**Re: To Error or Not to Error**
Yes we do that. When I multiply the equation by 2 is (I think) for having two variable inputs (machined and coating) and their respective measurement uncertainty values. For example, machined diameter is 1.0000 +/-0.0002 (5.15 x total gage error Standard Deviation) and the coated diameter is 0.9900 +/-0.0002 (same gage same error). If I need to have our coater at a minimum diameter to ensure a calculated thickness does meet at say a 95% confidence level, then I need to add twice the gage error to the print tolerance of minimum 0.0015 inch coating thickness. Gage error forces us to be over that thickness by some thickness for us to make a garrentee of that. Hope this helps.

Hi Brad

You need to add the variances, not the standard deviations.

Standard deviation of measurement 1 = S1

Variance of measurement 1 = S1^2 (S1 squared)

Standard deviation of measurement 2 = S2

Variance of measurement 2 = S2^2 (S2 squared)

If you add or subtract the measurements, the total (1 standard deviation) error in your result will be:

square root(S1^2 + S2^2)

This is the combined uncertainty of the calculation (measurement 2) - (measurement 1)

Also, you are using the wrong multiplier. The 5.15 value, I guess, is from the MSA manual. The above calculations give you the calculated thickness (let's call it T) and the total (1 standard deviation) error (let's call it S).

The estimate for the thickness is T+/- S.

Because this calculation uses 1 standard deviation, this would give you a 67% confidence interval. If you wanted about 99% as a confidence interval, you would use T +/-1.96S.

If you use T+/- 5.15S, I don't know what confidence interval this would give you, as I don't have tables that go out that far. As it is in the area of "six sigma", it would give confidence intervals in the area of 99.999?? %.

However it may well be wise to use a much bigger multiplier than 1.96 for safety. As Michael_M has said, you don't know how symmetrical the coating is and all you are accounting for is the gauge error.

NC