by Douglas C. Fair
I've been privileged to work in the statistical-software industry for the last 10 years, and frequently I receive phone calls from professionals who need information or guidance on statistical methods. Overwhelmingly, they call with excellent questions. Their interest and enthusiasm are exciting, and I'm grateful for the opportunity to help them.
I receive painful, distressing phone calls as well. In fact, I get the same inquiring phone call on a frighteningly consistent basis. It's a frustrating discussion, but at the same time it is curious and (in a statistically macabre way) a bit funny. When they ask the question, I usually tilt my head and squint my uncomprehending eyes like a dog who has just heard a strange sound. That phone call goes something like this:
Caller: Hi, Doug. Thanks for taking my call. I have some questions about control charts and control limits.
Doug: Great! I'm glad you called. What's your question?
Caller: Well, sometimes those dratted plot points fall outside of my chart's control limits. We hate it when that happens. Windows pop up in our software, charts turn red, and operators gotta enter some kinda codes. Our operators don't like it when their charts turn red. That sure is bothersome.
Doug: (Tilts head, squints eyes, and looks intently at his dog). Uh, OK. What's your question?
Caller: Is there some way of widening my control limits? If I remember correctly, aren't they pre-set at ± 3 standard deviations? That seems too close. Can't we just change them to be ± 5 standard deviations? Actually, ± 6 standard deviations would make them wider. Wait, even better, what if we just type in our own control limits? That way we can make them as wide as we want. Can we do that?
Doug: So why do you want to widen your control limits?
Caller: Gee, Doug, didn't I just tell you? We really don't like it when those dang dots fall outside limits! Plus, our customers force us to send them control charts of how their parts run on our machines. We don't want them to see any points outside of control limits.
Doug: Gosh. Wow.
Maybe I've changed some of the words and embellished a bit, but the nature and intent of the phone call is always the same. Basically, the caller is lamenting that fact that their process demonstrates a lack of statistical control. What they really seem to be saying is, I don't like that my process is out of control. Tell me what you can do to help me hide this fact." This, as you may have already concluded, is highly irritating to me, because out-of-control conditions should never be hidden-- they should be investigated. When a statistically significant event occurs in a manufacturing process, the control chart is supposed to alert us. It's doing its job. Control charts are designed to highlight unusual events. That's why they were invented in the first place. When a plot point falls outside control limits, the control chart is screaming at us, "Something has changed here! Look at me! Do something!" It's not an annoyance when plot points fall outside control limits. Instead, it's an immensely valuable piece of information that can be used for problem solving, process improvement, and cost reduction.
When properly applied, control charts and their limits are extraordinarily helpful. However, much is misunderstood about control limits, and the improper use and creation of control limits is more rampant than I had originally imagined. Before I get into the details of what not to do with control limits, let me be clear on my thoughts concerning out-of-control events. Everyone needs to understand this before we get into what should and should not be done with control limits.
Out-of-control events are good.
I don't mean good in the sense that we want out-of-control events. But when a process is inconsistent, manufacturers need to know about it. This type of communication is positive and useful as manufacturers strive to improve their processes. It's extremely helpful to be alerted to process changes that, if unaddressed, could potentially cause major problems later. A control chart that's out of control indicates that there are opportunities for improvement. It indicates that there's information to be learned, and it also tells us what needs to change for us to run processes more efficiently.
I like to think that a control chart is somewhat similar to the plotted results from a heart monitor. If your electrocardiogram reveals a highly irregular heartbeat, your doctor can recommend corrective actions before more serious health concerns manifest themselves. In other words, it would be beneficial to know if your heart had issues, and that's the job of the electrocardiogram and its attendant printout. If you're made aware of an issue with your heart, you can do something about it before it becomes a major problem. Being unaware of inconsistency in your heart's rhythm could spell disaster from a health standpoint. From a manufacturing standpoint, not knowing about process changes could cost a company millions of dollars. Out-of-control events are useful and can be leveraged to make processes better, cheaper, and faster.
I hope I have convinced you that out-of-control events are good. If so, please understand that control limits must be representative of the normal operation of a process. They must be based upon the actual process performance itself, not some extraneous, wishful thinking about how the machine should perform. Basically, control limits should specify what's normal process behavior and, conversely, what's considered abnormal. Calculated properly, control limits are extraordinarily useful because they'll ensure that the events you react to are worth your time and resources. When an event is triggered on a control chart and control limits have been calculated properly, you can rest assured that a significant event has happened and that your attention to the process is not only justified, but needed.