Tool wear is common cause. It is a cause intrinsic in the process and can not be eliminated. It affects every part. Special causes arenot intrinsic in the process, and do not affect every part - such as tool breakage, start-up, warm-up, etc. It is non-random - in fact it is a function.
The thinking that tool wear is a "special cause" arises from a narrow view that anything that fails a Western Electric rule is no longer common cause, and therefore special cause. That, however, is only true if a Shewhart chart is appropriate in the first place. With tool wear a a main variation,it is not.
Because variation from tool wear is non-random and not independent, Shewhart charts are not applicable. Their inputs must be random and independent for their statistical requirements to be met.
Never fear, however, since there is a charting methodology that deals with the sawtooth chart and resulting non-normal continuous uniform distribution that arises from toolwear/adjustment. It is the X hi/lo-R chart. It has been around for years and is extremely effective. See CorrectSPC.com !
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Is tool wear a special cause?
No...and I will explain why...