This tutorial will help you set up and interpret an individual control chart on quantitative data in Excel using the XLSTAT statistical software.
Dataset to create individual charts
An Excel sheet containing both the data and the results for use in this tutorial can be downloaded by clicking here.
The data are from [Pyzdek Th. (2003), The Six Sigma Handbook, McGraw Hill, New York].
They correspond to 25 inspections each having 5 measurements of a production process. To better compare the results with the tutorial on subgroup charts, the same data set was used. In this case only every 1st measurement was taken into account.
Control charts and individual charts
Control charts are an efficient method to decide, if a process is statistically under control or not. There is a variety of different control charts that can be used for different aims.
The individual charts tool lets you use the following chart types alone or in combination:
- X Individual
- MR moving range
An X individual chart is useful to follow the moving mean of a production process. Mean shifts are easily visible in the diagrams.
An MR chart (moving range diagram) is useful to analyze the variability of the production. Large differences in production, caused by the use of different production lines, will be easily visible.
Note 1: If you want to investigate smaller mean shifts, then you can also use CUSUM individual charts which are often preferred in comparison to the individual control charts, because they can detect smaller mean shifts.
Note 2: If you have more than one measurement for each point in time, then please use the control charts for subgroups.
Note 3: If you have measurements in qualitative values (for instance ok, not ok, conform not conform), then use the control charts for attributes.
In addition to the control charts connected functions are available:
- Box-Cox transformation
- Process capability
- Tests for normality
- Rules for special causes and Westgard rules
- Run charts
During this tutorial an X together with a MR chart will be used.
Generating individual charts
Once XLSTAT is activated, select the XLSTAT / SPC / Individual charts command.
The SPC / Individual charts dialog box is displayed.
In the Mode tab, we chose the combination X-MR individual/Moving Range chart.
Then move on to the General tab and select the data on the Excel sheet.
(Note: There are several ways of selecting data with XLSTAT - for further information, please check the tutorial on how to select data.)
In this example, the data start from the first row, so it is quicker and easier to use columns selection. This explains why the letters corresponding to the columns are displayed in the selection boxes.
In the Estimation tab, we chose the option Average Moving Range and a window lengths MR Lengths of 2.
The computations begin once you have clicked on OK. You are asked to confirm the number of rows and columns (this message can be bypassed by un-selecting the Ask for selections confirmation in the XLSTAT options panel).
Interpreting individual charts
The first results are the estimated mean and standard deviation values.
The following tables with their corresponding chart represent the X control chart including the different control limits and central lines.
In the first table the control limits of the X control chart are mentioned. If we compare the values of the control limits with the corresponding values out of the previous tutorial on subgroup charts, we see that the limits now are much wider. The value for LCL has changed from 90.974 to 77.327 and for UCL from 108 to 120.753.
A fundamental difference between the individual and subgroup charts become visible: Subgroup charts have a more narrow range of control limits caused by the average calculated. This may leads to the conclusion to look for special causes that are not really present. Individual charts tend to have wider control limits and may need more process tuning work
Then the data of the X control chart starts with the group mean, group min and group max. After this the central line (CL), the lower (LCL) and the upper (UCL) control limit and the lower and upper zone limits for the A and B area are displayed for each group.
The next table contains the details for the special cause rules. Only "No" can be read in the table. The data has a good quality with respect to this issue. Summing up you can discover all this in the X control chart. The group mean values are always between the lower and upper control limits.
Similar to the X chart the data of the MR chart is always inside the control limits and no special causes are present.
Both control charts lets us come to the conclusion that the process is “statistically under control”.
Further it is interesting to know, if the data follows a normal distribution and therefore the common rules for control charts and process capabilities can be applied. In the next section the results of 4 different normality tests and a Q-Q plot are displayed. All of the 4 tests conclude that the Hypothesis H0 of normal distribution can be accepted. In the Q-Q plot we see that the data are close to the first bisector line. We suppose that the data is normally distributed.
At last the run chart is displayed. It contains all the individual measurements in order to judge the range and trends. We see that the measurements inside a group have a wide range, lying between 91 and 110. The values are within the control limits.