Sigma Magic Help Version 19

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 the Voice of the Customer (such as LSL, USL, and a definition of defects) and the Voice of the Process (raw data points, 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 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 must 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; these data entry fields will not be enabled for this option.
3	Methodology: Specify the methodology to be used 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 up the normal capability analysis. If not, it will try to estimate the best distribution that fits your data and use that distribution to determine your process capability analysis. Box Cox Transformation The software will try to use the Box-Cox transformation to determine your capability analysis. First, it will identify the best possible Box-Cox distribution to normalize your data, and then, the transformed data will be used to estimate your process capability metrics. Note that, depending on your data, the Box-Cox transformation may not be successful in normalizing your data. Johnson Transformation The software will try to use the Johnson transformation to determine your capability analysis. First, it will find the best possible Johnson distribution to normalize your data, and then the transformed data will be used to estimate your process capability metrics. Note that, depending on your data, the Johnson transformation may not be successful in normalizing your data. 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. Non Parametric If the data is not normal and no transformation works to make the data normal, or no distribution adequately fits your data, you can use the Non Parametric methodology to estimate the process capability numbers. In this case, no distribution is suitable for the data, but the percentile values are used to estimate the process capability metrics. The Pp and Ppk values are computed and interpreted similarly to Pp/Cp and Ppk/Cpk values.
4	Param: Specify the required parameter value for some situations. If the data type is discrete (defects), you must enter the Opportunities for Error (OFE) value. This field would then enable the OFE value to be entered. 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 data variation 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 a 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 must specify the subgroup ID as one column. Each data point with the same subgroup ID is considered to belong 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, 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, the subgroup constant field is disabled, and the software will expect to find the subgroup information in the data file.
7	LSL: Specify your customer-defined lower specification limit (LSL). You can leave this value blank if no lower specification limit exists for your process. 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 those entered for LSL. Click the checkbox next to the LSL to mark that limit as a boundary. For example, if you mark the LSL as a boundary, 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, zero 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 those entered for LSL. Click the checkbox next to the USL to mark that limit as a boundary. For example, if you mark the USL as a boundary, the physical measurements for this product or service cannot exceed the USL. An example could be if your metric is efficiency numbers; then 100 could be a theoretical upper boundary for the data, and no numbers are expected to exceed 100, so 100 would be marked as the upper boundary in that case.
9	Flow Chart: Click 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 the 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 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, click on Compute Outputs to recompute the process capability calculations.

A sample screenshot of the menu options for continuous data when the methodology is set to "Auto" is shown below. Note that the specification of distributions is only displayed if the Data Type is set to Continuous and the method is set to Auto; otherwise, this section is not visible in your menus. Use the scrollbar on the right to scroll down and view this section.

1	Select Distribution: Specify the type of distributions to include when determining the best fit, especially if the data is not normally distributed. Option Description Auto The software will automatically pick the most commonly used distributions to determine the best fit. The selected distributions are: Cauchy, Erlang, Extreme Value, Exponential, Gamma, Laplace, Log Normal, Logistic, Log Logistic, Normal, Rayleigh, and Weibull. All All the continuous distributions that are available within Sigma Magic software are used to determine the best fit distribution. Currently, there are 22 different distributions available in Sigma Magic software. Bounded All the bounded distributions are selected for analysis. The selected distributions are: Beta, Pert, Power, Triangular, and Uniform. It is usually not recommended to use bounded distributions for this analysis. Custom You can pick and choose which distributions you want to use for this analysis. The distributions you pick could be based on experience with your data set or based on the laws of physics. Partially Bounded All the partially bounded distributions are selected for this analysis. Partially bounded implies that the distribution is bounded on one side (usually the lower bound is zero) and unbounded on the other side. The selected distributions are: Erlang, Exponential, F, Gamma, Log Normal, Log Logistic, Pareto, Rayleigh, and Weibull. Unbounded The software will pick all available unbounded distributions. The selected distributions are: Cauchy, Extreme Value, Laplace, Logistic, Normal, and T
2	Method: Specify the method to use for determining the best-fit distribution. Option Description Method of Moments Use the method of moments to estimate the distribution parameters. This method is usually robust but may not work well if there are fewer data points. Maximum Likelihood Estimates Use the maximum likelihood estimates to determine the distribution parameters. This method may have convergence issues for certain data sets.
3	Available Distributions: This list box contains the list of all available distributions currently programmed in Sigma Magic software. The available distributions are: Beta, Cauchy, Chi-Squared, Erlang, Extreme Value, Exponential, F, Gamma, Laplace, Log-Normal, Logistic, Log-Logistic, Normal, Pareto, Pert, Power, Rayleigh, T, Triangular, Uniform, and Weibull. You can drag and drop items from this list to the list of selected distributions if required.
4	Selected Distributions: This list box lists the distributions that will be used to determine the best-fitting distribution. Note that at least one distribution should be selected for this analysis. You can double-click on any item in this list to remove it from consideration.

