Indium Blog

Process Capability: Cpk and Cpu in Relation to Purity of Compounds from Indium Corporation

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  • Phil Zarrow: Robert, the industry standard for process characterization is Cpk, and sometimes Cpu; Dr. Lasky has discussed this as it pertains to assembly processes. With regard to materials, sometimes a normal distribution is not upheld. What do we do?
    Robert Ploessl: Excellent question. Process engineers love Cpk, because it's a single number that encapsulates process capability. However, when you deal with materials, especially impurities in those materials, you have to be aware of a couple of things. The material, the compound, that we manufacture is not manufactured to hit a certain impurity level. The impurity is not really a product performance specification that we're trying to manufacture to. An impurity is, of course, something that you're trying to get rid of.
    Phil Zarrow: Right.
    Robert Ploessl: There is no lower level that is best. You want to control the upper level, which explains the "u" part, of the Cpu part.
    Phil Zarrow: Right.
    Robert Ploessl: In addition to that, the distribution of impurities is usually non-normal. It's usually skewed toward the high end of the scale. On top of that, something happens on the left end of your data set, because you're dealing with detection technologies that always have a limit of detection. A limit of detection then introduces what statisticians call a “censoring of the data,” so you're dealing with left-censored data.
    You have a data set that, for instance, says we measured against an impurity like iron. Our detection limit is less than 1ppm. Out of your production line comes lot after lot, and in some of those you will measure less than 1ppm, because it's the detection limit.
    Phil Zarrow: Right.
    Robert Ploessl: If you then think about the distribution of your data set, that left-censoring now will make the distribution look decidedly non-normal. You will have this large bar at the left end, and you will have some kind of distribution above that. You can't just calculate a mean and a standard deviation, and plug it into the Cpk or Cpu formula, and expect that that value will really make sense.
    Sometimes, we need to educate customers on the effects of this distribution on this value. Sometimes, of course, we deal with customers; they have excellent process engineers that are well-educated in these problems.
    Phil Zarrow: Right.
    Robert Ploessl: We are very, very willing to work with our customers in working through the data set, and working towards what are sensible process capability indicators. They, of course, always depend on the specification of the customer. There is no “one-size fits all.” It's the voice of the customer that comes in, and it gets matched up with the voice of our process; and, of course, they have to work together.
    Phil Zarrow: Right, and as you said, this could present a real quandary for the customer. How would you recommend they proceed?
    Robert Ploessl: Dialogue and conversation. We love it when customers approach us about these specific issues. It's always best to start the conversation in person on these issues. Customers are always welcome to contact us via email or call me. Of course, our website, has a treasure of data and papers on process control issues by Dr. Ron Lasky. I would invite anybody to read the many, many papers he's written on these issues and understand process capability better.
    Phil Zarrow: Robert, thank you very much.
    Robert Ploessl: You're welcome.
    Phil Zarrow: It's a pleasure.