Sensitivity Analysis and Parameters

The graphical model of the Low Pressure Coolant Injection system contains many critical assumptions. In particular, it assumes:
  1. We have enumerated all the failure modes for each subsystem,
  2. The failure rates for each component is as stated, and
  3. The components fail independently.
We may want to assess the sensitivity of our results to these and other assumptions. This process is known as sensitivity analysis.

In this example, we will look at the first two kinds of sensitivity analysis. In both cases, they can be expressed as sensitivity to parameters of the graphical model. The third case requires us to study sensitivity to changes in the structure of the graphical model. The common-cause failure example shows how to make these kinds of changes.

Parameters

Graphical-Belief allows you to attach parameters to any rule (or the model itself). The values in the probability tables for a rule depend on the values of the parameter. For example, the "Lpci-Sys-And" rule is actually, a noisy-and rule. It has two sets of parameters: (:support-if-true :true), (:support-if-true :false); and (:support-if-false :true), (:support-if-false :false). The :support-if-true parameter set gives the probability distribution for the system variable given that the condition holds (i.e., both subsystems have failed). The :support-if-false parameter set gives the probability distribution for the system variable given that the condition does not hold (i.e, at least one subsystem is working).

The first assumption is that we have enumerated all failure modes for the system. If that assumption does not hold, then there will be a small probability of failure for the system even if one of the subsystems is working. This the the parameter (:support-if-false :true). We can study sensitivity to the assumption that we have enumerated all failure modes by varying this parameter.


Figure 1. Graphical Model for Low Pressure Coolant Injection System with no parameter changes (directed graph view).

To study sensitivity to this change, we open a parameter editor on the "Lpci-Sys-And" rule. We change the probability of failure if the condition is false from 0 to 0.01. We can then observe the change in the probability of system failure.

Probes Continue with this example and see how to use probes to monitor changes to a model.

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Last modified: Fri Aug 16 14:49:53 1996