Sigma Magic Help Version 17

Control Charts

Overview

Statistical Process Control (SPC) can be used to determine if a process is in control. This tool can be used to analyze both continuous data and discrete / attribute data. The control chart plots the data between two control limits (Lower Control Limit - LCL and Upper Control Limit - UCL) to determine if a process is in control.

The available control charts within this tool are shown in the figures below. The following figure shows the list of standard control charts for continuous data. The following figure shows the list of unique control charts for continuous data. The following figure shows the list of control charts for discrete (defects & defectives) data. This tool can be added to your active workbook by clicking on Stats and then selecting Control Charts.

Inputs

Click on Analysis Setup to open the menu options for this tool.

Setup

A sample screenshot of the setup menu for continuous data is shown below.

1	Data Type: Specify the type of data for which you want to create the control chart. The type of control chart created depends on the type of data entered. The available options are: Option Description Continuous Continuous data can take any arbitrary value (like the temperature of the room example, 34.53 degrees centigrade). Defects Defect refers to failing to meet what the customer/client wants or failing to achieve the customer/client CTQ. Depending on the product we are working with, a product may have N defects. Defectives Defective means the failure of the entire product/service to meet the required criterion. A defective product may have one or more defects, but not all defects make a product defective. A product or service can either be defective or not defective.
2	Input Type: Specify how the input data for this analysis is formatted. The available options are: Option Description Group Data Use this option if your data is organized in groups. You should have one data column and one group column. The information you provide in the group column determines the subgroups. This option is only available for continuous data. For discrete data, you can only specify grouped data. Raw Data Use this option if your data is stored in separate columns. For continuous data, if you specify multiple columns, all the columns are grouped to determine the subgroup data.
3	Chart Type: Specify the control chart you want to create. If you specify "Auto, " the software will automatically pick a chart based on your inputs. If you specify pre-control as the control chart, then instead of estimating the control limits, the control chart is based on the specification limits. For a pre-control chart, there are three zones. If any data points exceed the specification limits, they are in the red zone. In addition to the control limits, pre-control limits are plotted on the chart. If data points fall within the pre-control limits, they are in the green zone, and between the pre-control limits and the control limits, they are in the yellow zone. The following charts are available in this module: Option Description I-MR Chart Individual Value-Moving Range chart for continuous data where the subgroup size is 1. Z-MR Chart Z value-Moving Range chart for continuous data that is typically used for short runs. Xbar-R Chart Xbar-R chart for continuous data when subgroup size is between 2-10. Xbar-S Chart Xbar-S chart for continuous data when subgroup size is greater than 10. MA Chart Moving Average chart for continuous data (specify the MA length). EWMA Chart Exponentially Weighted Moving Average chart for continuous data. CUSUM Chart Cumulative Sum chart for detecting small shifts in process average. Pre-Control Chart Pre-control chart for continuous data where the number of subgroups is minimal.
4	Parameter: Some control charts require a design parameter to compute the control limits. The following parameters are required: Option Description CUSUM Chart For the CUSUM chart, you need to specify the target you are trying to achieve for your data points, the allowable slack (K), which is the difference in mean that you would like to be able to detect and the control limits parameter (H), which is used to determine the control limits. The default values are: k = 0.5 and H = 4. MA Chart For the Moving Average chart, you need to specify the MA length. The length is used to determine the moving average. For example, if the length is 2, the last 2 data points are used to compute the average. The default value for the MA length is 2. EWMA Chart For the Exponentially Weighted Moving Average chart, you need to specify the alpha constant. The alpha constant is used to weigh historical data points. The default value for the EWMA constant is 0.2.
5	Subgroup Type: Specify how you want to enter subgroup information. The available options are: Option Description Constant If you specify that the subgroup size is a constant, you will need to specify the constant subgroup size in the dialog box. Variable If you specify that subgroup is entered on the worksheet, then you must specify the subgroup information on the worksheet. You must specify this information when you select your data for analysis.
6	Subgroup Constant: If you specify that the subgroup is constant, you must enter the constant subgroup size in the input dialog box. Make sure that the subgroup constant is an integer greater than 0.
7	X Axis: Specify the type of X-axis you would like for the control chart. The available options are: Option Description Index If you specify an index, then the subgroups are displayed as 1, 2, 3. Dates If you specify dates, then a column will be shown in the Inputs area on the worksheet You can enter dates for each data point, and the subgroups will be displayed based on the dates entered.
8	Stages: Specify if you want to plot the control chart by stages. All the data points are plotted together if you don't have any stages. If your data has stages, each stage is treated as one entity, and control charts are created for each stage. You can have any number of stages on your control chart. If you specify that you have stages, then The software will display the stage column in the Inputs area on the worksheet, and you can specify the stages in the data (for example, before & and after improvement).
9	Flowchart: Click on this button to view the flowchart for this analysis. The flowchart shows the control logic for selecting a test based on the data type and subgroup size when the auto mode is selected for control charts.
10	Help Button: Click on this button to view the help file for this topic.
11	Cancel Button: Click on this button to discard the changes and exit the dialog box.
12	OK Button: Save changes and try to compute analysis if all the required data is available.

