I am using Minitab to evaluate the capability of a compounding process. The compound consist of 4 materials and is analysed after production by ashing. Three of the materials would have ~0% ash and the fourth ~100% if analysed independantly. Target ash values for the compound are 69% and the specification is 67% to 71%. This year we have produced ~315 lots of this material and have perfomed ash testing on each drum of material produced. The lots are based on recieved lots of one of the raw materials and varyi in size from 1 to 8 drums.

When I put all this into Minitab and group by lot, I get a Cpk value of 1.72 and a Cpm of 0.79. Minitab's help indicates that a difference between Within and Overall capability is an indication that the process is not in control. I am wondering if I can take this a step further. Because by within group is based on a lot of product and this is based on a lot of raw material. Can I infer that a significant part of my variability is due to raw material variability and not the compounding equipment itself?

Of course you can assume that the overall variability is raw material variability. This is easy to confirm as you can do control charting on the ash content of the one raw material that sets the compound lot. The within lot variability (Cpk) is truly the process capability since it measures the short term variability, and does not include any raw material lot variability.

How does the Cpk or Cpm look if you used only 50 lots or 100 lots? I venture to say that you might be surprised to see the Cpk does not change much, but the Cpm might. This is because process drift might be slow, but significant over a long period of time.

Steven:

Thank you, Indeed you are correct when I use fewer lots the Cpm does shift more than the Cpk. Your suggestion to plot the Ash values of the one material that contributes most to this result was considered. Unfortunatly, I only started a few weeks ago and my company has not been recording that data. I think that we will in the future?

Can the data be further subgrouped (smaller than lot size groups)?

bmccabe:

I can group the in any way you want. By lot seems to make the most sense as each lot corisponds to a different raw material lot. Some lots only have 1 drum. Why do you ask?

At the risk of starting a war :rolleyes: ... Sub-grouping is inversely proportional to CPn PPn ‘s

Instead of sub-grouping by lot, use the same data and subgroup by drum. ,,I'll bet the CPm gets higher.

I only have one data point per drum. So I used a moving range of 2. Cpm does not budge (0.79) Cpk shifts from 1.72 to 1.83. I am not sure I know what that means. Danger of using tools that you do not completly understand.

Try looking at the variation by classifying it as Within-subgroup vs Between-subgroup variation.

When you plot the data as one measurement per barrel as a subgroup on an I/MR chart, your within-subgroup variation that forms the moving range contains barrel-to-barrel (and possibly lot-to-lot) variation, machine cycle-to-cycle variation AND measurement error. The Between subgroup variation includes variation introduced by time such as setup to setup, lot-to-lot variation, etc.

As you change your subgrouping to averages of increasing size, you move the sources of Between subgroup variations into the Within subgroup variation. You can play with your subgroup size by conciously choosing what sources of variation to include in the Within-subroup variation and evaluating the Xbar/R charts.

At some point, the Rbar will jump much higher than the increased sample size would warrant. In addition, the Xbar plots will appear to hug the center line because the Xbar control limits have suddenly inflated. This tells you that the Between subgroup variation that you just moved to within subgroup variation is a (the?) major source of variation. If your data appears this way on the I/MR chart, you need to immediately check your measurement error (a good idea in any case), then the other sources of within subgroup variation.

Evaluating the data in this fashion will tell you much more than the Cpk/Cpm.