Statistical variations in plant models

Plant models, whether based on first principals physics or regression models based on real-world data are a cornerstone of the Model-Based Design controls development process.  During the initial development of the control algorithms a “static” physical model is sufficient; however when the development moves into the diagnostic and release phase physical models that demonstrate real-world variation are required.

Variations, not noise…

In a previous blog, I wrote about the importance of noise in testing.   Variations are different from noise in that they are a constant offset.  For instance, my height will always be 6’3″ while my wife Deborah’s will be 5’10”.  If we design an airbag system assuming everyone was 5’10” then there could be issues when the first 6’3″ person is in the car with an accident.

Working with variations

If we continue the “body variations” example and think of all the variables associated with the body, height, weight, leg length, arm length… we will observe two things

1. There is a correlation between some variables:  In general leg length increases as height increases, as does weight.
2. There are outliers:  While there are general correlations between properties there are still outliers which cannot be ignored.

So given these two considerations how do we proceed?

Data at the boundaries, data in the center

Test data should be defined that includes both data at the boundaries and in the ‘center’ of the test space.  Data at the boundaries exercises the edge cases while the data in the center is used to validate the mainline behavior.  When considering which boundary conditions to include consider the following issues.

1. For discreet variations:  In instances where the variations are discreet, e.g. on/off, flow/no-flow all discreet instances should be included
2. For continuous variations: In the example of height, values at the endpoints should be selected along with a set of points within the range.  (The total number should be a function of what a nominal unit is in the range.  For instance, if we took a height range from 4’10” to 6’6″ and assumed the nominal unit of 1″ then perhaps a spacing of 6″ would be reasonable)

Variations and variations… working with multiple variations

In any real-world system, there are multiple parameters that will vary.  Selecting which combination of variations (outliers and central points) needs to be determined in a rigorous fashion.  In an upcoming post, I will cover how six sigma style approaches can be used to determine which points should be selected.