Measurement Errors & Yield Loss: assigning relative measurement error and computing measurement absolute errors for multiple columns

Question

I want to estimate the absolute and relative error for a yield loss calculation that involves 10 input measurements and 15 output measurements. Think error propagation that you may have learned in chemistry lab... When is calculated yield loss < our measurement accuracy = can be ignored?

Yield.Loss = sum(inputs)-sum(outputs) (this can be 100's of tonnes/month for a large processing facility...)

The measuring devices vary: flow; level; weigh cell. I know the relative error for each measuring device (+/- 0.x%). Then I can calculate what is the lower limit of detection (LOD) for Yield.Loss and then ignore losses < LOD.

I could brute force this by creating a formula that multiplies each measurement by its relative error (hard coded in the formula).

Is there a more elegant solution using column properties or vector multiplication (i am essentially trying to calculate the dot product of the measurements vector and the measurement errors vector for the inputs and the outputs)?

Thanks in advance from rainy Kuala Lumpur!

WebDesignesCrow · Answer

I'm thinking if you can use JSL to perform the formula that refers to different tables for multiplication (Input table x Measuring device table = Output table), the result can be generated much faster for repetitive analysis.

But, I'm not sure if it is elegant.

statman · Answer

" I know the relative error for each measuring device (+/- 0.x%)."  How do you know?  How did you perform these studies?  Is the measurement error consistent?

I don't have any great ideas for you, just remember variances add, not standard deviations.  Your +/- is standard deviations.