A screenshot of the setup menu for discrete (defects) is shown below.
Most of the menu options are similar to the continuous case. The few differences are shown below:

1	Data Type: The data type in the discrete case would read either Defects or Defectives.
2	Input Type: For discrete data, this input box is disabled since only one option is allowed - Group Data.
3	Chart Type: If you change the data type to Defects Data, only those charts applicable to defect data are shown in this dropdown box. In this case, the available options are: Option Description Auto The software will try to pick the best possible chart for your situation. C Chart Count chart for defects data with constant subgroup size. U Chart Count per Unit chart for defects data with varying subgroup size. Laney U' Chart Count per Unit chart for defects data with huge subgroup sizes. If you change the data type to Defectives Data, the charts applicable to defective data are shown in the dropdown box. In this case, the available options are: P Chart Proportion chart for defectives data with varying subgroup sizes. NP Chart Subgroup Size times Proportion chart for defective data with constant subgroup sizes. Laney P' Chart Proportion chart for defective data with huge subgroup sizes.
4	Subgroup Constant: For discrete data, the subgroup constant refers to the total number of samples in the subgroup. Use this only if the subgroup size is constant. If your subgroup size is variable, you will need to change the subgroup type to Variable. The data you enter in the Data tab will be used to determine the subgroups, and the Subgroup Constant field will be disabled.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis.

1	Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and speed up the search for the right data for analysis. Enter a few characters in the search field, and the software will filter and display the filtered data in the Available Data box.
2	Available Data: The available data box contains the list of data available for analysis. If your workbook has no data in tabular format, this box will display "No Data Found." The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is crucial that you not only specify the column name but also the table name.
3	Add or View Data: Click on this button to add more data to your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens the Data Editor dialog box, where you can import more data into your workbook. You can also switch from the list view to a table view to see the individual data values for each column.
4	Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, you must select only numeric columns. If the code begins with a T, you can select numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, you must select a minimum of 2 columns of data and a maximum of 4 columns in this box. If the minimum value is 0, then no data is required to be specified for this box.
5	Select Button: Click on this button to select the data for analysis. Any data you choose for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to choose the data is to double-click on the columns in the list of Available Data. Finally, you can drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
6	Selected Data: The list box header will be displayed in black if the right number of data columns is specified. If sufficient data has not been specified, then the list box header will be displayed in red color. Note that you can double-click on any of the columns in this box to remove them from the box. The data you must select for this exercise depends on the options you specify in the dialog box. The following options are available: Field Description Control Variable This field is always enabled, and you will need to specify the column that contains the data for which you want to create the control chart. Subgroup Variable This field defines the subgroup for your analysis. This field is only enabled if you have specified that your Subgroup Type is a Variable. If your Subgroup Type is constant, then this field is disabled. X-Axis Variable If you have selected "Dates" for the X-axis variable in your setup, you will need to specify a column that contains the dates in this field. If your X-Axis variable has been set to "Index, " this field is disabled. Stage Variable If you have selected "Yes" for Stages, then you will need to specify a column that contains stage info. If you select "No" stages, this field is disabled.
7	View Selection: Click on this button to view the data specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

SPC Tests

You will see the following dialog box if you click the SPC Tests button. Here, you can specify the tests you want to perform for your analysis.

