Can you share a plot of the residuals that exhibit the non-normal distribution? A histogram and a normal quantile plot would help.

What have your tried in order to transform the data to normal?

How many replicate measurements do you observe? How many items are in your sample? How many instruments are included?

You are trying to show that the mean of the measurements is close to the standard value across the items and intruments? Lack of significance in a test for a difference is not the proper analysis. You might want to use an equivalence test instead.

Since the question is about the measurements, please see Help > Books > Quality and Process > chapters about Measurement System Analysis and Variability Chart might be helpful.

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