I have observed a number of problems and issues with the way that Six Sigma students gather data for, create and interpret control charts. The purpose of this article is to help you avoid these common problems and issues, and to help you understand how to use control charts as part of a Six Sigma improvement project.
Control charts are used to monitor the output of a process over time to determine whether or not the process is stable and exhibiting common cause variation, or unstable and exhibiting special cause variation. If special cause variation is detected, the special causes should be eliminated and the output of the process reevaluated before considering any fundamental changes to the process. If common cause variation is present and the output of the process is not acceptable, then changes to the process will be required in order to improve performance.
The first stumbling block for most students is failing to recognize that data must be gathered over time, and must be used in date order (oldest date first) to create control charts.
The time interval between each subgroup of data should be as equal as possible. For example: data from each hour, or each day, or each week, etc. The more frequently data is collected, i.e. the shorter the time horizon, the more micro the resulting view of the process. The less frequently data is collected, and the longer the time horizon, the more macro the view. For example, one student recently collected data over just one day in time and created control charts. These control charts were of no use in evaluating the performance of the process over time.
Prior to collecting data, stratification should be considered. The idea behind stratification is to subdivide the overall population of data into two or more groups based on some factor that may influence the data. For example, say we are evaluating how long customers need to wait for an appointment with a physician. There are two basic types of customers requesting appointments – those that have an emergency and those that do not. If we do not stratify, data from both types of customers will be mixed together. The resulting analysis will not give us a clear picture of what is going on with either of these two distinctly different types of customers.
The next issue is the number of subgroups of data to be collected and analyzed. We need 25 or more subgroups, arranged in date order, to generate meaningful control charts. So we will need data from a minimum of 25 time intervals – i.e. 25 days, or 25 weeks, or 25 months. Students often create control charts using far fewer subgroups of data.
The next two issues are related – how much of the available data to use and which control chart to use. The type of control chart that you should use under a given set of circumstances can be determined by using the following decision flowchart. In this chart, n refers to size of the subgroup of data that will be selected from each time period.
Consider the example of wait time for an appointment to see a physician. We are working with time in days which is continuous, i.e. variable, data. There are three possibilities for control charts for continuous data. They are XmR Chart (also known as I-MR chart), X bar and R chart, and X bar and S chart. In our example have a high volume of customers, around 250 per week, and the data is readily available in a computer system. If the volume of customers was much lower, we might use data from just one customer each week and make I-MR charts. If the volume of data was moderate but costly or difficult to collect each week, we might use a subgroup size of five customers each week and create X bar and R charts. Under the circumstances, the best choice is to select a subgroup (i.e. sample) of ten customers each week for 25 consecutive weeks and create X bar and S charts.
In the next article in this series we will continue the discussion of issues and problems when using control charts.
Your comments or questions about this article are welcome, as are suggestions for future articles. Feel free to contact me by email at firstname.lastname@example.org.
About the author: Mr. Roger C. Ellis is an industrial engineer by training and profession. He is a Six Sigma Master Black Belt with over 48 years of business experience in a wide range of fields. Mr. Ellis develops and instructs Six Sigma professional certification courses for Key Performance LLC. For a more detailed biography, please refer to www.keyperformance.com.