Knowing the difference between different kinds of charts depends on not only understanding the relative advantages that each offers, but also knowing what information one wants to derive from the data. As we saw in an earlier column, it is critical to know how the data can be analyzed with respect to specific information that is required, and perhaps to anticipate other uses that the data might serve at the same time. Steve Daum discusses the differences between run charts and control charts, and offers perspectives on the benefits of control charts.
I recently received the following question:
‘The process certification program at my company says that in order to certify a process it must be in control, be capable and be centered. Capability is measured by the process Cp and centering is measured by the Cpk. What measurement is used to determine if a process is “in control”? Is there a crisp definition of “in control”?’
“In control” is a term used to describe a process that is predictable and does not contain any special causes of variation. A special cause is something you did not expect to occur. I often refer to these as hiccups because, like a hiccup, you do not get them often.
There are many out-of-control or special cause tests you can use to help identify if the system you are evaluating appears to have special causes of variation. In general, if one of the out-of-control test rules is broken, you have license to investigate the hiccup or out-of-control point. Upon investigation, you will make a determination if the anomaly is a special cause. Then, if it is a special cause, you will determine what action to take.
In short, if you look at a control chart and it shows only common cause variation, it is said to be in-control and you should be comfortable predicting the future based on the past (“in control”) process.
I received a lot of e-mails in response to my last blog entry and a few of you have posted comments on the blog. It is fantastic to see such a lively debate! And while I like to win a debate as much as the next guy, I am more concerned with utility. After all, if your control charts don’t give you information that helps you control your processes, what’s the point?
We must remember the purpose of a control chart, which is to provide guidance as to when to investigate and when not to investigate. Essentially, a control chart should create an effective balance between reacting too quickly and not reacting quickly enough. While it is evident that we aren’t all using the same operational definition of a run, the nice thing about SQCpack and CHARTrunner is that they allow you define your own run rules.
Note the two distinct runs of points between samples 8 and 18 on the following chart of fictitious data.
A CHARTrunner customer in the UK recently contacted me to ask why her control chart was not flagged with an out-of-control condition.
Specifically, note the run down of points in her chart. I replied that the out-of-control test that she defined is looking for seven consecutive samples that are decreasing. I agree that a run of points exists; however, my assertion is that there are six consecutively decreasing points.
She counts seven consecutively decreasing points. How many consecutively decreasing points do you count on the chart above?
I used an analogy to explain. When one counts steps in a staircase, the initial starting point (the base or landing) is not counted as a step; the first step up is an increasing step if one is going up (and the first step below the top is a decreasing step if descending), but the beginning point is really just a beginning. It is not considered to be increasing or decreasing. The stair could also be an ending step, if one is descending, but it in itself, is neither increasing nor decreasing. Comparatively, I am not aware of a method to identify a point as both increasing and decreasing.
I also pointed to a well respected text by Acheson J. Duncan’s “Quality Control and Industrial Statistics,” Fifth Edition. In this book, he states (page 429) “… Thus in the series 5, 4, 6, 8, 10, 12, 11, there is a run up (increasing) of 4, since there are four increases in a row. Likewise, 7, 10, 8, 6, 5, 4, 3, 2, 4 illustrates a run down of 6.”
I’m interested in your thoughts. When a run up or down exists, where do you begin to count the number of consecutively increasing or decreasing values in the run?
I often tell others that a control chart is one of the most effective and easy-to-use quality tools. Some argue that experimental design is more effective. Maybe so, but can you teach a novice experimental design as quickly as you can teach him a control chart?
A control chart is a simple tool that works well for many applications. One key component of a control chart is the control limits. Without control limits, you don’t have much … unless, of course, you like run charts. So if the control limits are such a key part to a control chart, why do so many problems and questions exist related to control limits?
In a class on capability analysis that I recently taught, several participants asked: “What is the difference between Cpk & Ppk?”
The quick answer is… ’1 letter’. The mathematical answer is that each statistic uses a different calculation for the standard deviation.
The practical answer is…’it depends’. Now I know, some of you are saying statistics (math) isn’t subjective. I mean, we’re dealing with numbers here! Yes, the numbers are real and yes, you should trust the results. (Unless, of course, someone like Bernard Madoff is gathering the data for you.)
I received a question after my last blog post asking me to clarify the concept of within and between subgroup variation which is used in calculating Cpk, Cp, Cr, Ppk, Pp, Pr and other statistics. Here is an example I used to help explain the differences.
Let’s say that every day I run about 30 minutes with my chocolate labrador, Cadbury (pictured below).
While running, I decide to measure how fast we are going. I measure the speed (pace) three times throughout the run: toward the beginning, the middle, and the end of the run. This data tells me a few things:
1. The pace at the beginning, middle, and end of the run.
2. The average pace we keep. This average pace is also called an X-bar.
3. The difference between the fastest pace and the slowest pace, also called the range.
4. Cadbury, like me, has a lot more energy at the beginning of our run than at the end.
I often get asked SPC application questions such as: Can Ppk be larger than Cpk? Can Cpk be larger than Cp? Do you recommend CPM, Cpk, Ppk or something else? I prefer to answer these process capability questions with simple one-word answers, but that doesn’t usually satisfy the quality zealot’s curiosity. So here’s the long and the short of one of the questions.
In short, Yes, Ppk can be larger than Cpk. If you are doubtful, or consider yourself a quality zealot, grab a cup of joe, and read on.