Control limits for individual series of subgroups of the Shewhart control chart

The function of constructing control limits calculated for separate series of subgroups selected by the user allows you to highlight areas with short-term stable process states. The best short-term periods of a stable state with a minimum scatter of points around the average and the best adjustment of the average to the goal of the process - nominal, in the general flow of an unstable process, will require an in-depth study of the accompanying conditions of this state of affairs. Next, you can start looking for the reasons that led to changes from series to series “What has changed?” The interpretation of such a control chart gives a new understanding of the process and allows for measures to be taken to significantly improve it in the shortest possible time.

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. The button for going to the control panel for constructing control limits for individual series of points (subgroups) is highlighted. Main control panel.

In Figure 2 (below), a control XmR-chart of individual values ​​was constructed for the data from Figure 1 with the calculation of control limits for individual series: the first up to subgroup 16 inclusive, the second for the remaining points:

Figure 2. Control limits for individual series of points on the Shewhart XmR control chart for the data shown in Figure 1. The first series is from the 1st to the 16th point (subgroup) inclusive, the second is for the remaining points. The control limit control panel for individual series of points (subgroups) is open. The histogram displays the area of ​​the original control limits before constructing the control limits for individual series of points. The scatter plot shows modified control limits for individual series of points. The analysis of the control chart will be complicated by the absence of the [Operator] indication in the data for a series of subgroups from 27 to 40 - a signal to start working with the employees keeping records.

The numbers of subgroups (points) can be entered by the user in any convenient sequence. The list of subgroups added to divide the control chart into separate series will be automatically sorted from smallest to largest. If more than one point is added to the [Selected subgroups:] list, they will be reflected in the drop-down list to the right of the subgroup list field (Figure 3) for the ability to remove any subgroup from the list by clicking on the [Delete] button, this button is located under the drop-down list subgroups

Figure 3. Control limits for individual series of subgroups (points) of the Shewhart XmR control chart. A drop-down list is opened to remove the selected subgroup from the list of subgroup numbers to separate series.

To make it easier to determine subgroup numbers, you can left-click on the selected point (subgroup) to display its number with additional information in the form of a tooltip. By right-clicking on the pop-up tooltip with the subgroup number, it is hidden.

Figure 4. Function for constructing control limits for individual series of subgroups (points) of Shewhart’s XmR control chart. Tooltips with subgroup numbers are displayed. "Red Dots" ◆ tinted using the apply function zonal criteria (rules) of Western Electric.

The choice of series end points must be contextual. For example, you know about any changes at the beginning of the following series, and sometimes an educated guess from competent specialists is enough. This function will allow you to check the version of the significant impact of such changes.

Figure 5. Control limits for individual series of points on the Shewhart XmR control chart for the data shown in Figure 4. Analysis of the control chart will be complicated by the absence in the data of the indication [Lots of raw materials] for a series of subgroups from 16 to 27 - a signal to start working with employees leading records.

But the Shewhart control chart also allows you to look for feedback. Visible differences in data series allow you to ask the right questions and look for connections to context. For example, a control chart has recorded changes, and observers begin to look for a connection between what is shown on the control chart and events that have occurred or are ongoing. Many factors may not even be differentiated by observers until the observers, thanks to this function, receive from the control card the coordinates of the start time and duration of their action. For example, in Figure 2 (above), the operator is more likely not the cause of the process change.

Effect of combining functions

When combining two functions on a control card vertical dot series separators dotted lines indicating long-term factors and setting control limits for individual series of points - the amount of information transmitted by such a map, useful for improving processes, can hardly be overestimated.

You can easily track which of the known and recorded source variations (factors) changes in the process coincide with changes. Often when you first start using control charts to improve processes, the process changes don't match any of the factors captured in the data. In this case, most likely, the source of variation influencing the process changes has not been recorded by you or has not even been identified. Look for new reasons. The best way to track such causes is to keep control charts at the shop level by operators and controllers, and as soon as the process demonstrates changes, quickly determine the cause (factor), the characteristics of which will have to be recorded in the future. Below in Figure 6, for the vertical dotted lines, we have chosen the factor type [Raw Materials].

Figure 6. Control limits for individual series of points on the Shewhart XmR control chart for the data shown in Figure 1. Analysis of the control chart will be complicated by the absence in the data of the indication [Lots of raw materials] for a series of subgroups from 16 to 27 - a signal to start working with employees leading records.

Before this, you simply didn't have a tool to help you ask the right questions about what data to collect, and the people in the field were lukewarm about this responsibility because they didn't see the point of "data for data's sake."

This function allows you to conduct analytical research in reverse order. When you select subgroups (points) of the end of the series that coincide with the boundaries of the factor. If in series limited by the action of one source of variation, the process will be in short-term stable states, but will change its position along with a change in the source of variation, with some degree of probability, this type of factor is the special reason for the change in the process.

But if, on the contrary, the process within such separate series of points coinciding with the zones of action of the selected factors is unstable - most likely, this type of factor is not the reason that should be blamed for the instability of the process under study. In this case, either the factor itself behaves unpredictably for special reasons under the influence of another type of factor that you will have to deal with, which again indicates an incorrect assumption of the dependence of the process behavior on the factors of the selected type in your option for recording records. For example, one batch of raw materials contains different heterogeneous raw materials. This can happen for many reasons, for example, the same supplier batch contains significantly different supplier production batches, or the supplier's production process is statistically out of control and produces heterogeneous raw materials. In this case, the Factor Type [Raw Materials] with the factors [Raw Material Lot-1, Raw Material Lot-2,...] is too aggregated and does not sufficiently define the properties of raw material lots, which requires additional division into supplier production lots rather than shipping ones.

“The guiding principle of control charting should be to reveal the unknowns of a process rather than to demonstrate what is already understood.”

[4] Donald Wheeler, Statistical Process Control.
Business optimization using Shewhart control charts"
(Donald J. Wheeler, "Understanding Statistical Process Control")

In Figure 8, we demonstrate control limits for individual series of control chart subgroups. The series were selected by the number of the subgroup, after which the process (Figure 7) demonstrated process changes in the form of “red dots” ◆ colored using the function Western Electric zonal criteria and the last subgroup in a series of "red dots".

Figure 7. Shewhart control XmR-chart of a statistically uncontrolled process.

Figure 8. Control limits for individual subgroup series for data from Figure 7.

Video 1. Control limits for individual series of points (subgroups) of the Shewhart control chart. “Shewhart control charts PRO-Analyst +AI (for Windows, Mac, Linux)”