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I'm trying to optimize a manufacturing process for work, and was stuck when trying to estimate our confidence in a settings update procedure.

We are trying to configure an instrument setting (x) from a measurement (y) so that y is at our target output mean (within some tolerance level).

I have our target output mean, it's standard deviation (all y(x) have same stdev), the slope between y & x (from multiple regression categorized by instrument), and the sample size during manufacturing.

We've used a TOST Equivalence test to determine if we need to update x to achieve our target y, but I'm curious if there is a way I can determine how likely updating x will actually achieve our target y (again within our tolerance level).

Any suggestions would be much appreciated!

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