Unilateral and bilateral fixation of control limits to increase the sensitivity of the Shewhart control chart for operational process control and for analytical work.

The function of fixing control limits on Shewhart charts can be applied in the classical one-way way, when the control limits calculated up to the specified point of a statistically stable state of the process are extended by a dotted line into the future. It is used to predict the behavior of a stable process in the future (for a new series of points) and to adjust the sensitivity of the control chart. New points are controlled relative to fixed control limits.

This function is included in the list of parameters saved in the chart properties when saved in the list for automatic chart updates with a selected timeout or to quickly open them with updated data.

Figure 1. Button to go to the control panel for the function of fixing control limits on Shewhart charts.

In the figure below, one-sided fixation of control limits was carried out on the 15th subgroup (data point).

Figure 2. Calculation and fixation of control limits was carried out up to the 15th subgroup (point) of the XmR-chart with the extension of control limits to the entire data series with a dotted line. A tooltip appears when you hover your mouse over the [Pin] button.

Figure 3. Calculation and fixation of control limits was carried out up to the 15th subgroup (point) of the XmR-chart with the extension of control limits to the entire data series with a dotted line.

Figure 4. Calculation and fixation of control limits was carried out up to the 15th subgroup (point) of the XmR-chart with the extension of control limits to the entire data series with a dotted line. A tooltip appears when you hover the mouse over the [Restore] button.

The figure below shows the normal control limits for the process data from Figure 4, but before the control limits are secured. Note the significant simplification of the control chart interpretation, namely the identification of the process shift in the figure above compared to the control chart in the figure below for the same data, but without assigning control limits.

Figure 5. Control limits for the entire data series - without pinning. The same data series was used as in Figure 4.

Bilateral fixing allows you to fix control limits on a Shewhart control chart indicating the beginning subgroup and the end subgroup of a series of points. Based on the selected series of points, control limits will be calculated and secured with their extension by a dotted line in both directions from the selected series of points. This option is especially popular among analysts.

Figure 6. Calculation and fixation of control limits was carried out from 27 to 59 subgroups of the XmR-chart with the extension of control limits to the entire data series with a dotted line on both sides of the selected series of points.

The analyst can display the blue area of ​​the original control limits on the histogram after applying the control limit pinning feature. This will demonstrate the position of the original control limits relative to the fixed ones.

Figure 7. The area of ​​the original control limits is shown in blue on the histogram. Calculation and fixation of control limits was carried out from 27 to 59 subgroups of the XmR-chart with the extension of control limits to the entire data series with a dotted line on both sides of the selected series of points.

The figure below shows the process data from Figure 7 but without fixing the control limits.

Figure 8. Control limits for the entire data series - without pinning. The same data series as in Figures 6 and 7 was used.

The function of fixing control limits makes it possible to simplify the understanding by shop personnel of the essence of Shewhart control charts for tracking changes (variations occurring under the influence of special causes) in the process that require attention and prompt response to identify special causes and their elimination. Conversely, if new points fit into the interval between the fixed boundaries of a stable process, this will indicate that adjustments to the process in this case will only worsen the situation in the form of, at a minimum, an increase in variability (the spread of data up and down from the center line).

If you are deliberately trying to shift a stable process to better center it within the tolerance, assigning control limits to a series of points before such an adjustment will help track the effectiveness of efforts to move the process relative to the assigned control limits from the first point after the adjustment. So if, after your measures to shift the process, no points are recorded that went beyond the previously established control limits in the direction of a controlled shift, then your measures are not effective. The process didn't even notice them.

Another example of the use of this function by shop personnel and quality control department employees for periodic monitoring of the stability and displacement of the used measurement systems into the calibration interval. It is important to understand that in any manufacturing plant, machine operators use their own measuring system to evaluate the results of their work and make adjustments to the technological process, and quality control department employees to control the quality of products produced by operators. Perform periodic input of repeated test-retest measurement values ​​of a known standard to monitor the stability and displacement of the corresponding measurement systems relative to the control limits assigned to the first 25 points of previously carried out test-retest tests, for example, once at the beginning of each working day or every Monday .

Video 1. Unilateral and bilateral fixation of control limits to increase the sensitivity of the Shewhart control chart. Software “Shewhart control charts PRO-Analyst +AI (for Windows, Mac, Linux)”

The function of one-sided and two-sided fixation of control limits is applicable to XmR-charts of individual values, XbarR-charts of average and range of subgroups, three-way control charts .