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.
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.