Help Manual

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Sigma Magic Help Version 15

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 list of available control charts within this tool is shown in the figures below. The following figure shows the list of standard control charts for continuous data. spc charts 2 The following figure shows the list of special control charts for continuous data. spc charts 2 The following figure shows the list of control charts for discrete (defects & defectives) data. spc charts 2 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.
inputs
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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:
OptionDescription
ContinuousContinuous data can take any arbitrary value (like the temperature of the room example 34.53 deg centigrade).
DefectsDefect refers to failing to meet what the customer/client wants or fails to achieve the customer/client CTQ. Depending on the product we are working with, a product may have N number of defects.
DefectivesDefective means the failing 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.
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Input Type: Specify how the input data for this analysis is formatted. The available options are:
OptionDescription
Group DataUse 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 is used to determine the subgroups. This option is only available for continuous data. For discrete data, you can only specify grouped data.
Raw DataUse this option if your data is stored in separate columns. For continuous data, if you specify multiple columns then all the columns are grouped together to determine the subgroup data.
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Chart Type: Specify the control chart you want to create. If you specify "Auto" then 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:
OptionDescription
I-MR ChartIndividual Value-Moving Range chart for continuous data where the subgroup size is 1.
Z-MR ChartZ value-Moving Range chart for continuous data that is typically used for short-runs.
Xbar-R ChartXbar-R chart for continuous data when subgroup size is between 2-10.
Xbar-S ChartXbar-S chart for continuous data when subgroup size is greater than 10.
MA ChartMoving Average chart for continuous data (specify the MA length).
EWMA ChartExponentially Weighted Moving Average chart for continuous data.
CUSUM ChartCumulative Sum chart for detecting small shifts in process average.
Pre-Control ChartPre-control chart for continuous data where the number of subgroups is very small.
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Parameter: Some of the control charts require a design parameter to compute the control limits. The following parameters are required:
OptionDescription
CUSUM ChartFor 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 ChartFor 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, then the last 2 data points are used to compute the average. The default value for the MA length is 2.
EWMA ChartFor 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.
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Subgroup Type: Specify how you want to enter subgroup information. The available options are:
OptionDescription
ConstantIf you specify the subgroup size is a constant, you will need to specify the constant subgroup size in the dialog box.
VariableIf you specify that subgroup is entered on the worksheet, then must specify the subgroup information on the worksheet. You will need to specify this information when you select your data for analysis.
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Subgroup Constant: If you specify that the subgroup is constant, then you will need to enter the constant subgroup size in the input dialog box. Make sure that the subgroup constant is an integer greater than 0.
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X Axis: Specify the type of X-axis you would like for the control chart. The available options are:
OptionDescription
IndexIf you specify index, then the subgroups are displayed as 1, 2, 3.
DatesIf you specify dates, then a column will be shown in the Inputs area on the worksheet where you can enter dates for each data point and the subgroups are displayed based on the dates entered.
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Stages: Specify if you want to plot the control chart by stages. If you don't have any stages, all the data points are plotted together. If your data has stages, then 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 sages in the data (for example before & after improvement).
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Flowchart: Click on this button to view the flowchart for this analysis. The flowchart shows the control logic for how a test is selected based on the data type and subgroup size when the auto mode is selected for control charts.
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Help Button: Click on this button to view the help file for this topic.
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Cancel Button: Click on this button to discard the changes and exit the dialog box.
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OK Button: Save changes and try to compute analysis if all the required data is available for analysis.
A sample screenshot of the setup menu for discrete (defects) is shown below.
inputs Most of the menu options are similar to the continuous case. The few differences are shown below:
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Data Type: The data type in the discrete case would read either Defects of Defectives.
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Input Type: For discrete data, this input box is disabled since there is only one option allowed - Group Data.
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Chart Type: If you change the data type to Defects Data then only those charts that are applicable for defects data are shown in this dropdown box. In this case, the available options are:
OptionDescription
AutoThe software will try to pick the best possible chart for your situation.
C ChartCount chart for defects data with constant subgroup size.
U ChartCount per Unit chart for defects data with varying subgroup size.
Laney U' ChartCount per Unit chart for defects data with very large subgroup sizes.


