SPCGregory Ferguson
 Recipe for SuccessA good process study requires a splash of investigation, a dash of statistics and a little teamwork.

 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