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Process Control for capability analyses

Use Normal Capability to evaluate the potential (within) and overall capability of your process based on a normal distribution. Use Nonnormal Capability to evaluate the capability of your process based on a nonnormal distribution.

In This Topic

Add a capability analysis

To add a capability analysis, drag and place the analysis from the Assets pane onto the canvas. Minitab Solution Center adds a placeholder asset card that contains the default title, a representation of the asset, and a dropdown list that contains the data associated with the dashboard. Select the data that you want to use. Then select Open to open the dialog for the capability analysis.

Enter your data

The capability analysis requires your data to be in a single column of the worksheet.

Data column

Enter the column of numeric data that you want to analyze.

Subgroup size

For Normal Capability, enter a column that identifies the subgroup for each measurement or enter a number that indicates the subgroup size. Enter a number for subgroups of the same size. For example, if each subgroup contains measurements for five items, enter 5. If you collected data over time without subgroups, use a subgroup size of 1. If you enter a column of subgroup IDs, the subgroup sizes do not need to be equal.
Note

Observations within each subgroup should be in adjacent rows of the worksheet. For more information on using columns to define subgroups, go to Using subgroups to assess process capability.

In this worksheet, the Diameter column contains the diameters of the piston rings. The Subgroup ID column identifies the subgroup for each measurement.
C1 C2
Diameter Subgroup ID
74.030 1
74.002 1
74.019 1
73.992 1
73.995 2
73.992 2

Fit distribution

For Normal Capability, select a nonnormal distribution to fit your data. To produce a reliable estimate of process capability, the data must follow the distribution that you select. For more information on choosing an appropriate distribution for nonnormal data, go to Capability analyses with nonnormal data.

Lower spec and Upper spec

Enter the minimum or maximum acceptable value for the product or service. If it is not possible for measurements to fall above or below this value, select Boundary to define the specification limit as a boundary.

Note

When you define a specification limit as a boundary, Connect reports the expected capability indices related to the spec limit/boundary as missing values (*). Therefore, define a limit as a boundary only if it is theoretically impossible for measurements to fall beyond the limit. For example, an upper specification limit of 100% purity is a boundary because it is not possible to exceed 100% purity. A lower specification limit of 0% purity is a boundary because it is not possible to fall below 0% purity.

Historical parameters (optional)

For Normal Capability, if you know the historical mean or the historical standard deviation of your process, or if you have an estimate obtained from past data, enter the value to use in the analysis.

Historical mean
Enter a value for the mean of the population distribution.
Historical standard deviation
Enter a value for the standard deviation of the population distribution.

If you do not enter historical parameters, Connect estimates the mean and standard deviation from your sample data and uses those estimates to calculate process capability.

Note

If you want to specify the method that Connect uses to estimate the standard deviation from your sample data, select Estimate.

Transform

For Normal Capability, you can transform your data to fit a normal distribution in order to satisfy the assumptions for the analysis.
No transformation
Do not use a transformation if your data already follow a normal distribution.
Box-Cox power transformation (W = Y^λ)
Use the Box-Cox transformation if your nonnormal data are all positive (> 0) and you want to obtain estimates of within-subgroup (potential) capability as well as overall capability. The Box-Cox transformation is a simple, easy-to-understand transformation.
Select the lambda (λ) value that Connect uses to transform the data.
  • Use optimal λ: Use the optimal lambda, which should produce the best fitting transformation. Connect rounds the optimal lambda to 0.5 or the nearest integer unless the confidence interval for lambda does not contain a rounded value.
  • λ = 0 (ln): Use the natural log of your data.
  • λ = 0.5 (square root): Use the square root of your data.
  • Other (enter a value between -5 and 5): Use a specified value for lambda. Other common transformations are square (λ = 2), inverse square root (λ = −0.5), and inverse (λ = −1). In most cases, you should not use a value outside the range of −2 and 2.
Johnson transformation (for overall analysis only)
Use the Johnson transformation if your nonnormal data contain negative values (or 0) or if the Box-Cox transformation is not effective. The Johnson transformation function is more complicated than Box-Cox, but is very powerful for finding an appropriate transformation.
In P-Value to select best fit, enter a value between 0 and 1. The value that you enter defines the significance level for a normality test of the data before and after the transformation. A higher value makes the criteria for normality more rigorous. A lower value makes the criteria for normality less stringent.

