Sigma Magic Help Version 15

Capability Analysis

Overview

Capability Analysis can be used to determine if the process is capable of meeting customer needs. Capability analysis can be used to compute the Sigma Level of the process, Defects per Million Opportunities (DPMO), and capability indices such as Cp and Cpk. To perform the capability analysis, you would need both the Voice of the Customer (such as LSL, USL, and/or definition of defects) and Voice of the Process (raw data points or mean, standard deviation, number of defects, etc.). It can be used for both continuous data and discrete data.

This tool can be added to your active workbook by clicking on Stats and then selecting Capability Analysis.

Analysis Setup

Click on the Analysis Setup button on the main menu bar to specify the options for this tool.

Setup

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

1	Data Type: Specify the type of data you are dealing with. Option Description Continuous Continuous data refers to measurements on a continuum or scale that can be meaningfully subdivided into infinitely small increments, depending on the precision of the measurement system. Examples of continuous measurements are time, temperature, weight, currency etc. Defects Defects are any item or service that exhibits a departure from specifications. A defect does not necessarily mean that the product or service cannot be used. Defectives Defectives refer to the entire product or service and refer to the condition that the product or service is not usable. A product may have many defects - not all of these defects may cause the product to be defective.
2	Input Type: Specify the data source for this analysis. Option Description Summarized Data If you specify Summarized data, then you will need to enter a statistical summary of your data directly in the input dialog box. For continuous data, you will need to specify the mean and standard deviation. Note that the mean and standard deviation inputs will be enabled for this option. Raw Data If you specify the option worksheet, the system expects that you will specify the data file from a data file using the Analysis Data option. The software will automatically calculate the required statistics from the data you specify. You will not need to specify the mean and standard deviation in the input dialog box and these data entry fields will not be enabled for this option.
3	Methodology: Specify the methodology to use for computing the process capability. Option Description Auto If you select this option, the software will automatically pick the best approach to use for computing process capability. It will check if your data is normally distributed and if so, it will pick the Normal capability analysis. If not, it will try to estimate the best distribution that fits your data and uses that distribution to determine your process capability analysis. Box Cox The software will try to use the Box-Cox transformation to determine your capability analysis. First, it will find the best possible Box Cox distribution that will make your data normal and then use the transformed data to estimate your process capability metrics. Distribution If you specify a specific distribution to use (for example based on historical factors), the software will estimate the parameters for this distribution and use this distribution to estimate your process capability numbers.
4	Param: Specify the required parameter value for some situations. If the data type is discrete (defects), then you would need to enter the Opportunities for Error (OFE) value. This field would then be enabled to enter the OFE value. If this parameter is not required, then this field is disabled.
5	Subgroup Type: Specify if your data has subgroups. Subgroups are data collected within a small time interval such that the variation of data within the subgroup is governed by common cause variation. Option Description None If you do not have any subgroup then you can enter the subgroup type of None. If you pick this option then no within subgroup analysis is performed only the overall capability numbers are reported. Constant If you specify the subgroup size as constant, then you will need to specify the constant subgroup size on the input dialog box. For example, if you specify the subgroup size as 3, then the first 3 data points are treated as belonging to the first subgroup, the second three points to the second subgroup and so on... Variable If you specify the subgroup source as worksheet, then the software will expect that you provide this information through a data file specified in the Analysis Data section. For continuous data, you need to specify the subgroup ID as one column. Each data point that has the same subgroup ID is treated as belonging to the same subgroup. Note that you can have the same or different number of points within each subgroup.
6	Subgroup Constant: You can specify a constant subgroup size by entering a subgroup size here. Note that if you have a variable subgroup size, then you will need to specify the Subgroup Source to a worksheet and select your data from the data file. If you have specified the subgroup source as a worksheet, then the subgroup constant field is not enabled and the software will expect to find the subgroup information through the data file.
7	LSL: Specify your customer-defined lower specification limit (LSL). If no lower specification limit exists for your process, you can leave this value blank. Note that only numeric values are allowed for the specification limits. Both LSL and USL cannot be blank at the same time. The values entered for USL should be greater than the values entered for LSL. Click on the checkbox next to the LSL to mark that limit as a boundary. For example, if you mark the LSL as a boundary, this means that the physical measurements for this product or service cannot be lower than the LSL. An example could be surface finish, where the values cannot be lower than 0. Hence, 0 would be marked as a lower boundary for this data. This limit will not be used to calculate the process capability numbers.
8	USL: Specify the customer-defined upper specification limit (USL). If no upper specification limit exists for your process, you can leave this value blank. Note that only numeric values are allowed for the specification limits. Both LSL and USL cannot be blank at the same time. The values entered for USL should be greater than the values entered for LSL. Click on the checkbox next to the USL to mark that limit as a boundary. For example, if you mark the USL as a boundary, this means that the physical measurements for this product or service cannot be greater than the USL. An example could be if your metric is the efficiency numbers then 100 could be a theoretical upper boundary for the data and no numbers are expected to be greater than 100, so 100 would be marked as the upper boundary in that case.
9	Flow Chart: Click on this button to open and view the flowchart for the various process capability analysis methods. Note that you can also click on the buttons on this flowchart to select that methodology for your analysis.
10	Help Button: Click on this button to open the help file for this tool.
11	Cancel Button: Click on the Cancel Button if you want to exit this dialog box without performing any computations.
12	OK Button: Click on the OK button to compute the process capability calculations. If not all the required data has been specified, you will need to specify the data before you can perform the computations. If you change or update the data, you wil need to click on Compute Outputs to recompute the process capability calculations.

