What about using that approach for SPC? At least one article is HERE about it:
Bayesian Statistical Process Control
and some dispute is HERE:
Why isn't bayesian statistics more popular for statistical process control
Note there is a "Bayesian statistical process control chart"...
In my experience we often do not have too many data to be used for mean, UCL and LCL calculations, so based on "An Application to Bayesian Methods in SPC":
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