the Oil Ruler is 5.
Group costs
Group cost is used when several components are all under a few components. A typical example of a group cost is taking a blood sample (the cost of the blood sedimentation rate test incurs the cost of first drawing a blood sample from a patient) or performing a test of an internal part of a locomotive engine (which involves removing the engine cover of a locomotive to access engine parts). Once a blood sample is drawn or the locomotive cover is open, any other tests will incur only simple costs. A group of nodes, with a common group cost can be defined in the Node properties window. Group cost is one time cost associated with performing the first test of a particular group. The group cost node also designates the cost group.
To add a group cost for a node, the user must go to the User Properties tab and Add a property named DIAG_TESTGROUPCOST. This is shown below:
Group costs are entered in a fashion similar to simple costs and conditional costs.
In the figure below, the node Engine Cover is a node that distinguishes the group that is being observed.
The nodes that are the children of Engine Cover will incur the cost associated with opening the Engine Cover. As mentioned, this cost will only be applied to child nodes as long as none of the nodes of that group have been instantiated. Assume that the group cost of opening the Engine Cover is set to 10 units. In the example, the cost of observing the state of Spark Plugs is set at 2 units and the cost of checking the Battery is set at 5 units. As long as neither of the nodes is observed, the total cost of Spark Plugs is 12 units and the cost of Battery is 15 units. If either node, Spark Plugs or Battery, is set to a state, then the group cost will be set to 0 units. For example, if Battery is set to pass, the cost of performing the Spark Plugs test will now be 2 units. The 10 unit cost associated with the node Engine Cover no longer applies.