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 defect data follows the Poisson distribution and defective data follows the Binomial distribution.
2	OFE Value: If your discrete data type is defects, you must specify the Opportunities for Error (OFE) value. For defective data, the OFE value is set at 1. This value is used to translate DPMO values into Sigma Levels.
3	Subgroup Constant: Specify the number of samples in your subgroup for the discrete data type. For example, if you inspect 100 units for defects and find four defects, your subgroup size is 100.
4	Target: For the discrete data type, you can optionally specify a target value. This is the target value of defects per unit (DPU) for the defects data. For the defective data, the target value is the percentage of defects. 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 speed up finding 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 has 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 this button, the Data Editor dialog box opens, allowing you to import additional 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 the data that can be entered 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 minimum and maximum 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 for selecting 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, the list box header will be displayed in red. 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 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 specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

If your input data type was "Summarized Data," the Data dialog box may appear as 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 standard deviation (stdev) value. You will need to specify the standard deviation (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 want to report from this analysis. Click on the checkbox to specify the metrics 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 chosen 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 to report the percentage of defective items in your dataset.
2	PPM, DPMO: Click this checkbox to report the PPM or DPMO values. Note that the PPM values are reported for continuous data. For discrete data, the DPMO values are reported.
3	Sigma Level: Click this checkbox to calculate and report the Sigma Level for your process.
3a	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 the software will report. This is provided for historical compatibility when calculating the Sigma Levels. The default option is not to use the Sigma Shift in the calculations.
4	Capability Indices: Click this checkbox to compute the potential capability values (Cp and Pp) and process capability values (Cpk and Ppk). This analysis is only available for continuous data and requires that you specify both the LSL and USL values.
4a	Confidence Intervals: Use the dropdown box to specify if you want to report the confidence intervals for the capability indices. Note that the confidence intervals shown are based on the normal distribution assumption. To change the confidence levels, you can modify the default confidence level settings under Options. Option Description None No confidence intervals will be reported for this analysis Two-Sided A two-sided confidence interval will be reported for this analysis. (LB, UB) Lower Bound A one-sided confidence interval will be reported for this analysis. (LB, INF) Upper Bound A one-sided confidence interval will be reported for this analysis. (-INF, UB)
5	Target Capability: Click this checkbox to calculate the target capability (Cpm). Note that you must specify the target value to calculate this metric. This metric is only available for continuous data.
5a	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. Ensure that you enter a numeric value for the target.
6	Calculate Sample Size: Use this option to determine the number of samples required to achieve a specified level of confidence interval. For example, suppose your capability index is 1.5, and you use too few samples to calculate the capability index. In that case, the report capability index may be significantly off - it could report a value like 1.1 or 1.9, for example. You will have to collect more data to ensure that your reported capability indices are close to 1.5. Selecting this checkbox will tell you how many samples of data you should be using. Note that this analysis assumes that your data is normally distributed.
6a	Width: This value can be entered only if you select the calculate sample size option. Ensure that you enter a numeric value for the CI width. For example, if you specify a width of 0.1, then the 95% confidence intervals for this analysis will be 1.45 to 1.55 if the nominal value is 1.5.

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 specify the minimum, increment, and maximum values separated by a semicolon. 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. Please note that this input is currently disabled and cannot be changed.
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 semicolon. 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: You can specify the values here if you want to add a few extra horizontal reference lines on top of your chart. The format for this input is a series of numeric values separated by semicolons. 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 a series of numeric values separated by semicolons. 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.

Optional Chart Formating

If a chart has already been created earlier and you have made any changes to the chart format directly on the chart, it is possible to copy the settings and save them to memory. The next time you regenerate the chart, the same settings will be applied by the software, and you won't have to reapply them manually. The following image appears in the Charts tab if a valid chart exists on the worksheet. If no charts are found on the worksheet, the image shown below is hidden and will not appear in your dialog box.

1	Copy Format: Click on this button to copy the chart settings to memory. The chart settings will be saved and reapplied the next time you regenerate the chart.
2	Clear Format: Click on this button to clear any existing settings you have made to the chart. The default software settings will be applied to your chart.