1	Control Limits: Specify how you want to determine the control limits. The following options are available: Option Description Auto The software will determine the control limits from the data you have specified. This is the default option. Historical Parameters The software will estimate the control limits from historical data. You will need to specify the parameters for the historical data for this analysis. Note that the data you have entered will be plotted against the control limits derived from historical data. Use this option if you want to freeze your control limits.
2	Test for Special Causes: Determine what tests you want to perform to check if your process is controlled. The following options are available. Option Description None Do not perform any tests to check if the process is in control. AIAG Use the AIAG standards for checking if a process is in control. Basic Only use the control limits to determine if a process is in control. If data points fall outside the control limits, the process is reported as not being in control. Custom Define your standards to check if the process is in control. Montgomery Use the tests recommended by Montgomery to check if the process is in control. Nelson Use the tests recommended by Nelson to check if the process is in control. Western Use the tests recommended by Western to check if the process is in control. Westgard Use the tests recommended by Westgard to check if the process is in control.
3	Include Points: Specify what groups should be included to calculate the control limits. If you leave this field blank, all subgroups in your input columns will be used to calculate the control limits. If you want to include only certain groups, you need to specify the groups. For example, if you want the first 20 groups to be used to calculate control limits, specify the include as 1-20. If you want to include groups from 1-20 and 22-25 (that does not include group 21), then you would specify it as 1-20 and 22-25. Note that you may not have the option to specify the Include Points for analysis in some cases. In those cases, the textbox will change so that you can select other options for analysis. For example, if you create a CUSUM control chart, this option will change, and you will be asked to enter the Slack (K) variable. The slack variable determines the mean shift for the control chart, and the default value is 0.5. If you create a Pre Control chart, this option will change to an LSL/LB value, and you will need to specify the Lower Control Limit or the Lower Bound for your analysis.
4	Exclude Points: Specify what groups you would like to exclude when calculating the control limits. For example, if you specify exclude as 21;26;27, these specific groups (21, 26, and 27) will not be used to calculate the control limits. For example, if include groups are blank and exclude groups contain 22, all groups are included in calculating the control limits except group 22. If the included groups contain 1-30 and excluded groups contain 22, then the groups used to compute the control limits are 1-21 and 23-30. Note that you may not have the option to specify the Exclude Points for analysis in some cases. In those cases, the textbox will change so that you can select other options for analysis. For example, if you create a CUSUM control chart, this option will change, and you will be asked to enter the Limits (H) variable. The limits variable is an option for the CUSUM chart to determine how to compute the control limits. The default value is 4. If you create a Pre Control chart, this option will change to a USL/UB value, and you will need to specify either the Upper Control Limit or the Upper Bound for your analysis.
5	Test: When you change the test in the "Test for Special Causes," the corresponding test limits are shown in the dialog box. Note that you can only view the AIAG, Basic, Montgomery, Nelson, Western, and Westgard standards. If you want to define your standards, you can modify the value of K for the Custom tests. Modify this with caution since these values have been derived from probability theory and should not be changed unless there is a strong reason to make a change. Here are the tests currently available within the software for the standard control charts. Test # Description AIAG Basic Montgomery Nelson Western Westgard 1 K points more than three stdev. From the center line. 1 1 1 1 1 1 2 K points in a row are on the same side of the center line. 7 8 9 8 8 3 K data points in a row are all increasing or decreasing. 6 6 6 7 4 K points in a row are alternating up and down. 14 14 14 5 K out of K+1 points more than two stdev from the center line. 2 2 2 2 2 6 K points out of K+1 are more than one stdev from the center line. 4 4 4 4 7 K points in a row are within one stdev of the center line. 15 15 15 8 K points in a row are more than one stdev from the center line. 8 8 8 For the pre-control charts, the tests for special causes are shown in the following table: Test # Description 1 Any data point falls outside the control limits in the red zone. 2 If 2 data points fall in the yellow zone. We require five consecutive data points that should fall in the green zone for a pre-control chart and pre-qualification of the process setup. If any data point drops in the yellow or red zone, the counting is restarted until five successive data points are in the green zone. Note that for pre-control charts, if you specify "Basic," only test #1 will be performed; otherwise, all the pre-qualification tests will be performed.

