This is where black box theoretical statistics goes horribly wrong. Look at the histogram. That tells you what you need to know in this case. That process is great. At least for the time frame in which you sampled. The disparate points that likely broke ‘normailty’ are trivially small. The goal is to make good parts not to make good p values. Sorry about your customer. Perhaps try talking to them. Even the American statistical association has finally acknowledged the weaknesses and century long misinterpretations regarding the p value.
The manipulation of mathematical formulas is no substitute for thinking.
Yes, the out of control points are trivially small as you’ve put it, my goal in pointing this out is to encourage viewing and interpreting the process behaviour in the first instance. Looking at histograms gives you an idea of elbow room but tells you nothing about behaviour.
Yes, the effect is small but it gives a legality to the indexes and that’s the correct and proper order of data analysis. I’m guessing that the customer in this instance ignores behaviour and pays homage to minitab.
Proud Liberal - the low p value is only an indication the data used in your study do not follow a "Normal" distribution as Steve alluded to. But there is no magic to a Normal distribution. Minitab allows you to calculate a Cpk value for the distribution at hand. (NOT that I'm advocating for Cpk I still know that it's an abomination. There is nothing 'legal' about the indexes as there is no such thing as a Normal distribution, which real statisticians have been saying for a hundred years.) but I recognize that the Customer is probably a black box thinker). There is more value in understanding if your process is stable - via the control chart AND knowledge of the physics of the situation. In this case your Customer may not care about the control chart given their obsession with the useless p value. If they do it would be good to understand the 4 disparate values, there may be a solid reason for their appearance that is not related to a lack of REAL control. and this where the histogram comes in. I'm usually all about the time series plot of the data as it contains the most information, but a control chart that has no comparison to the specification is missing a critical element. in this case the real point is that the process variation is so small compared to the specifications that the trivial non Normal variation is irrelevant. Remember that statistical significance doesn't mean practical importance.
I think you have several avenues of relief. You could understand the 4 points control for them and redo the study (a waste of useful time but it might get your Customer to go annoy someone else). Or you could talk to your Customer quality rep and discuss the situation as we've laid it out here...
Yeah, that customer needs some statistical training. A normal distribution on a lathe means it is either out of control or has a lot of measurement error. Your data looks like measurement error. Hi/lo measurement for that diameter on each part diameter would be more appropriate to reduce that. Should show a steady rise in OD as the tool wears. That would prove that it is running well and Cpk and Ppk do not apply - continuous uniform distribution. (Kooky new idea for the customer - read the books. Cpk and Ppk do not apply to non-normal distributions) Also, double-check the errant part.