SPC
Gregory Ferguson

A process study is like a detective novel. You investigate, collect facts and try to solve the mystery. Let me give you an example.  Let's say you are studying a lathe, grinding the outside diameter (OD) of Teflon shafts. You get the production operator to measure the OD with a pair of calipers, and then you have the measurements recorded as in Table 1.  So, at the end of the first day of your process study you have 91 data points. The first thing I'd like to point out is that if the production operator is using a pair of calipers, the readings shouldn't be reported to the fourth decimal place. Calipers aren't that accurate. This is a form of measurement error called spurious accuracy. The second point is that 91 data points aren't enough to compute reliable control limits. The recommended number is 125. But this is a real-world example and it is often the case that you don't have as much data as you would like. We will use this data and consider our control limits to be preliminary and we will refine them when we have more data.  We now enter the analysis phase of our study. The first step in the analysis is to make a histogram. The histogram for this data set is shown in Figure 1.

Figure 1: Histogram of Teflon Shafts' Outside Diameters

With a simple inspection, we know we're not dealing with a normal distribution. The normal distribution is symmetrical; it's the famous "bell-shaped curve" that teachers love to talk about. This part of the data set looks more like the uniform distribution up to the value of 0.752, then it shifts to what looks like a uniform distribution with a different mean. This is our first clue that something may be wrong: If our process were stable, we'd see only one distribution. But, in this example, we might see two or more distributions.  Because our data isn't normally distributed, it isn't appropriate for us to use an individuals control chart. Instead, we will use an X-bar and R chart. Because we don't have much data, we'll start by using subgroups of two. The X-bar and R chart is shown in Figure 2.

Figure 2: X-Bar and R Chart for Subgroups of Two

The range chart shows a point outside the control limits at point 29. You would usually stop the analysis at this point--if the range chart is out of control, something is seriously wrong with the process. But because this is an example, let's continue with the analysis. The X-bar chart shows points out of control at points 28 and 29. This confirms the range chart's indication that something is wrong with the process. It's easy to plot another control chart; this time, we'll use subgroups of five.

Figure 3: X-bar and R Chart for Subgroups of Five

Here the range chart is almost out of control at point 12 and the X-bar chart is out of control at points 11 and 12--evidence that something is wrong with the process. Because we're using subgroups of five, these points correspond to data points 55 through 60 in Table 1.  An out-of-control control chart indicates that the process has changed. Now we know that the points between 55 and 60 are significantly different that the points before and after.  Our process study enters a new phase. We have to find out why the process changed. One clue is the time at which it changed. Looking at Table 1, we see that point 55 was measured at about 12:30 p.m. We also see that point 52 was .7532. Out control chart tells us that the upper control limit for this process is .752. Point 52 didn't show up as an out-of-control point on the control chart because it was averaged with other readings. But it is unusual. What could have changed? We head out to the production floor and ask the operator, Bill.  "Well," he says, "I did go to lunch at noon."  "But why are there measurements between noon and one if you were at lunch?"  "Oh," Bill laughs. "We can't have the machines sitting idle just because I go to lunch. Charlie took over for me. He ran the lathe while I was at lunch."  We have another clue: We now know the process changed when the operator changed at noon. We track down Charlie.  "Hey Charlie, I'm doing a study on lathe seven and I understand you were operating it from noon to one yesterday."  "That's right," Charlie says, suspiciously. "Why? Is there a problem?"  "No, there's no problem really. It's just that my control chart here shows that the process changed at noon and I'm trying to find out why. Did you make any adjustments?"  "No. I didn't adjust it. Bill said it had been running good. I just ran the parts."  Our process study has entered still another phase. We not only know that the process changed but we have persuaded two production operators that it changed. We know the change was not the result of operator adjustment. What could it be?  The production operators are an invaluable source of information on what might have made the process change. Two operators were making the same part number on the same machine, but their parts are different. We now need to get the operators to demonstrate to you and to each other how they make the parts.  "Okay, Bill, please show us how you mount the part in the lathe."  "Sure," Bill says with a smile. "I slide the collet back and I put the Teflon rod in like this. Then I clamp it down and turn on the lathe." A slender white thread of Teflon spins into the air as the lathe cuts down the shaft.  "Is that the way you do it, Charlie?"  "Yeah, I do it just like he showed ya," Charlie says.  "Would you mind showing me?"  "Why? Bill just showed you."  "Humor me, please?"  "Look, I got better things to do. I don't know what you're doing with your charts and your statistics. I need to get back to work."  "I'll give you a dollar if you'll do it."  Charlie laughs. "Okay, okay," he says. "I do it just like this.  Then Charlie opens the collet, puts in the part and turns the crank three times.  "Whoa!" Bill cries. "What are you doing? That's way too much pressure. If you clamp it down like that, you'll make the Teflon distort. It will no longer spin true. It can give you all kinds of crazy results. You have to use a light touch. Put the part in and just use half a turn to hold it."  "I've been running lathes all my life," Charlie says.  "Yeah," Bill says. "But with steel. This is Teflon. It's a plastic material. It's easy to distort. No wonder you were getting screwy readings on the OD."  Using our process study, we've discovered why the dimension changed during the day. The best part of this study is that it helps operators teach each other. Everyone works together as a team to make the process better. Do a little investigating and add a dash of statistics, and you can solve any mystery.   About the author  Gregory P. Ferguson is quality manager of Parker Hannifin's Tucson, Arizona, facility. Comments can be e-mailed to him at gferguson@qualitydigest.com .