A sample screenshot of the menu options for discrete data is shown below. The menu options are similar to the continuous case but with a few changes as listed below:

1	Data Type: Specify the data type. For discrete data, this could be either defects or defectives. Note that defects data follows Poisson distribution and defectives data follows Binomial distribution.
2	OFE Value: If your discrete data type is defects, you will need to specify the Opportunities for Error (OFE) value. For defectives data, the OFE value is set at 1. This value is used to translate the DPMO values to Sigma Level.
3	Subgroup Constant: For the discrete data type, you need to specify the number of samples in your subgroup. For example, if you inspect 100 units for defects and found 4 defects, then your subgroup size is 100.
4	Target: For the discrete data type, you can optionally specify a target value. For the defects data, this is the target value of defects per unit (DPU). For the defectives data, this is the target value of % defective. The data you specify here will be used to update the histogram.

Data

If you click on the Data button, the following page is shown to enter your data if you specified "Raw Data" as your input data type:

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 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.
2	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.
3	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.
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, 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.
5	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.
6	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 specify for this analysis depends on the options you have specified in the Setup tab. Option Description 1 If your data type is Continuous and your subgroup type is None or Constant then you would enter the data for which you want to compute process capability under Analysis Variable and the Subgroup Variable field is disabled. 2 If your data type is Continuous and your subgroup type is Variable, then you would enter the data for which you want to compute process capability under Analysis Variable and the data which contains the subgroup id under Subgroup Variable. 3 If your data type is Discrete (Defects or Defectives) and your subgroup type is Constant then you would enter the column that contains the number of defects or defectives under Analysis Variable and the Subgroup Variable field is disabled. 4 If your data type is Discrete (Defects or Defectives) and your subgroup type is Variable then you would enter the column that contains the number of defects or defectives under Analysis Variable and the number of items in each subgroup under Subgroup Variable.
7	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.

If your input data type was "Summarized Data", then the Data dialog box may look like the one shown below.

1	Param 1: For continuous data, the first parameter is the mean value. You will need to specify the mean value for this analysis. For discrete data, it could either be the number of defects or the number of defectives.
2	Param 2: For continuous data, the second parameter is the stdev value. You will need to specify the stdev value for this analysis. For discrete data, it could be the total number of units.

