# R&R for Dimension Differences

Six Sigma – iSixSigma Forums General Forums Methodology R&R for Dimension Differences

• This topic has 1 reply, 2 voices, and was last updated 1 year ago by Semoi.
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• #253139

ntmhx
Participant

Hello everyone,

Is it a good practice to apply R&R processes for Delta measurements? We measure 2 (eg A1, A2) dimensions in a part for which R&R is OK (below acceptance limit) but the client wants to perform R&R on the difference of these dimensions. When we perform R&R for differences A1-A2 R&R is not OK. How can I explain to him that by taking the difference of the values I calculate twice the equipment variation. Am I wrong? Is there any documentation to justify this? Is there any other method to perform R&R for differences.

thank you,

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#255784

Semoi
Participant

Hi,
suppose we have two random variables, y_1 and y_2, and that their population mean and standard deviations are mu_1, mu_2, and sigma_1, sigma_2, respectively. Then the standard deviation of the difference y_tot = y_2 – y_1 is given by sigma_tot = sqrt(sigma_1^2 + sigma_2^2) — note that we use a plus (!) in the standard deviation. Hence, the standard deviation has increased. E.g. if we simplify and assume that sigma_1=sigma_2 we have increase the standard deviation by a factor of sqrt(2) \approx 1.4.

If you are unable to follow the math argument just draw random numbers of standard normal distributions and plot a histogram for a single random variable and for the difference of two random variables. You will observe that the later is “broader”.

Hope this helps.

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