If you change the data type to Defectives Data then the charts that are applicable for defectives data are shown in the dropdown box. In this case, the available options are:
P ChartProportion chart for defectives data with varying subgroup sizes.
NP ChartSubgroup Size times Proportion chart for defectives data with constant subgroup sizes.
Laney P' ChartProportion chart for defectives data with very large subgroup sizes.
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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 and the data you enter in the Data tab will be used to determine the subgroups and the Subgroup Constant field will be disabled.

Data

If you click on the Data button, you will see the following dialog box. Here you can specify the data required for this analysis. Data
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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 to speed up finding the right data to use 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.
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Available Data: The available data box contains the list of data available for analysis. If your workbook does not have any 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 important that you not only specify the column name but also the table name.
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Add or View Data: Click on this button either to add more data into 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 up the Data Editor dialog box where you can import more data into your workbook, or you can switch from the list view to a table view to see the individual data values for each column.
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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, then you will need to select only numeric columns. If the code starts with a T, then you can select both 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, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data in this box. If the minimum value is 0, then no data is required to be specified for this box.
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Select Button: Click on this button to select the data for analysis. Any data you select 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 select the data is to double click on the columns in the list of Available Data. Finally, you can also 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.
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Selected Data: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the 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 have to select for this exercise depends on the options you specify in the dialog box. The following options are available:
FieldDescription
Control VariableThis 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 VariableThis 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 VariableIf 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" then this field is disabled.
Stage VariableIf you have selected "Yes" for Stages, then you will need to specify a column that contains stage info. If you have selected "No" stages, then this field is disabled.
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View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in a tablular format or in a graphical summary.

SPC Tests

If you click on the SPC Tests button, you will see the following dialog box. Here you can specify the tests you would like to perform for your analysis. Data
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Control Limits: Specify how you want to determine the control limits. The following options are available:
OptionDescription
AutoThe software will determine the control limits from the data you have specified. This is the default option.
Historical ParametersThe 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.
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Test for Special Causes: Determine what tests you want to perform to check if your process is in control. The following options are available.
OptionDescription
NoneDo not perform any tests to check if the process is in control.
AIAGUse the AIAG standards for checking if a process is in control.
BasicOnly use the control limits to determine if a process is in control. If any data points fall outside the control limits, then the process is reported as not being in control.
CustomDefine your own standards to check if the process is in control.
MontgomeryUse the tests recommended by Montgomery to check if process is in control.
NelsonUse the tests recommended by Nelson to check if process is in control.
WesternUse the tests recommended by Western to check if process is in control.
WestgardUse the tests recommended by Westgard to check if process is in control.
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Include Points: Specify what groups should be included to calculate the control limits. If you leave this field blank, then all subgroups available 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;22-25.

Note that for some cases you may not have the option of specifying the Include Points for analysis. In those cases, the textbox will change so that you can specify other options for analysis. For example, if you are creating a CUSUM control chart, then this option will change and you will be asked to enter the Slack (K) variable. The slack variable is used to determine the mean-shift for the control chart and the default value is 0.5. If you are creating a Pre Control chart, then 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.
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Exclude Points: Specify what groups you would like to exclude in calculating the control limits. For example, if you specify exclude as 21;26;27 then 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, then all groups are included to calculate the control limits except group 22. If the include groups contain 1-30 and exclude groups contain 22, then the groups used to compute the control limits are 1-21 and 23-30.

Note that for some cases you may not have the option of specifying the Exclude Points for analysis. In those cases, the textbox will change so that you can specify other options for analysis. For example, if you are creating a CUSUM control chart, then 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 are creating a Pre Control chart, then 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.
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Test: When you change the test in the "Test for Special Causes", the correponding test limits are shown on the dialog box. Note, that you can only view the standards for AIAG, Basic, Montgomery, Nelson, Western, and Westgard. 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 that are currently available within the software for the standard control charts.

Test # Description AIAG Basic Montgomery Nelson Western Westgard
1 K points more than 3 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 2 stdev from the center line. 2 2 2 2 2
6 K points out of K+1 are more than 1 stdev from the center line. 4 4 4 4
7 K points in a row are within 1 stdev of the center line. 15 15 15
8 K points in a row are more than 1 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.

For a pre-control chart, for pre-qualification of the process set up, we require five consecutive data points that should fall in the green zone. If any data point falls in the yellow or red zone, then the counting is restarted until there are five consecutive data points are in the green zone. Note that for pre-control charts, if you specify "Basic", then only test #1 will be performed otherwise all the pre-qualification tests will be performed.