Estimate for Normal Capability

(for subgroup size > 1)
Select a method for estimating the within-subgroup standard deviation when you have multiple observations in each subgroup.
  • Rbar: Rbar is the average of the subgroup ranges. This method is a common estimate of the standard deviation and works best with subgroup sizes from 2 to 8.
  • Sbar: Sbar is the average of the subgroup standard deviations. This method provides a more precise estimate of the standard deviation than Rbar, especially with subgroup sizes > 8.
  • Pooled standard deviation: The pooled standard deviation is the weighted average of subgroup variances, which gives larger subgroups more influence on the overall estimate. This method provides the most precise estimate of standard deviation when the process is in control.
(for subgroup size = 1)
Select a method for estimating the within-subgroup standard deviation when you have individual observations. When the subgroup size is 1, sample standard deviations or ranges within subgroups cannot be calculated. Instead, Connect estimates the standard deviation using moving ranges.
  • Average moving range: The average moving range is the average value of the moving range of two or more consecutive points. This method is commonly used when the subgroup size is 1.
  • Median moving range: The median moving range is the median value of the moving range of two or more consecutive points. This method is best to use when data have extreme ranges that could influence the moving range.
  • Square root of MSSD: The square root of MSSD is the square root of the mean of the squared differences between consecutive points. Use this method when you cannot reasonably assume that at least 2 consecutive points were collected under similar conditions.
Use moving range of length
Enter the number of observations used to calculate the moving range. The length must be ≤ 100. The default length is 2 because consecutive values have the greatest chance of being alike.
Unbiasing constants
You can choose to use unbiasing constants in the calculations for the within-subgroup and the overall standard deviation. Unbiasing constants reduce the bias that can occur when a parameter is estimated from a small number of observations. As the number of observations increases, unbiasing constants have less effect on the calculated results.
  • Use unbiasing constant: Use unbiasing constants in the estimate of the within-subgroup standard deviation. This option applies to the Sbar, pooled standard deviation, and square root of MSSD methods.
  • Use unbiasing constants to calculate standard deviations: Use unbiasing constants in the estimate of the overall standard deviation.
Note

Often, the choice to use unbiasing constants depends on company policy or industry standards.

Estimate for Nonnormal Capability

You can have Connect estimate the parameters of the nonnormal distribution used for the capability analysis, or you can choose to enter some or all of the parameters below.

Estimate parameters of distribution
Estimate the distribution parameters from the sample data. Connect estimates any of the following parameters that you do not specify.
  • Set shape (Weibull or gamma) or scale (other dists) at: Enter the shape or scale parameter, depending on the type of distribution you selected. The shape parameter affects the shape of the distribution, such as its skewness. The scale parameter affects the spread of the data.
  • Set threshold at: If you selected a 3-parameter distribution, enter the threshold parameter. The threshold parameter sets the minimum location of the data distribution.
    Note

    For more information on the shape, scale, or threshold of a distribution, go to Process data for Nonnormal Capability Analysis and click the parameter that you want to learn more about.

Use historical estimates
Specify historical estimates of the parameters. Enter constants or a column using the parameter order shown. The number of constants and rows in the column must equal the number of parameters in the distribution.

Options

This topic describes the full set of options for Normal Capability. If you perform a Nonnormal Capability, you will see only a subset of these options.

Target (adds Cpm to table)

If your process has a target, enter the value. If you enter a target value, Connect calculates Cpm, a capability index that also considers how much the data deviate from the target.

Use tolerance of K × σ for capability statistics

Enter the width of the tolerance in number of standard deviations (σ). By default, the tolerance is 6 standard deviations wide (3 standard deviations on each side of the process mean).

Connect interprets the K value as the width of a two-sided tolerance. If you want to use a one-sided tolerance, enter a two-sided tolerance value that is twice that of the one-sided tolerance. For example, if you want to use a one-sided tolerance of 3σ, enter 6.

Perform Analysis

By default, Connect performs both within-subgroup and overall capability analyses. If you do not want to perform one of the analyses, deselect that checkbox.

Within subgroup analysis
Perform the within-subgroup analysis, which indicates the potential (short-term) capability of your process. This analysis estimates how well your process could perform if the shift and drift between subgroups were eliminated.
Note

If you use the Johnson transformation on your data, within-subgroup analysis cannot be calculated. In that case, Connect reports only overall capability.

Overall analysis
Perform the overall analysis, which indicates the actual (long-term) capability of your process. This analysis estimates what your customer actually experiences.

Display

Select how you want to display the expected and observed out-of-specification values:
  • Parts per million: Display the values in parts per million (PPM).
  • Percents: Display the values as percentages.
Include confidence intervals
Select to display confidence intervals for the capability indices.
Confidence level
Enter a confidence level between 0 and 100. Usually, a confidence level of 95% works well. A 95% confidence level indicates that if you took 100 random samples from the process, you could expect approximately 95 of the samples to produce confidence intervals that contain the actual value of the capability index for the process (if all the process data could be collected and analyzed).
For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size, as follows:
  • If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, will produce a narrower interval. However, the likelihood that the interval contains the capability index for the process decreases.
  • If your sample size is large, you may want to consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval while increasing the likelihood that the interval contains the capability index for the process.
Confidence intervals
Select the type of confidence interval or bound that you want to display:
  • One-sided: Displays lower confidence bounds for capability indices and upper confidence bounds for PPM or % out-of-specification limits. Use one-sided confidence bounds for the following:
    • To be more confident that a capability index is greater than a required value. For example, to be more confident that Cp is greater than 1.33.
    • To be more confident that a PPM or % out-of-specification limits is less than a required value. For example, to be more confident that PPM Total out-of-specification is less than 100.
  • Two-sided: Display a confidence interval that has both a lower and an upper confidence bound.
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