Charts

You will see the following dialog box if you click the Charts button.

0	Pick Charts: Select the charts you would like to display for this analysis.
1	Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
2	Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
3	X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
4	Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.
5	X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum x-axis scale is set at 10, and the maximum x-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the x-axis increment is set at 2. Note that this input is optional.
6	Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum y-axis scale is set at 10, and the maximum y-axis is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
7	Horizontal Lines: If you want to add a few extra horizontal reference lines on top of your chart, you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15, two horizontal lines are plotted at Y = 12 and Y = 15, respectively. Note that this input is optional.
8	Vertical Lines: You can specify the values here if you want to add a few extra vertical reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5, two vertical lines are plotted at X = 2 and X = 5, respectively. Note that this input is optional.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange exclamation mark, and finally, any checks that are required to be performed by the user are shown as blue info icons.

1	Item: The left-hand side shows the major tabs and the items checked within each section
2	Status: The right-hand side shows the status of the checks.
3	Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Worksheet

When the tool is opened, the main menu at the top may change to a task-specific menu, as shown below. If this menu does not open, click on the F4 button or the small arrow at the bottom right portion of your menu group to open this menu bar. On the task menu bar, we can perform the following actions. Click on Show Tests to open the special causes tests. A sample screenshot of the dialog box is shown below. This will show the currently active tests - the test number and description of the test. The tests displayed in this dialog box are those you selected in the input dialog box. Click on Format Charts to open the format control charts dialog box. A sample screenshot of the dialog box is shown in the figure below.

1	Subgroup From: If you leave this textbox blank, the charts will display from the first subgroup. However, if you want to focus on a part of the graph, you can enter a starting subgroup number in this textbox. All subgroups below this value will be excluded from the control chart. Note that this is only for display purposes, and these points will continue to be used for other analyses, such as determining control limits, etc.
2	Subgroup To: If you leave this textbox blank, then the charts will display all the subgroups until the last subgroup. However, you can enter if you want to focus on a part of the graph. An ending subgroup number in this textbox. All subgroups above this value will be excluded from the control chart. Note that this is only for display purposes, and these points will continue to be used for other analyses, such as determining control limits, etc.
3	Chart 1 Min: You can specify the minimum value for the Y-axis for Chart 1. If you leave these fields blank, the software will automatically pick the best possible values for this chart. However, if a value is specified here, it will override the automated selection.
4	Chart 1 Max: You can specify the maximum value for the Y-axis for Chart 1. If you leave these fields blank, the software will automatically pick the best possible values for this chart. However, if a value is specified here, it will override the automated selection.
5	Chart 2 Min: You can specify the minimum value for the Y-axis for Chart 2. If you leave these fields blank, the software will automatically pick the best possible values for this chart. However, if a value is specified here, it will override the automated selection.
6	Chart 2 Max: You can specify the maximum value for the Y-axis for Chart 2. If you leave these fields blank, the software will automatically pick the best possible values for this chart. However, if a value is specified here, it will override the automated selection.
7	Chart 1 LB: You can specify a lower bound for Chart 1. No action is taken if the LCL calculated is higher than the lower bound value. However, if the LCL value of the chart is less than the lower bound value, then the LCL value is replaced by the lower bound value.
8	Chart 1 UB: You can specify an upper bound for Chart 1. No action is taken if the UCL calculated is lower than the upper bound value. However, if the UCL value of the chart is greater than the upper bound value, then the UCL value is replaced by the upper bound value.
9	Chart 2 LB: You can specify a lower bound for Chart 2. No action is taken if the LCL calculated is higher than the lower bound value. However, if the LCL value of the chart is less than the lower bound value, then the LCL value is replaced by the lower bound value.
10	Chart 2 UB: You can specify an upper bound for Chart 2. No action is taken if the UCL calculated is lower than the upper bound value. However, if the UCL value of the chart is greater than the upper bound value, then the UCL value is replaced by the upper bound value.
11	Stdev 1: Selecting this checkbox, you can superimpose the 1-stdev lines on the control chart. Note that by default, only the 3-stdev lines are shown on the control chart.
12	Stdev 2: Selecting this checkbox, you can superimpose the 2-stdev lines on the control chart. Note that by default, only the 3-stdev lines are shown on the control chart.

