Process Capability

Three questions you must ask

Published: Monday, June 25, 2007 - 22:00

I frequently hear discussions among engineers, managers, and higher-ups concerning process capability, an alphabet soup of indexes and three-letter designations. The indexes are bandied about as though a single number communicates knowledge, understanding, and certainty. My experience is that this is simply not the case, and I have come to the depressing conclusion that most people are confused as to how capability indexes 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. 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, such as 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 dependent 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 import items:

1. The part (part number, stock-keeping unit, 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 has differences based upon—the three items above, and although reporting capability for a part and feature seems second nature, it is the process that is typically forgotten. Therefore, be sure 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?,” 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 by process XYZ?”

And for heaven’s sake, even if the question is correctly stated, don’t answer it with a number. Instead, answer it with three important questions. These questions will help clarify capability-index queries, uncover meaningful process-capability information, and, quite likely, befuddle your hapless questioner:

1. Which capability index do you want?
There are 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 indexes 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” indexes, while Cpk and Ppk are better described as “process performance” indexes. 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 indexes has subtle, important differences when compared with the others. If you ask your questioner which capability index he or she wants, the right answer is “Several.” When asking about capability, one should expect to hear at least three different indexes.

If I were king and could require certain indexes 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.

The bad news is that just three numbers are simply not enough. The next two questions are extremely important, and much more important than receiving information concerning three capability indexes. Without asking these questions, 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 indexes 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 indexes 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 four 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 indexes separately by machine—even if those machines are supposedly 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 indexes 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 like what you hear at your local burger joint, 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 of or consideration given to process consistency with respect to central tendencies and variability? If your experiences have been similar to mine, probably not. I applaud the person who answers, “Of course, we always evaluate control charts when discussing capability.” If you’re 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 unchanging means and standard deviations, Cpk values mean little. Why? Because without a consistent control chart with an unchanging mean and standard deviation, it’s impossible to reliably predict what those statistics might be in the next week, or in the next 24 hours. Therefore, with a mean and standard deviation that are unpredictable, Cpk values could likewise be significantly different from one hour to the next, rendering the reported Cpk 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 indexes 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?”

About The Author

Douglas C. Fair

A quality professional with 30 years’ experience in manufacturing, analytics, and statistical applications, Douglas C. Fair serves as chief operating officer for InfinityQS. Fair’s career began at Boeing Aerospace, and he worked as a quality systems consultant before joining InfinityQS in 1997. Fair earned a bachelor’s degree in industrial statistics from the University of Tennessee, and a Six Sigma Black Belt from the University of Wisconsin. He’s a regular contributor to various quality magazines and has co-authored two books on industrial statistics: Innovative Control Charting (ASQ Quality Press, 1998), and Quality Management in Health Care (Jones and Bartlett Publishing, 2004).