We will use some batching data to illustrate the process. If we were to look at the batch weight for each component of each batch we process for a period of months, we might be able to spot changes, trends or increased (or decreased) variability in the data. We might miss a lot of that, however, because our minds don’t visualize well from raw data. If we instead made a simple plot of that data sequentially over time, we could see trends or changes much more easily and quickly. This is called a run chart. While it helps our visualization, it does not tell us if the process is in control or not. We expect that there will be some level of variability in a process—no worker or piece of equipment does exactly the same thing every time.
The most common control chart consists of a run chart with the average for all of the data and the upper (UCL) and lower (LCL) control limits superimposed on the data plot. Usually, the control limits are set at plus or minus three sigma (±3ð), or three times the standard deviation for the data, on either side of the average. We would expect all but about one quarter of one percent of the data, or all but one in 400 points, to fall within the 3ð limits. The process is in control if it never varies outside its normal range of variability. If data moves outside the control limits, we can assume that the process is being influenced by an extraneous or non-usual factor and is out of control.
If we were measuring mechanical strength of a small fraction of our production (or of sample bars), we would plot the average of these individual daily groups, and the generation of the control limits would be a bit more complex. We can also impose control limits that are not statistically generated from the data when, for example, critical property values must be met. A minimum strength level, for instance, might be used as the lower control limit.
From batches 100 to about 600, a much greater amount of variation appeared and there were a number of weights outside the control limits. The process was out of control, but because this control chart was not generated until about batch 600, the manufacturing personnel did not perceive the lack of control. A mechanical problem was found and corrected, and the system returned to its previous level of performance.
This has been a very cursory coverage of control charts—our goal here is to try to make clear how critically useful they can be. As with all statistical control methods, a little knowledge can be dangerous. It is important to learn a lot more about control charts before we can make intelligent use of them.