Graphical-Belief in Action

The following example illustrates the main ideas of Graphical-Belief.

This example is a emergency Low Presure Coolant Injection (LPCI) system analyzed by Martz and Waller [1990]. In the case of a loss of coolant accident, the two motor operated valves (MOVs) should open and the four pumps should add extra coolant (water) to the reactor. All six of these components are protected by Check Valves (CVs). The reactor will successfully respond to the accident as long as at least one of the four pumps in delivering water to the system.

Figure 1. Graphical Model for Low Pressure Coolant Injection System.

Figure~1 shows the graphical model corresponding to this system. The nodes (oval shaped boxes) in the graph represent the states of components and subsystems in the LPCI. The square boxes are rules which define the probability distribution of the output variable given the input variables. Note that we can derive these probability distributions in many ways, either from logical rules (for example, and-gates and or-gates), directly from tables, or from another graphical model.

This is a rather simple model: all of the variables are binary and there are no loops in the graph. Graphical-Belief can analyze more complex models, but this simple example can still illustrate many of its features.

Using the data from Martz and Waller [1990], the risk of a failure of the Loss of Coolant System during an accident is 0.000004.

But "What is the overall risk of system failure?" is not the most interesting question we can ask. Graphical-Belief can answer the following kinds of questions:

Diagnosis and Importance Analysis. Find out which components are most likely to cause a system failure.

Sensitivity Analysis. Explore the implication of critical assumptions on the system failure rate estimates. This topic also shows how the object oriented model construction procedure simplifies the analysis.

Parameters and Data. Graphical-Belief can represent complex dependencies among probabilities using a parameter network. This example explores how this simplifies the analysis of this model.

Model Construction. Explore the implication of loops in the graphical model. This example also shows how the model construction features work.

Valuations. Graphical-Belief can use many representations of uncertainty, including probability and belief functions this example explores a few.

Evidence and Explanation. Graphical-Belief contains some powerful test selection capabilities based on the idea of weight of evidence. This example explores a few.

Back to overview of Graphical-Belief.

View a list of Graphical-Belief in publications and downloadable technical reports.

The Graphical-Belief user interface is implemented in Garnet.

Get more information about obtaining Graphical-Belief (and why it is not generally available).

get the home page for Russell Almond , author of Graphical-Belief.

Click here to get to the home page for Insightful (the company that StatSci has eventually evolved into).


Martz, HF and RA Waller [1990]
``Bayesian Reliability Analysis of Complex Series/Parallel Systems of Binomial Subsystems and Components.'' Technometrics 32, 407--106.

Russell Almond, <lastname> (at)
Last modified: Fri Aug 16 18:24:19 1996