Metrics

If you click on the Metrics button, the following page is shown: You can use this to specify the metrics you would like to report from this analysis. Click on the checkbox to specify the metrics that you want to report for your analysis. Note that not all metrics may be available for all data types. The metrics that cannot be selected will not be enabled. For example, the capability indices are reported only for continuous data. If no metrics are selected here, the system will still compute and report the Sigma Level metrics at a minimum. The following options are available:

1	Percentage(%): Click this checkbox if you want to report the % of defective items in your data set.
2	PPM, DPMO: Click this checkbox if you want to report the PPM or DPMO values. Note that for continuous data, the PPM values are reported. For discrete data, the DPMO values are reported.
3	Potential Capability: Click this checkbox if you want to compute the potential capability values (Cp and Pp). This analysis is only available for continuous data and requires that you specify both the LSL and USL values.
4	Actual Capability: Click this checkbox if you want to compute the actual capability values (Cpk and Pp). This analysis is only available for continuous data.
5	Target Capability: Click this checkbox if you want to calculate the target capability (Cpm). Note that you will need to specify the target value to calculate this metric. This metric is only available for continuous data.
6	Sigma Level: Click this checkbox if you want to calculate and report the Sigma Level for your process.
7	Target Value: This value is used to calculate the Target Capability (Cpm) and is enabled only if you select the reporting of target capability. This analysis is only available for continuous data.
8	Use 1.5 Sigma Shift: You can use the 1.5 Sigma Shift to compute your process capability metrics. This will specifically impact the Sigma Level that will be reported by the software. This is provided for historical compatibility in calculating the Sigma Levels. The default option is to not use the Sigma Shift in the calculations.

Charts

If you click on the Charts button, you will see the following dialog box.

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 would like to override that with your own 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 would like to override that with your own subtitle you can 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 own 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 own 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 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 currently disabled and you will not be able to change this setting.
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 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.
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 then two horizontal lines are plotted at Y = 12 and Y = 15 respectively. Note that this input is optional.
8	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. 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.

Analysis Data Format

If you need to specify data for this analysis, you need to format it in a specific way. An example screenshot of the data format is shown in the figure below. For continuous data, you need to specify the group ID and the data for analysis. All the rows with the same subgroup ID are considered as one subgroup. For discrete data, you need to specify the subgroup size and defects or defectives as appropriate. Each row is considered as one subgroup. In the above example, the defects data has a constant subgroup size of 100, and for the defectives data, the subgroup size varies between groups. Once the inputs in the dialog box are specified, click on OK to compute the analysis outputs.

Outputs

Click on Compute Outputs to update the output calculations.

Continuous Data (Summarized)

A sample screenshot of the worksheet for continuous data when summarized data is entered is shown below.

1	Input Summary: The Input Summary section shows a summary of the inputs used for this analysis. In this example, we have specified the process mean and standard deviation and the specification limits LSL and USL.
2	Assumption Checks: This section shares a summary of any assumption checks that are performed. Note that for summarized data, the process is assumed to be normally distributed.
3	Capability Metrics: This section shares a summary of the capability metrics that are computed for your data. Note that for summarized data, only the overall capability numbers are displayed.
4	Conclusion: This section shares a brief conclusion of your analysis - whether the capability is poor, acceptable, or good.
5	Capability Plot: This plot shows how the process capability compares with other processes - by showing where the process capability falls with respect to Green, Yellow, Red zones.
6	Probability Plot: This plot shows a histogram, probability plot, or any other suitable graphical representation of data.

Continuous Data (Worksheet)

If raw data would have been entered for analysis, a sample screenshot of the outputs is shown below.

1	Input Summary: The Input Summary section shows a summary of the inputs used for this analysis. In this example, we have specified the USL and used the diameter data for analysis. The software automatically calculates the required statistics from the entered data.
2	Methodology: If the methodology is set to Auto, then the software will use the capability analysis flowchart to determine the appropriate test. For this, it will check the normality of the data and information about the data type and subgroup size. In this example, it has chosen the Normal analysis. You can override these checks by specifying the type of analysis you want to perform in the Methodology tab of the input dialog box.
3	Assumption Checks: This section shares a summary of any assumption checks that are performed. If data is entered, the software will check if the data is normally distributed and if not, it will report it as such in this section. For this example, the process was found to be stable. Note that stability is a pre-requisite for capability analysis.
4	Within Capability: If data contains subgroups, then the software will calculate the within process capability analysis using standard deviation of the data within subgroups. These are reported in this section.
5	Overall Capability: This section reports the overall capability of the process which is calculated by taking all the data points together. It reports this for the LSL side, USL side, and considering both LSL and USL. In our example, the LSL is not specified, so the metrics are only reported for USL and both.
5	Capability Plot: This plot shows how the process capability compares with other processes - by showing where the process capability falls with respect to Green, Yellow, Red zones. In this example, the computed process capability is in the acceptable region.
6	Probability Plot: This plot shows a histogram of the data along with the super-imposed capability specifications (LSL & USL). Any data points that fall outside the specc limits are shaded.

