More Types of Control Charts in Six Sigma Methodology: The X-Bar/R Chart, EWMA Chart, and the P Chart for Data That Is Not Time Ordered

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It’s All About the Data

Six Sigma focuses on improving processes by identifying sources of performance variation and taking steps to reduce variation and better meet customer requirements. It distinguishes between two types of variation: common cause and special cause. Common cause variation is basically random variation within the process itself, and must be addressed using a different approach than special cause variation, which is the existence of specific external factors causing differences in performance.

The control chart is perhaps the tool most commonly associated with Six Sigma. The main purpose of a control chart is to identify sources of special cause variation and show the performance you can expect if only common cause variation is present. This is accomplished using statistical techniques. Control charts include control limits, which show the extent of variation due only to common cause. Any data points lying outside these limits are due to special cause factors. In addition, control chart functions in software such as Minitab provide the option to test for trends in the data and other statistical oddities that indicate special causes are present.

The most common type of control chart is the individuals chart, which you can learn about in our introduction to control charts. Also check out our control chart example. Depending on the [type of process data]( t) you have, the individuals chart may or may not be the best choice. Other types of control charts provide more power in distinguishing between common cause and special cause for specific types of data.

For discrete attribute data, the best chart to use is a p or np chart, while the c or u chart is best for discrete count data. Learn more about these chart types in the companion article, Types of Control Charts and also in Types of Attribute Control Charts. More specialized situations and types of data call for more specialized control charts.

Chart Variations

X-bar/R chart

Six Sigma originated in the manufacturing sector, and the X-bar/R chart is particularly useful in such a setting. With an assembly line, it is reasonable to assume that the variation in output is minimal for data taken all within a brief time period, as the machine settings and the people staffing the machines do not vary. Over longer periods, however, more variation is expected due to drifts in machine performance and changes in staffing.

Thus in this type of setting, it makes sense to gather data for a short period as a sample of process performance under specific conditions. Each of these samples is known as a subgroup sample, and the data for the samples is compared to determine if the variation among subgroups exceeds the variation within each subgroup. If so, it indicates that special cause factors are at play.

The X-bar/R chart provides optimal results in such a situation. “X-bar” indicates the mean or average performance, which is plotted on one graph, while “R” is the moving range, which is plotted in a matching graph. Analysis of both graphs is needed to make appropriate conclusions about process performance.

EWMA chart

The exponentially weighted moving average (EWMA) chart provides quicker information about shifts in process performance. It is ideal when identifying a process shift quickly is critical, for instance when measuring levels of contamination in the public water supply. If an increase in contaminants is not identified quickly, the health of the public could be at risk.

When the control limits are calculated, more weight is given to more recent data points. Compared to an individuals chart, a process shift can be detected within fewer data points of the start of the shift using an EWMA chart.

P chart for data that is not time-ordered

Typically a control chart plots data over time, and the objective is to identify special causes in the form of outliers and process shifts. In some cases, though, a project leader may want to compare data for a specific time period among different groups or conditions. For example, a financial institution might want to look at loan acceptance rates for different types of loans or different types of applicants. In this case each data point represents a category rather than a point in time.

A p chart allows this type of analysis. Interestingly, since the control limits are dependent on the sample size, the limits for each data point may not be the same if the sample sizes are different. Generally the larger the sample size, the tighter the control limits. Thus each data point is compared to its own control limits, regardless of its position relative to the control limits for other data points. Any outliers are indications of special cause and should be investigated.

This post is part of the series: Types of Control Charts

Control charts are a powerful tool for Six Sigma projects, allowing analysis of special cause and common cause process variation. Learn about the different types and their uses.

  1. Types of Control Charts
  2. More Types of Control Charts For the Six Sigma PM
  3. The Basics of Attribute Control Charts
  4. The Basics of X-Bar/Range Control Charts
  5. Using a P Chart For Quality Control