Process Capability (Quality Insider)

by Douglas C. Fair

May 2007

Frequently I hear discussions among engineers, managers and higher-ups concerning process capability, an alphabet soup of indices and three-letter designations. The indices are bandied about as though a single number communicates knowledge, understanding and certainty. My experience is that this is simply not the case. In fact, I have come to the depressing conclusion that most people are confused as to how capability indices should be used and what they truly mean.

"Say, what's the capability of that part?" I cringe when I hear this question and its related variations. But I shake my head and wonder about the future of our planet when I hear someone answer quickly with a single-number response.

When overhearing capability discussions, I have found that critical issues are simply not a part of the conversation. Issues that seem obvious to me, like to which process the capability index refers, are often ignored. When evaluating capability, one simply cannot separate part capability from process capability. That is, a part's capability index is dependant upon the machine, or process, from which the part was made. I find it curious that the very thing that SPC helps to control, the Process, is rarely, if ever, considered when discussing capability. So before even beginning a discussion on capability, you must consider a minimum of three distinct and very important items:

  1. The Part (Part number, SKU or manufactured product) of interest.
  2. The Feature (width, weight, diameter, etc.) that is evaluated on the part.
  3. The Process (machine) that produced the part.

Every capability index, whether explicitly stated or not, is a product of (and is different based upon) the three items above, and while reporting capability for a Part and Feature seems second nature, it is the Process that is typically forgotten. Therefore, make certain that any capability index discussions include the Process along with the Part and Feature.

This approach might seem obvious as you are reading it, but in almost all capability discussions and within almost all statistical software products, the Process is either forgotten or simply not considered. So, when discussing capability, keep these three items in the forefront while asking the questions found below. Know that when someone asks you, "What's the capability of that part?" that the question itself is erroneous. What they really should be asking you is "What is the capability of that Part for Feature ABC when it was made on Process XYZ?"

  1. Which capability index do you want?
    Lots of choices here, folks. Most of us have heard of Cp, Cr, Cpk, Ppk, Pp, Pr, Cpm, Ppm and others. But, hey, let's keep it simple. The most commonly discussed capability indices these days seem to be Cp, Cpk, Pp and Ppk. I won't go into the mathematics for each, but Cp and Pp can be considered "process potential" indices while Cpk and Ppk are better described as "process performance" indices. Cp and Cpk use a short-term estimate of standard deviation in their denominators while Pp and Ppk use sample standard deviation as a long-term estimate.

    Each of these indices has subtle, important differences when compared with the others. If you ask your questioner which capability index he wants, the right answer should be, "several." When asking about capability, one should expect to hear at least three different indices.

    If I were king and could require certain indices to be quoted, they would be Cp, Cpk and Ppk. This way, I can understand the actual process capability (Cp). Plus, by comparing Cp and Cpk, I would know about process centering. Then, I would compare Cpk and Ppk, to determine if the short-term and long-term standard deviations are different.

    But, the bad news is that just three numbers is simply not enough. The following two questions are extremely important (much more so) than receiving information concerning three capability indices. I cannot overemphasize the importance of the following two questions. Without asking them, you could be completely in the dark, even with answers to this first question.
  2. For which Process do you want capability?
    We can't discuss capability of just a part without talking primarily about the machine (process) on which it was made. For example, a single part may have a hole whose diameter is cut to a specific dimension. The same part, however, might be run on different machines. Unfortunately, each machine has its own "personality." That is, more likely than not, each machine operates a bit differently than others.

    As I have seen many, many times, this is true even for the same model machine made by the same machine manufacturer. Even if two machines are identical, they always operate a little differently. Again, each has a unique personality. These common differences in machine performance require capability indices to be quoted for each machine that made the part. And it should make sense, given that the "P" in SPC stands for "process."

    Continuing with our example, the same part number and the same hole might be cut in several different operations. The first operation might be a rough cut of the hole using a drill press followed by a higher precision boring operation, then followed finally by a honing operation. In this example capability indices would need to be reported for three different operations for the same part and part feature.

    To complicate matters, there might be several different machines that can perform the identical manufacturing operation. Take the boring operation for example. There might be 4 different boring machines for boring the same hole on the same part. Guess what? Because each machine's mean and standard deviation (its "personality") is different, you will need to ask for capability indices separately by machine - even if those machines are "identical." Never assume that two identical machines, separated solely by serial number, will perform the same. They won't. So make certain that you inquire about capability indices for each process that manufactures your parts.
  3. Would you like a control chart to go with that?
    Yes, I know that this question sounds eerily similar to what you might hear from your local burger joint's teenage cashier, but stick with me on this. Basically, I have rarely, if ever, heard capability discussions where control charts are considered.

    Think about it. The last time you discussed a Cpk value, did anybody whip out a control chart and talk about mean and standard deviation? Was there any discussion or consideration given to process consistency with respect to central tendencies and variability? If your experiences have been similar to mine, then probably not. However, I applaud the person who answers, "why of course, we always evaluate control charts when discussing capability." If you are that person, then kudos to you. Unfortunately, this is, indeed, a rare event.

    Why would someone want to display a control chart in a capability discussion? Answer: As evidence of consistent means and standard deviations. Without consistent, statistically non-changing means and standard deviations, Cpk values mean little. Why? Because without a consistent control chart with an unchanging mean and standard deviation, it is impossible to reliably predict what those statistics might be in the next week. Or the next 24 hours. Therefore, with a mean and standard deviation that is unpredictable, Cpk values could likewise be significantly different from one hour to the next, rendering the reported Cpk as an unreliable, inconsistent number itself.

Conclusion
The more personality in us humans, the better. Not so with manufacturing processes. Striving to understand those personalities via capability indices and control charts allows previously unknown process information to be uncovered. By doing so, quality professionals have the ability to pinpoint process improvements and take the personality out of manufacturing. By asking the three questions above, you should be much better equipped to understand process capability and much better prepared to answer the inevitable question, "Say, what's the capability of that part?"

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