Under a high volume production scenario, we can collect large sample size for process capability study weekly. Then we'd like to track the Cpk trend from week to week to see any special cause for Cpk value.
Does anyone have similar experience for this or it makes sense for that? The concerns from me is how can we get a UCL/LCL for Cpk. Same process as production characteristics? Customer requirement is Cpk higher than 1.33.
Cpk is a manipulation of results, a ratio of SD to average. A real control chart on the characteristic of interest will be more sensitive and allow you to detect and correct changes faster than a chart on Cpk....
Characteristics are monitored with SPC control chart and any OCC signal will be handled on time, and we'd like to have Cpk value reported regularly, e.g. weekly. Then we have many single Cpk and want to have a run chart to see whether there is any patterns.
Before monitoring Cpk, you need to know if it is even applicable to the process. Cpk only applies to bilateral toleranced specifications with a target in the center, and with expected random and independent variation! If the process variation is expected to be a function, such as tool wear, then there should be no change in Cpk over time - since it is determined by the points the process is adjusted between....and that never should change.
I agree with the others from a statistical view, but I'm a visual guy and I'd probably take a few minutes to plot it out and see if anything unusual shows up. It is not a control mechanism, but it may show something that will get you asking some questions.
Or it may be gibberish. I've encountered both. The key (IMHO) is if nothing clearly pops out that is of interest or unexplainable , move on.
So we must assume you are measuring enough parts over time to even bother. And you want to trend this. In some kind of scheme of go back the last n subgroups from today in history and calculate the Cpk. Plot it. Then tomorrow the earliest subgroups fall out of the set replaced by newer subgroups in a "rolling Cpk."
The math could be done. You would be getting a trendable line. But the biggest question is WHY?
Capability is a statistical model that predicts if a process will be capable with a little more to it than just a bunch of shop guys standing around saying "Yep. We think we can hit that tolerance." It's done when a process is new and you don't have a lot of history. And the result is along the lines of "based on the initial sampling, we think we can do this (or not) and here's a metric."
But once it goes into production, you use SPC. At that point, why do you want to predict long term behavior based on small samplings? When you have a model that's been around for YEARS (SPC) that does exactly that.
If you really wanted to get snazzy with long running data on a trend chart, you would want to do it like this:
Pick some sample size: Let's say n=30.
For your last 30 samples you plot the average. Then you calculate your uncertainty based on your sampling size and plot average +/- uncertainy. This will generate a band that you know your mean is within. Then, you can also calculate sigma and you have to decide what sigma level you want to control it to, so let's say for argument you decide on 3 sigma. You take your average + uncertain line and shift it up by 3 sigma and your average - uncertainty line and shift it down by 3 sigma. And between THESE lines, you know that 99.97% of your parts fall within here.
Overlay that against your spec limits and you'd get everything you wanted to know.
Again - you can plot whatever you want, but Cpk is not intended to be a trended number.