Part 2. MM4XL Tools > 1. Strategic Tools > Quality Manager > 2. SPC Variable Charts > X-Sigma Control Charts

Quality Manager

X-Sigma Control Charts

These two charts are used instead of the Xbar and Range chart when the sample size is larger than 5 units, which assumes that the rate of data production is high and it is not a problem to produce more data for better sample stability. The main difference is that the Range chart is replaced by the Sigma chart, which is more accurate because the range value is found using only two values of a sample, the largest and smallest one, while sigma uses all values in the range.

The Xbar chart indicates changes in the process average compared to the average during the base period. The sigma chart shows changes in the variation of the process (sigma) comparing the variation of subgroups to a base period. You should read also the material in this help file concerning the Xbar and Range charts, in order to get a clear view of how the Xbar and Sigma charts work and the assumptions they set.

The picture below shows X-S charts drawn with MM4XL's Quality Manager tool. If an input range was not selected in window 1, the X charts will not be available in the list of chart types and the right side of the window below will be blank. After the desired Chart type is selected the charts will display in the right side of the window as shown below. The result can, of course, be printed in a worksheet.

Total Quality Management Control Charts Excel Add-In Software


Technical notes

In order to detect a change, the average and the range of the input data are shown in two charts within boundaries as shown below.

Total Quality Management Control Charts Excel Add-In Software


Input data

When working with X-S charts, follow the same instructions as for X-R charts. The only difference is that X-S charts should use 6 or more columns of data for each sample. The picture below shows suitable input data in the range B1:K26, mind the hidden rows.

Total Quality Management Control Charts Excel Add-In Software


Output results

The output results of X-S charts are interpreted in the same way as already explained for X-R charts.

The output from the X-S charts is made up of two charts and two tables, in accordance with the user selection in the third Quality Manager window (see Introduction to Quality Manager). The first table, shown below, contains 2 indexes. Xdbar is the overall process mean computed on all observations. StDevBar is the average standard deviation value of standard deviations for all groups of observations.

Total Quality Management Control Charts Excel Add-In Software


For the sake of brevity, the second table is not shown here. In 9 columns it shows the details of the chart limits by item. The second, fourth, fifth and sixth columns from the picture below are used to draw the Xbar chart, while columns 3, 7, 8 and 9 are used to draw the Range chart.

Total Quality Management Control Charts Excel Add-In Software


The Xbar Chart in the picture below refers to an input variable with all observations within confidence limits. The input data does not exhibit any trend, so we assume it is stable and can be used for the purpose of control.

Total Quality Management Control Charts Excel Add-In Software


The X-Sigma Chart below shows a change in average for samples number 4, 9 and 10, and it also shows a slight negative bump for sample 23. Again, no noteworthy changes are detected, for all observations lie within limits. However, this cyclic tendency to peak closer and closer to the UCL should be explained and, if necessary, removed from the process.

Total Quality Management Control Charts Excel Add-In Software


The joint reading of the two charts helps us to monitor that a given process performs as expected. This implies a thorough knowledge of the process in analysis in order to explain any cause of variation detected by the charts.

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