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, it is displayed with an orange exclamation mark. Finally, any checks that the user is required to perform are indicated by blue information 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 displays a green thumbs-up sign if everything is okay and a red thumbs-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.

Analysis Data Format

If you need to specify data for this analysis, it must be formatted 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 must specify the appropriate subgroup size and the number of defects or defectives. Each row is regarded as a separate subgroup. In the above example, the defect data have a constant subgroup size of 100, while the subgroup size for the defective data varies between groups. Once the inputs in the dialog box are specified, click 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 summarizes 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 the process is assumed to be normally distributed for summarized data.
3	Capability Metrics: This section provides a summary of the capability metrics computed for your data. Note that only the overall capability numbers are displayed for summarized data.
4	Conclusion: This section provides a brief conclusion to your analysis, indicating whether the capability is poor, acceptable, or good.
5	Capability Plot: This plot illustrates how the process capability compares with other processes, highlighting where the process falls in relation to the Green, Yellow, and Red zones.
6	Probability Plot: This plot displays a histogram, probability plot, or other suitable graphical representation of the data.

Continuous Data (Worksheet)

A sample screenshot of the outputs is shown below if raw data have been entered for analysis.

1	Input Summary: The Input Summary section summarizes 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, the software will use multiple methods to calculate the capability values. Normal Assumption Best Distribution Box-Cox Transformation Johnson Transformation Non-Parametric Analysis It will check the data's normality and determine the P values for each of these methods. Based on the results from all the above analyses, it will then recommend the best method to use for your given data set and then display the capability values based on this recommended method. You can override and specify which set of distributions you want to use for your analysis.
3	Assumption Checks: This section shares a summary of any assumption checks that are performed. If data is entered, the software checks whether the data is normally distributed. If not, it reports this in this section. For this example, the process was found to be stable. Note that stability is a prerequisite for capability analysis.
4	Within Capability: If the data contains subgroups, the software will calculate the within-process capability analysis using the standard deviation of the data within each subgroup. These are reported in this section. Note that the within capability analysis is only reported if you select the Normal analysis methodology.
5	Overall Capability: This section reports the overall capability of the process, which is calculated by combining all the data points. It reports this for the LSL and USL sides, considering both LSL and USL. If LSL is not specified as in our example, the metrics are only reported for USL.
5	Capability Plot: This plot illustrates how the process capability compares with other processes, showing where the process capability falls in relation to the Green, Yellow, and Red zones. In this example, the computed process capability is in the acceptable region.
6	Probability Plot: This plot displays a histogram of the data, along with the superimposed capability specifications (LSL & USL). Any data points that fall outside the spec limits are shaded.

Discrete Data (Summarized)

Below is an example of process capability analysis outputs for discrete data. The Outputs section displays the DPU, DPMO, and Sigma Level for this process, based on the summarized data entered for analysis.

1	Input Summary: The Input Summary section summarizes 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 the Sigma Level is low and 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 had been specified for this analysis, a sample screenshot of the outputs is shown below.

1	Input Summary: The Input Summary section summarizes 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 the Sigma Level is low and marked as poor (falling in the red zone).
3	Defects Chart: The graphs section displays the process capability plot and a convergence plot for the DPU, along with confidence intervals. As the number of data points increases, the DPU value stabilizes, indicating that we can relatively trust our analysis results.

Notes

Here are a few pointers regarding this analysis:

• You can override 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 time, then it is better to use worksheet data and let the system perform the appropriate analysis. More checks are performed when you use worksheet data than 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, 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 prerequisite for process capability.
• Entering a target value for defects or defective data will display the target value on the plot. If no target value is specified, the target value is omitted in the plot subtitle.
• If subgroups exist and are defined on the worksheet, you must specify the subgroup ID for continuous data and the subgroup size for discrete data. Subgroup ID can be text or numeric, while subgroup size should always be numeric. The data column should always contain numeric values.
• For continuous data, at least you need to specify either LSL or USL - both cannot be blank. If both LSL and USL are specified, ensure the LSL value is less than the USL value.

Examples

The following examples are in the Examples folder.

• Calculate the process capability (Sigma Level, Ppk, and DPMO) for summarized data shown in the reference file (Capability 1.xlsx).
• Calculate the process capability for delivery time data shown in the reference file. Data is collected in subgroups (3 points per group) (Capability 1. xlsx).
• Calculate the process capability for lead time data shown in the reference file. Note that this data is not normally distributed (Capability 1. xlsx).
• Calculate the process capability for the number of defective DVD units manufactured. The reference file (Capability 1. xlsx) shows the data.
• Calculate the process capability for the 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. xlsx).

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