Stevenli said:

Sometimes we can't collect the equipment data, then we have to collect the data from the production characteristic to calculate the Cmk.

Steven,

I haven't clearly understood what you mean by this statement. I believe Cmk pertains to machine capability and the data does come from a production characteristic for which specs or tolerance limits would be defined. you need to ensure that the variation in the process is due to machine alone.

Cmk is calculated just as Ppk. The idea is that you must do what you can to exclude every source of variation except the machine itself (same operator, same gauge, same enviroment, same raw material, nearly same time). To do so, the ussual procedure is to let the process stabilize and then collect the sample with all consecutive parts. Be careful, you shold keep the right order and avoid mixing the parts to assure that the subgroups are actually in the same order as their parts where produced. In that way you can plot a control chart, asses for stability, and calculate Cm/Cmk just as if it was Pp/Ppk.

A lot of confusion exists about capability metrics because different companies use different symbols to define various facets of capability. Before you can truly understand what a particular index means, you must look at its formula as well as how the data are supposed to be collected for its calculation.

Having given that disclaimer, the Ppk index is typically used to measure short-term process performance capability. The formula is as follows:

Ppk = Minimum (Ppl, Ppu)

where Ppl = (mu - LSL) / (3 sigmaST) and Ppu = (USL - mu) / (3 sigmaST)

Here, mu is the process average (estimated from X-double bar) and sigmaST is the short-term standard deviation, estimated from RMS formula.

I have seen the Cmk index defined in two different ways. In the first, it is used to measure machine capability (the "m" stands for "machine"). Its formula is similar to the one given above for Ppk, but the data used to estimated mu and sigmaST come from a special study conducted in such a manner as to focus on only process variation originating from the machine under study. Thus, the same operator would be used for the entire study, the same batch of material, the same setup, etc. Be aware that some companies will replace the 3 sigmaST with 4 sigmaST.

In the second definition I have seen, Cmk is used to quantify the performance of a measurement system, so here the "m" stands for "measurement." Again, its definition is similar to that given above for Ppk, but the data come from a properly conducted gage study. To further complicate the issue, some companies use 5 sigmaST in place of the 3 sigmaST that is normally used.

As you can see, to really appreciate the difference between any two capability metrics, you must first obtain the formulas and then an understanding of how the data are to be collected. Without knowing this, there really is no way to correcttly answer the question "What's the difference between Cpk and Cmk?".

By the way, I have also seen the following indexes: Cm, Cpm, and Cpmk !

Hope this helps.