Date and time formatting, labels for points, vertical separators, breaking the connecting line of the graph for visual separation of series of points, blocks of formulas for calculating σ (sigma) and σ (sigma) values ​​with reproducibility indices Cp and Cpk on Shewhart control chart graphs

You can show/hide point labels, vertical separator lines, and plot line breaks for series of points on control chart plots from value fields (dimensions) or from an unlimited number of Factor variation source fields (columns). Activation/deactivation of the function is carried out by clicking the mouse on the switch button in the corresponding control panel.

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.

Using the point labels and vertical factor zone separators functions, for example, for only 18 Factor columns, you can get 18x18-18=306 cross unique variants of labels for points on the control chart.

Figure 1. Main button panel, button for switching to the control function for formatting the [Date and time] field on Shewhart control cards. Software version (3.30).

Figure 2. The button panel for the control function for formatting the [Date and Time] field on Shewhart control cards is activated. A drop-down list is opened to select formatting for the date and time field.

When importing data into our program, by default the [Date and time] field is formatted in the format of the second line from the drop-down list ['DD:MM:YYYY hh:mm'] for the Russian interface and ['MM:DD:YYYY hh:mm' ] for English speakers. If your data has a more verbose format, you can select it from the drop-down list in this date and time formatting control panel.

Figure 3. Button panel for controlling the formatting of the [Date and Time] field on Shewhart control charts. In the drop-down list, a different date and time field format is selected.

Figure 4. Main button panel, button for managing point labels on Shewhart control charts.

Figure 5. Control panel for [red] dot labels on Shewhart control charts activated. The source data table column [Date and Time] is selected for labels.

Figure 6. The panel for managing the labels of all points on Shewhart control charts is activated. The source data table column (Values) is selected for labels.

Figure 7. The control panel with vertical dotted lines dividing series of points by areas of action of factors of the selected type is activated. The source data table column (Raw Materials) is selected as this type of factor.

The drop-down list of factors in the control panel with vertical dotted lines dividing a series of points (Figure 4) is formed only from columns that have rows of conditionally constant conditions (repeating values). And empty values ​​of factors (conditions) are replaced with the text “Factor not specified”

Below is the function of breaking the connecting line for visually separating a series of points in accordance with the areas of action of the sources of variations [Factors], displayed in the form of vertical dotted lines, which makes it much easier to interpret Shewhart control charts. For example, when studying parallelism, position and consistency of individual series of subgroups. See the use case in Donald Wheeler's article: Evaluating the Measurement Process (EMP) using simple graphical methods .

Figure 8. The control panel for graph line breaks by areas of influence of factors of the selected type is activated. The source data table column (Raw Materials) is selected as this type of factor.

You can move through the drop-down lists (columns) of factors in the corresponding control panels by selecting from the drop-down list or by sequentially scrolling with the mouse roller in the drop-down list area.

We recommend using the Sources of Variation [Factors] fields to record the conditions under which the controlled characteristic of the product or service was produced and the analyzed value was obtained. For example, a tool (in the Tool column), a batch of raw materials (in the Raw Materials column), full name of the operator (in the Operator column), machine (in the Equipment column), machine adjustments (in the Equipment Settings column), measuring tool (in the Measuring Tool column), controller (in the Controller column), etc. to record any conditionally constant and variable external conditions.

All this will be needed to identify the variations identified by the control chart, the source of which is the special causes of process changes that can and must be eliminated at the shop level.

And vice versa, if signs of the presence of special causes in the observed variations are not identified by the control chart, this will make it possible to confidently attribute such sources of observed variations to the general causes of variability (systemic causes), which are in the field of activity of the enterprise management, and not the shop personnel.

This function allows you to visually search for the relationship of various factors with identified signs of the action of special causes of variations at points highlighted in red in accordance with the user's applied Western Electric zonal criteria .

The user can show or hide the block with formulas for calculating control limits. By default, the block with formulas for calculating control limits is hidden.

Figure 9. Main control panel. The [Show formula and value blocks] button is highlighted.

Figure 10. Control panel for demonstrating and hiding formula blocks for calculating the boundaries of Shewhart’s XmR control chart (individual values). The formula block is hidden.

Figure 11. Control panel for demonstrating and hiding formula blocks for calculating the boundaries of Shewhart’s XmR control chart (individual values). The formula block is displayed in the graph area.

Figure 12. Control panel for demonstrating and hiding formula blocks for calculating the boundaries of Shewhart’s XbarR control chart (means and ranges of subgroups). The formula block is displayed in the graph area.

Annotations with subgroup numbers for user-selected points

Figure 13. Opening an annotation with a subgroup number for a user-selected point is done by clicking the left mouse button while hovering the cursor over the point. Hiding an annotation is done by clicking the right mouse button while hovering the mouse cursor over the annotation area (not over a point).

Reproducibility indices Cp, Cpk

Reproducibility indices Cp (vital space of the process relative to the tolerance field), Cpk (centering of the process in the tolerance field) are automatically calculated for the initial construction of the control chart. Further, when modifying control limits using the functions fixation of control limits , control limits for individual batches , deleting points - reproducibility indices Cp, Cpk are not recalculated.

Starting from version v.3.23, the values ​​of the calculated reproducibility indices Cp, Cpk and Sigma of the process [σ] are displayed in a separate text block in the center of the canvas with graphs by clicking on the [Sigma, Cp, Cpk] button under the graphs.

Figure 14. If a process exhibits a statistically uncontrolled state, a warning button “Attention!” is displayed to the left of the [Sigma, Cp, Cpk] button.

Figure 15. Text block with calculated process Sigma [σ] and reproducibility indices Cp, Cpk, which is hidden by clicking the [Sigma, Cp, Cpk] button again.

Attention! If the process is in a statistically uncontrollable state, the indices (Cp, Cpk) are meaningless; such a process is, by definition, irreproducible.

Important! Reproducibility indices have serious disadvantages compared to simple graphical methods (control chart and histogram of the distribution of values ​​with tolerance limits). Apart from the above, reproducibility indices must be used in pairs, otherwise you will be easily misled by each of them.

The living space index (Cp) does not say where the process is located relative to the tolerance limits, inside or even entirely outside the tolerance boundaries. The centering index (Cpk) does not give an idea of ​​the side of the displacement of a stable process from the center of the tolerance field, and therefore hides information important for improving the process, and is meaningless if the value does not coincide with the center of the tolerance field (asymmetric tolerance fields).

To understand the method for calculating the reproducibility indices Cp, Cpk and their disadvantages, read the article: Is it enough to analyze distribution histograms and reproducibility indices Cp, Cpk? Start your analysis by building Shewhart control charts!

Figure 16. A warning message window about the application of reproducibility indexes to an unstable process has opened, which can be opened by left-clicking on the “Attention!” button. to the left of the [Sigma, Cp, Cpk] button.

Legend

The content of the symbols depends on the context of the graphic canvas and is displayed in separate text blocks by clicking the left mouse button. Closing by pressing the same button again.

Figure 17. Text blocks with symbols.

Video 1. Captions for points, vertical separators, a break in the connecting line of the graph for visual separation of a series of points, blocks of formulas, reproducibility indices Cp and Cpk on graphs of Shewhart control charts. Software Shewhart control charts PRO-Analyst +AI