Part 2. MM4XL Tools > 1. Strategic Tools > Quality Manager > 1. SPC Attribute Charts > U-chart

Quality Manager


The U-chart works the same way as the C-chart, but is used to control nonconformities in lots rather than in single units. For instance, the daily number of errors in a whole newspaper, the weekly number of orders won with cold calls, the monthly number of transactions in a store, and so on.

User selections

The picture below shows a U-chart drawn with MM4XL's Quality Manager tool. After selecting Chart type, as shown in the following picture, if you have selected a range with more than one variable (column) in input, choose the variables for Num inspected and Num defectives to analyze, otherwise, the tool will show automatically the data of the first two input series available. If an input range was not selected in window 1, the C-chart will not be available in the list of chart types and the right side of the window below will be blank. Click on Next to go to the window where you select options for printing the results on sheet.

Total Quality Management Control Charts Excel Add-In Software

Technical notes

The control concept of the U-chart is the same as for the C-chart. Read also the material in this help file concerning the C-chart in order to get a clear view of how the U-chart works and what assumptions it sets. The control limits are placed at 3 standard deviations (see field Z ) in the window above and below the average (Ubar) of nonconformities. Measurements falling outside control limits indicate a change in the process. Items beyond limits are highlighted with a red, round marker, as shown in the window above.

Input data

The input data for the U-chart requires two columns of counts. The picture below shows a suitable data series in the range A1:B26, mind the hidden rows. These can be negative or positive nonconformities (defects) in lots of a given sizes.

Total Quality Management Control Charts Excel Add-In Software

In order to speed up the tool, uncheck the Simulate data option when working with long data series.

Output results

The U-chart can show in output two charts and three tables according to the user selection in the third window (see section Introduction to Quality Manager). The first table, shown below, contains indexes describing the input data in terms of:

  • Size of the variable: Max, Min, Sum, Range and Counts
  • Central tendency: Average, Median, Mode and Standard deviation (of a variable)
  • Chart limits: Upper Control Limit (UCL), Cbar, Lower Control Limit (LCL), Sigma
  • Z stands for the number of standard deviations where the control limits should be placed
  • Sigma is the standard deviation of a subgroup

Total Quality Management Control Charts Excel Add-In Software

For the sake of brevity, the second table is not shown here. In 8 columns it shows the details of the chart limits by item. In the picture below, the small, red triangle in the upper right corner of the first column label is a Comment which displays a short message. A number of comments are created by Quality Manager. Place the mouse pointer on the red triangle to display the message. The column Fr/def stands for the fraction of defectives.Sigma stands for the standard deviation, and is found with =SQRT(Ubar/Num inspected).

Total Quality Management Control Charts Excel Add-In Software

The U Control Chart in the picture below refers to an input variable (thick blue line) presenting one observation outside of the UCL while all other points lie within limits. The thin green line on the left refers to simulated random data produced by Quality Manager, in this case, according to the Poisson distribution. Comparing the random data to the user input data can help you get a visual understanding of the departure of the input data from normality. In this case, both simulated and user data take a shape that does not show any particular sign of an existing trend. Should the peak exceed the control limit again, you should explain the reasons for departure and consider whether to stabilize the process, removing the noise, if any. For a better way to assess normality, read also the material on the Process Capability tool available in Quality Manager.

Total Quality Management Control Charts Excel Add-In Software

The third table is made of four columns relating to the data fordrawing the histogram chart. The Levels column refers to the intervalsclasses. n, the column on the right, shows the counts for each class. Column Count Exp reports the expected number of items in each class for a normally distributed variable.

Total Quality Management Control Charts Excel Add-In Software

The histogram in the picture below shows two series:

  • The blue bars refer to the observed frequency of count classes in the input data. The first bar, for instance, tells us that there are 2 items with 1 nonconformity. The second bar shows 1 count for two nonconformities in the data, and so on. The axis value below the second bar is 2.2 due to a rounding effect. To remove the decimal place, select the horizontal axis with the mouse, double-click on it, and on the Figures page of the window that opens, set the Decimal places option to zero.
  • The bell-shaped red line shows the expected normal curve for avariable with the same range as the input data, and it helps toverify with a quick visual inspection whether the input data followa normal distribution or not. U-charts, however, follow the Poissondistribution that they tend to approximate normality only with a large number of observations.

Total Quality Management Control Charts Excel Add-In Software

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