Click on Annotate to open the annotation control charts dialog box. A sample screenshot of the dialog box is shown in the figure below.

1	Pick Point: Click this button to pick a point on the control chart you want to annotate. Note that if you click on a data point the first time, it may pick all the points. If this is the case, you may need to click on the data point a second time only to pick that one point for annotation.
2	Point Num: When you click on a point from the previous step, it should automatically list the selected point in this dropdown box. If not, you can manually select or type in the point in this box.
3	Chart Num: The chart number should automatically be displayed when you select a point. If not, you can specify the chart that you want to annotate.
4	Add Text: Enter a text you want to use for the annotation in this textbox.
5	Delete Text: Click on this button to delete any previously selected point for annotation.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. The notes section summarizes the input data used for the analysis. Specifically, it lists the data type, the methodology to determine the control chart, the subgroup size, the method used to determine the control limits, any tests for special causes, the number of data points entered on the worksheet, and the number of stages in the input data. The assumptions check if there are sufficient data points to perform this analysis. The analysis results section specifies the name of the control chart and the mean, lower, and upper control limits for each of the control charts displayed. The control limits are displayed for each stage of the data set. If any data points fail the test for special causes, Sigma Magic will list the data point number and the failed test (if any). Finally, the conclusion lists whether the data is in control.

If you had specified stages for your control charts, an output such as the one below will be plotted. Each stage will have its own control limits and tests for special causes. For discrete data, such as defects, a control chart, such as the one shown below, will be plotted. For unique control charts, such as the exponentially weighted moving average charts, a chart like the one shown below will be plotted. The graphs section contains the control charts. Each chart contains the raw data points (shown in blue) plotted concerning the control limits. If any points are out of control, they are shown in red. The raw data points that are plotted are as follows:

• I-MR Chart: individual values and moving ranges
• Xbar-R Chart: sample averages and sample ranges
• Xbar-S Chart: sample averages and standard deviations
• P Chart: proportions of defectives
• NP Chart: the actual count of defectives
• C Chart: count of the total defects in each subgroup
• U Chart: count per unit of the defects in each subgroup

An example pre-control chart with the different zones is shown below. There are three types of pre-control charts depending on the specification limits. If there are bilateral specification limits (both LSL and USL), then a Type I pre-control chart is used. The pre-control limits lie precisely between the lower and upper control limits and the centerline. If a unilateral specification limit with an LSL is specified (the most significant value is optimal), then the Type II pre-control chart is plotted. The pre-control limit is calculated based on the LSL value and the upper bound. Finally, a Type III pre-control chart is plotted if a unilateral specification limit with a USL is specified (which means that the lowest value is optimal). The pre-control limit is calculated based on the USL value and the lower bound.

Notes

Here are a few pointers regarding this analysis:

• You can set the calculation of the control limits to the historical process. For example, if you set the historical process mean and standard deviation, the system will not calculate the control limits from the data you entered; instead, it will use the historical mean and standard deviation to estimate the control limits.
• Use the pre-control charts cautiously, as they may drive the wrong behavior. When given a choice, you should use the regular control charts to determine if a process is in control.

Examples

The following examples are in the Examples folder.

• Create a control chart for the lead time between customer order and delivery. The data points are collected randomly (one point per week randomly selected). Is this process in control? (SPC.xlsx).
• Create a control chart for the diameter of a machined part measured in cm. The part specification limits are LSL = 100 and USL = 102. Is this process in control? (SPC.xslx).
• Create a control chart for the number of defective components manufactured in a factory. The data is collected by week, including the number of items inspected and the number of items defective. (SPC.xlsx).
• Create a control chart for the number of defects in the process. Each part can be an opportunity for ten defects per part. The data is collected by week, including the number of items inspected and the number of defects found. (SPC.xlsx).