Charts

If you click on the Charts button, you will see the following dialog box. Charts
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Pick Charts: Select the charts you would like to display for this analysis.
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Title: The system will automatically pick a title for your chart. However, if you would like to override that with your own title you can specify a title for your chart here. Note that this input is optional.
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Sub Title: The system will automatically pick a subtitle for your chart. However, if you would like to override that with your own subtitle you can specify a subtitle for your chart here. Note that this input is optional.
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X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your own label for the x-axis you can specify a different label here. Note that this input is optional.
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Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your own label for the y-axis you can specify a different label here. Note that this input is optional.
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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 specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20 then 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.
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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 specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20 then the minimum y-axis scale is set at 10 and the maximum y-axis scale 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.
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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 then two horizontal lines are plotted at Y = 12 and Y = 15 respectively. Note that this input is optional.
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Vertical Lines: If you want to add a few extra vertical 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 2;5 then two vertical lines are plotted at X = 2 and X = 5 respectively. Note that this input is optional.

Verify

If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the dialog box is shown in the figure below. Verify The objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software may check 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, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.

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. spc task menu 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 on this dialog box are the ones that you have selected in the Input dialog box. show tests 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. format spc charts
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Subgroup From: If you leave this textbox blank, then 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 analysis such as to determine control limits etc.
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Subgroup To: If you leave this textbox blank, then the charts will display all the subgroups until the last subgroupo. However, if you want to focus on a part of the graph, you can enter 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 analysis such as to determine control limits etc.
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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.
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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.
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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.
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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.
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Chart 1 LB: You can specify a lower bound for Chart 1. If the LCL calculated is higher than the lower bound value, then no action is taken. 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.
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Chart 1 UB: You can specify a upper bound for Chart 1. If the UCL calculated is lower than the upper bound value, then no action is taken. 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.
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Chart 2 LB: You can specify a lower bound for Chart 2. If the LCL calculated is higher than the lower bound value, then no action is taken. 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.
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Chart 2 UB: You can specify an upper bound for Chart 2. If the UCL calculated is lower than the upper bound value, then no action is taken. 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.
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Stdev 1: You can superimpose the 1-stdev lines on the control chart by selecting this checkbox. Note that by default, only the 3-stdev lines are shown on the control chart.
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Stdev 2: You can superimpose the 2-stdev lines on the control chart by selecting this checkbox. 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. annotate spc points
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Pick Point: Click on this button to pick a point on the control chart that 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 to only pick that one point for annotation.
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Point Num: When you click on a point from the previous step, it should automatically list the point that was selected in this dropdown box. If not, you can manually select or type in the point in this box.
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Chart Num: When you select a point, the chart number should automatically be displayed here. If not, you can specify the chart that you want to annotate.
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Add Text: Enter a text that you want to use for the annotation in this textbox.
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Delete Text: Click on this button to delete any point that was previous selected for annotation.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. outputs The notes section contains a summary of 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 and 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, 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, then Sigma Magic will list the data point number and the test that has failed (if any). Finally, the conclusion lists if the data is in or not in control.

If you had specified stages for your control charts, then an output such as the one shown below will be plotted. Each stage will have its own control limits and tests for special causes. outputs with stages For discrete data, let's say defects, the control chart such as the one shown below will be plotted. defects control chart For special control charts - like the exponentially weighted moving average charts, a chart such as the one shown below will be plotted. ewma charts The graphs section contains the control charts. Each chart contains the raw data points (shown in blue) plotted with respect to the control limits. If any points are out of control, then 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 is shown below with the different zones. There are three different types of pre-control charts depending on the type of 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 exactly between the lower and upper control limits and the centerline. If a unilateral specification limit with an LSL is specified (which means that the largest 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, if a unilateral specification limit with a USL is specified (which means that the lowest value is optimal), then a Type III pre-control chart is plotted. The pre-control limit is calculated based on the USL value and the lower bound. pre control

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 then the system will not calculate the control limits from the data you have entered but use the historical mean and standard deviation to estimate the control limits.
  • Use the pre-control charts with caution 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

Following examples can be found in the Examples folder.
  • Create a control chart for the overall 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.xlsm).
  • 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 with the number of items inspected and the number of items defective. (SPC.xlsm).
  • Create a control chart for the number of defects found in the process. Each part can be an opportunity of 10 defects per part. The data is collected by week with the number of items inspected and the number of defects found. (SPC.xlsm).