Demonstration of removing selected points (subgroups) from a Shewhart control chart, histogram and scatter plot. Hypothetical Process Possibilities

This function allows you to remove points (subgroups) that clearly show signs of typo when entering values ​​and allows you to obtain hypothetical "what if" possibilities of the analyzed process, provided that special causes are eliminated. Data from demo-deleted points is not deleted and remains in the database. You can experiment with this feature in a data-safe manner.

When the user deletes points, the control limits on the control chart, histogram and scatter plot are automatically recalculated.

The user can delete single points (subgroups) and/or entire series of points by specifying the range of series (from-to).

Deleting points with errors in recording values

Figures 1-4 display the same data series before and after removing the selected point (input error), and the structure of the remaining data series that appears in Figure 4 is associated only with a change in the graph scale along the Y axis.

Figure 1. Button to go to the control panel for deleting individual points and series of points. Point No. 80, which went far beyond the lower control limit of the control X-map of individual values.

Figure 2. Control panel for deleting points. The checkbox for displaying deleted points is checked, the checkbox for showing the area of ​​the original control limits is unchecked. Point 80, which is far beyond the lower control limit of the control X-map of individual values, is selected for deletion.

Figure 3. Control panel for deleting points. The checkbox for displaying deleted points is checked, the checkbox for showing the area of ​​the original control limits is unchecked. Point 80 has been removed and a purple cross is displayed in its place.

Figure 4. Result after removing point (subgroup) No. 80. The control limits and center line are calculated taking into account only the remaining points. The checkboxes for displaying deleted points and displaying the area of ​​the original control limits are unchecked. Control chart plots are scaled along the Y axis.

We strongly recommend that you remove identified write errors from your data source so that you can continue working with cleaned data.

Hypothetical Process Possibilities

Suggested [4] by Donald Wheeler.

The analyst can find out the capabilities of an unstable process when it is brought into a statistically controlled state. Although the calculated control limits, even for an unstable process, indicate the lowest potential of the process (functioning limits) when eliminating the special causes that caused its statistically uncontrollable state, we can go further in clarifying the hypothetical capabilities of the process.

For example, an analyst can delete points (subgroups) that go beyond the control limits, followed by automatic reconstruction of the control chart.

For example, for an XmR-chart of individual values, this operation must be done first for the mR chart of moving ranges, and then for the X chart of individual values, until all points outside the control limits have been removed. When removing some "red" points, new points may move into an area outside the control limits, becoming "red", they will need to be dealt with as described above. Eventually, you will be able to see the hypothetical possibilities of your process.

The entire history of deleting individual points and series of points is saved in the corresponding fields of the control panel. To quickly return the graphs to the state before the points were deleted, you must click on the [Restore] button. To display graphs of control charts, histograms and scatter plots, taking into account the removal of points, you must press the [Delete] button again.

The user can display distant points on the graph in the form of a [ sign × ] or hide by unchecking the [Show deleted points] checkbox.

Figure 5. On the control chart, in the “red” points, signals of the presence of special causes of the observed variations are identified. The checkbox for displaying deleted points is checked, the checkbox for showing the area of ​​the original control limits is unchecked. Obtaining the hypothetical capabilities of a process brought into a statistically controlled state begins with the removal of “red” points that go beyond the control limits on the range map.

Figure 6. On the control chart, in the “red” points, signals of the presence of special causes of the observed variations are identified. The checkbox for displaying deleted points is checked, the checkbox for showing the area of ​​the original control limits is unchecked. A new “red” point has emerged that has gone beyond the control limits on the range chart - a candidate for the next deletion.

Figure 7. On the control chart, in the “red” points, signals of the presence of special causes of the observed variations are identified. The checkbox for displaying deleted points is checked, the checkbox for showing the area of ​​the original control limits is unchecked. A new “red” point has emerged that has gone beyond the control limits on the range chart - a candidate for the next deletion.

Figure 8. Consistently, “red” points are removed from the Shewhart control chart, which are stored in the field with a list of deleted points. The [Show deleted points] checkbox is enabled - on the control chart graph, deleted points are shown as a [ sign × ]. The checkbox for displaying the area of ​​the original control limits is unchecked. The control limits and center line are calculated taking into account only the remaining points. We have brought the process to a hypothetical statistically controlled state.

Figure 9. Deleted points are shown as [ × ]. The checkbox for displaying the area of ​​the original control limits is checked. The control limits and center line are calculated taking into account only the remaining points. A control chart demonstrates a process in a potentially statistically controlled state. The blue area in the histogram shows the area of ​​the original control limits calculated before the points were removed.

Below, for clarity, the reflection of remote points on the control chart graph is another example.

Figure 10. On the control chart, in the “red” points, signals of the presence of special causes of the observed variations are identified. The [Show deleted points] checkbox is enabled. The checkbox for displaying the area of ​​the original control limits is unchecked. Control panel for deleting points.

Figure 11. After removing entire series of "red" dots. The control limits and center line are calculated taking into account only the remaining points. The [Show deleted points] checkbox is enabled - on the control chart graph, deleted points are shown as a [ sign × ]. The checkbox for displaying the area of ​​the original control limits is unchecked. Control panel for deleting points.

Figure 12. After removing entire series of "red" dots. The histogram shows the blue area between the lower LNPL(x) and upper UNPL(x) control limits of the process before the user begins deleting points. The [Show deleted points] checkbox is enabled - on the control chart graph, deleted points are shown as a [ sign × ]. The checkbox for displaying the area of ​​the original control limits is checked.

Video 1. Hypothetical possibilities of the process. Software “Shewhart control charts PRO-Analyst +AI (for Windows, Mac, Linux)”