Welcome to Six Sigma Black Belt. Course 7, Module two, SPC Selection and Analysis Control charts are considered one of the most powerful tools in our arsenal for analyzing variation. The origins of control charts can be traced back to Walter Chouard. Over the next several lessons, we will be discussing the different types of control charts, how and when to deploy them and their interpretation. Maintaining a control chart is like a long-term investment. When a process is in control, it is predictable. Our ability to predict behavior allows us to be safely ahead of potential issues, resolving them before they become unmanageable. The two primary types of control charts are variables and attributes. Variables charts require measurable data, but it may be impractical or uneconomical. Despite the power associated with control charts, they do have some pitfalls that are all too common. First, our chart cannot be created properly. Even with technology, this does happen on occasion. Next, we could also deploy the wrong chart based on the type of data or application. Like all statistical tests, control charts are grounded in certain distributions. If the behavior of our process does not conform, we will get erroneous results. Thankfully, we have technologies to maintain control charts, but if we are charged to maintain them manually, they could be neglected. We also need to be mindful of our corrective action. Sometimes we take the inappropriate action. Other times we take no action at all. Flow charting the different types of charts can help us in deciding which one to use. Our first chart is the Xbar-R chart. Xbar stands for the sample average, R is the range. This chart is suited for continuous data. We use these charts when data is readily available and subgroup sizes are relatively small and constant. They are relatively easy to construct manually, at least in comparison to other charts that will be discussed. Please note that we must assume that the data is normally distributed to deploy this chart. Here we have a summary of the symbols associated with this chart. Some of these symbols you have already seen before. n is the subgroup size, X is the data value. X bar is the average of each subgroup. X double bar is the grand average. This is the center line of the Xbar chart. R is the range of the subgroup. R bar is the average of all the ranges and the center line of the, our chart. UCL/LCL are the upper and lower control limits respectively. They bound 99.73% of the data, or +/- 3 standard deviations from the main. Please note, that these are specification limits. Of course, the use of technology to create and maintain any of these charts is strongly advised. But an understanding of how we construct each of these charts can be very insightful. First, determine the subgroup size. We look for this number to be between three and 10 typically. Next, collect data. We will want between 20 and 25 groups because we have a subgroup size between three and 10. This will mean that we need between 60 and 250 data points. We want to ensure this data is collected over a localized time interval and set of conditions. Next, find the average and range for each group. Now find the X double bar and the R bar values. Finally, calculate the control limits. These control limits are based on the grand average. The average range and an anti biasing factor that is determined by the type of control chart and the subgroup size. Let's consider this example. We have a subgroup size of six and we collect six groups of data. Each row represents a group of data. Using technology we can create the Xbar and our charts. The green lines represent the grand average and average range. The red lines are the upper and lower control limits. These values are found through a series of anti biasing constants based on the subgroup size and the type of control chart. We see that the range chart exhibits well behaved behavior. But the Xbar chart shows that Group D has an average that is below the lower control limit, and Group B has an average that is above the upper control limit. In another lesson we will discuss how to best interpret the behaviors we see. Xbar sigma charts are preferred over Xbar charts when the subgroup size is large and we require more sensitivity. As a result these charts do not lend themselves well to manual calculations. This chart is also suited for continuous data. The Xbar chart is constructed as before, but the range chart is replaced with an average sample standard deviation across the groups. Normality is also important for us to deploy this chart type. An added benefit here is that the subgroup sizes are not required to be the same. Let's expand on our last example. Now we have a subgroup size of 15 for six groups. The Xbar and S charts are shown here. Following the process before, the green lines represent the grand average and average standard deviation. The red lines are the upper and lower control limits. These values are found through another series of anti biasing constants based on the subgroup size, yet suited for standard deviations. We see that the S chart exhibits a well behaved process. But the Xbar chart shows that Groups A and D have an average that is below the lower control limit. Median charts are useful when we desire group continuous data. Yet we are not demanding as high of an efficiency. The method for medium charts is the same as that for the Xbar chart. However, the anti biasing constants for the Xbar chart are somewhat different and adjusted given the higher amount of variation associated with the median. The anti biasing constants for the range chart or the same though. Medium charts are particularly useful at the onset of an improvement to assess stability. We can also use medium charts to analyze the outcome of a process improvement. It can also be a useful alternative when we see huge swings in the subgroup range values. In this instance, our median chart would be of each value in the subgroup. In general, our upper and lower control limits for the central tendency of the data are set by the overall main + or- and anti biasing factor multiplied by the measure of spread. Our upper and lower control limits for the dispersion of the data are set by a factor multiplied by the measure of spread. For the Xbar-R and medium control charts spread is the range. For Xbar-S, the spread is standard deviation. For moving average and individual charts, spread is the moving range. Although technology is far more effective and functional when it comes to the construction of a control chart. A summary of the anti biasing factors for each type of continuous control chart is found here. Clearly, this table is not exhausted, as it only provides coverage through a subgroup size of 10. But it can be useful to have these values available should a quick manual calculation, or analysis be required.
