# Measurment model correlation

#### metrologist01

##### Registered
Hi Everyone!

I'm studying measurement uncertainty. I'm confused with a pretty basic measurement model that features correlated input variables. Can someone help me?

Setup:
Let's say I have a tape measure from ACME tape. It came with a calibration cert that says it reads with a systematic error of 0. But the standard uncertainty in this systematic error is 1mm. Possible values of systematic error are normally distributed.

I have been tasked with measuring the length of two easy to measure things and adding them together to get a total length. We will call these objects item 1 and item 2.

Here is my initial measurement model:
Y = X1 + X2 where X1 is the tape reading for the length of item 1 and X2 is the tape reading for the length of item 2, and Y is the desired total length.

For the sake of the example, let us say there exists only two sources of uncertainty for the inputs. The first is the systematic error of the tape measure described on the calibration certificate, and the second is common random measurement error with no identifiable cause.

As I understand it, the two inputs X1 and X2 are correlated by the systematic error of the tape measure that is used for both length measurements.

Question:
How can I reformulate my measurement model to eliminate the correlated inputs and replace them with independent inputs? (Such that I can make use of the easier version of the Law of Propagation of uncertainty that does not require the additional terms for correlated inputs.)

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