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What is Deming Orthogonal Regression?

Linear regression assumes that the Y values will include measurement error. Deming regression assumes that both X and Y values will have measurement error. It's useful in metrology to determine if two measurement systems at different locations get the same results.

* Included in the October 2024 version of QI Macros *

Deming (Orthogonal) Regression Example

If a supplier makes parts, the customer usually has to inspect the parts to accept them. This leads to techniques such as AQL. Deming never liked the costs of unnecessary inspection. What if the supplier could measure 30 parts and the customer measured the same 30 parts? Deming regression allows us to compare the two measurement methods to determine if they are close enough to consider them a match. If so, the customer doesn't have to inspect each shipment. The parts can go straight "from dock to stock," one expert told me. This is known as "metrology matching."

First, use Gage R&R to determine if the measurement processes at both supplier and customer are acceptable (%R&R < 10%).

1. Destructive Testing: Measure the 30 parts at the supplier and and another 30 at the customer. Collect the data.
   Use lambda = 1 for Orthogonal Regression.
2. Paired Testing: Select 30 parts and label them 1-30. Measure all 30 parts at both supplier and customer. Use Paired t-test to determine variance and lambda (VarX/VarY). If 95% CI contains zero, then no bias. Otherwise, run Equivalence test for 5-10% tolerance.
   
3. Non-Paired Testing: Select 30 parts and label them 1-30. Measure all 30 parts at both supplier and customer. Measure one part 30 times at both supplier and customer. Use XmR charts to determine stability and estimate the error variance ratio (lambda):
   
   
   
4. Select F1:F31, then G1:G31 and run XmR Charts to determine stability. The average range will be used to calculate lambda.
5. Select F1:G31 and run Deming Regression to get lambda for the single part measurements:
   
   
6. You will receive a prompt to select whether the Y values in your data set are in the First or Last Column.
   
7. You will then be given your calculated Lambda results. This macros uses Rbar/d2 to estimate standard deviation. When squared, this yields the variation required to calculate lambda.
   Changing the value in cell I9 will change intercept (B0) and slope (B1).
   
   
   
8. Select B1:C31 and run Deming Regression for parts 1-30.
9. With previously calculated lambdas (0.635 and 1.575 from step 7), manually input each of the results from step 8 (Cell I9) to determine if the measurement systems are comparable. If the intercept is ~= 0 and the slope ~= 1, the supplier system is acceptable:
   
   
   
   *AND*
   
   
   
   Cannot Reject Null Hypothesis:
   If the intercept and slope are within the upper and lower confidence intervals, then the measurement system is acceptable.
   Conditional formatting turns Lower 95%/Upper 95% Green
   
   Reject Null Hypothesis:
   If the intercept and slope are outside of the upper and lower confidence intervals, then the measurement system is not acceptable.
   Conditional formatting turns Lower 95%/Upper 95% Red
10. Establish a long term stability monitor using the artifact parts and measure over time.
    

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