Calculation control limits

That formula is just dumb. If I am interpreting you correctly someone thinks that if they guardband the process specification to make correction when a value exceeds the 75% limit then the process will have a Ppk of 1.33 because IF they could correct the process then the ratio of the specification range to allowed (forced) process spread is 4/3 = 1.33. That formula that multiplies 1.33 x 75 is STUPID and meaningless. It is known as fake math or jabberwocky. The only way to visually see capability is to plot the individual values against the specification limits in a histogram or better yet a run chart. period.

If I gave you my email that would be consulting and I charge $1000 an hour. You are better off posting here for free input.

And yes if you have out of spec parts you need to investigate to determine root cause and improve the process.

If you really want to understand all of this I suggest you start reading the articles by Donald Wheeler at the SPCPress.com website.

 

You can use the average moving range to calculate these capability indices for any sample size. Leaving aside the value of these indices and focusing on the math, the problem lies with the confidence intervals surround these indices. These are calculated using a mean value (with its confidence interval) and a standard deviation (with its own confidence interval). So you are using two numbers with an uncertainty about their true values to calculate another number. I ran a simulation using sample sizes of 7, 30 and 100 then calculated the capability indices and their confidence intervals. I generated random, normally distributed data with a mean = 0 and a standard deviation = 1 then used spec limits of +/- 4, so that the Pp/Ppk should = 1.33. I also used the average moving range to calculate the indices. See the results below. Note how wide the confidence interval of each index is for the smaller sample sizes.