Discrete Data (Summarized)

An example of process capability analysis outputs for discrete data is shown below. The outputs section shows the DPU, DPMO, and Sigma Level for this process when summarized data was entered for the analysis.

1	Input Summary: The Input Summary section shows a summary of the inputs used for this analysis. In this example, we have specified the defects (15) and Units (100). The Opportunities for Error (OFE) is set at 10. This data is used to determine the capability of the process.
2	Analysis Results: The software computes the Defects per Unit (DPU), the Defects per Million Opportunities (DPMO) and the Sigma Level (Z) for this process. Note that since the Sigma Level is low, it is marked as poor (falling in the red zone).
3	Defects Chart: The graphs section shows the process capability plot and a pie chart of the defects.

Discrete Data (Worksheet)

If raw data would have been specified for this analysis, a sample screenshot of the outputs is shown below.

1	Input Summary: The Input Summary section shows a summary of the inputs used for this analysis. In this example, we have specified the data for TV Defects as the input variable.
2	Analysis Results: The software computes the Defects per Unit (DPU), the Defects per Million Opportunities (DPMO) and the Sigma Level (Z) for this process. Note that since the Sigma Level is low, it is marked as poor (falling in the red zone).
3	Defects Chart: The graphs section shows the process capability plot and a convergence plot for the DPU with confidence intervals. Note that as the number of data points increases, the DPU value stabilizes which is an indication that we can relatively trust our analysis results.

Notes

Here are a few pointers regarding this analysis:

• You have the option of overriding the auto selection by specifying the distribution of your choice. The system picks the best distribution that fits your data based on Chi-square value (P-values).
• If you have collected data over some time, then it is better to use worksheet data and let the system perform the appropriate analysis for you. There are more checks performed when you use worksheet data as opposed to summarized data.
• For continuous data, if you don't have subgroups, leave the subgroup option blank in the input dialog box. In this case, only the overall process capability will be calculated. If you enter a subgroup size of 1, then it will be assumed that there are subgroups, and both within and overall capability metrics will be reported.
• If raw data (rather than summarized data) has been entered, the system will automatically check if your process is stable and report the conclusions under assumption checks since process stability is a pre-requisite for process capability.
• Entering a target value for defects or defectives data will display the target value on the plot. If no target value is specified, then the target value is omitted in the subtitle of the plot.
• If subgroups exist and are defined on the worksheet, you need to specify the subgroup ID for continuous data and subgroup size for discrete data. Subgroup ID can be text or numeric while subgroup size should always be numeric. The data column should always be numeric.
• For continuous data, you need to at least specify either LSL or USL - both of them cannot be blank. If both LSL and USL are specified make sure that the LSL value is less than the USL value.

Examples

Following examples can be found in the Examples folder.

• Calculate the process capability (Sigma Level, Ppk, and DPMO) for summarized data shown in the reference file (Capability 1.xlsm).
• Calculate the process capability for delivery time data shown in the reference file. Note that data is collected in subgroups (3 points per group) (Capability 1.xlsm).
• Calculate the process capability for lead time data shown in the reference file. Note that this data is not normally distributed (Capability 1.xlsm).
• Calculate the process capability for number of defective DVD units manufactured. The data is shown in the reference file (Capability 1.xlsm).
• Calculate the process capability for number of defects on a form. Each form has an OFE = 10. The data for this example is shown in the reference file (Capability 1.xlsm).