# When to use a nonnormal capability analysis

If you have nonnormal data, you can either transform your data or select a nonnormal distribution that fits your data.

## Transform your data and use a normal capability analysis

If a Box-Cox transformation is effective for your data, you can specify the value of lambda to transform and use a normal capability analysis.

1. Go to the Components page and select a product. Then select the process flow step of your product.
2. Open the process step and go to the Process Summary section.
3. Select Additional Settings to access the control chart and capability analysis options for each measure.
4. Select Normal Capability Analyses 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.
5. Select the lambda (λ) value to transform the data.
• Optimal λ: Use the optimal lambda, which should produce the best fitting transformation.
• λ = 0 (ln): Use the natural log of your data.
• λ = 0.5 (square root): Use the square root of your data.
• Specify λ: 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.
6. Select OK.

## Choose an appropriate distribution and use a nonnormal capability analysis

Selecting an appropriate distribution is an essential first step in conducting a capability analysis. If the chosen distribution does not fits the data well, then the capability estimates will be inaccurate.

1. Go to the Components page and select a product. Then select the process flow step of your product.
2. Open the process step and go to the Process Summary section.
3. Select Additional Settings to access the control chart and capability analysis options for each measure.
4. Select Fit distribution. Most often, it is best to use engineering and historical knowledge of your process to identify a distribution that fits your process data. However, Minitab® Statistical Software has many tools, such as Individual Distribution Identification, that can help you assess the fit of various distributions.
5. Select the distribution that best fits your data.
6. Select OK.

## A comparison of normal and nonnormal capability models

Consider the following when deciding whether to use a nonnormal distribution or a normal distribution with a transformation.
• Generally, you should choose the model that is most effective for your data. If a nonnormal distribution or a transformation is equally effective, some practitioners recommend using a nonnormal model because it uses the actual data units. However, others may prefer the normal model because it provides estimates of both overall and within process capability.
• If you plan to perform repeated capability analyses on your process over time, try to choose a distribution or transformation that is likely to adequately characterize your process consistently over time. Using the same distribution or transformation lets you easily and directly compare the indices from the repeat analyses.
Normal capability
• Uses actual or transformed data for the histogram.
• Calculates within, between/within (when both within-subgroup and between-subgroup variation exists), and overall capability.
• Draws a normal curve on the histogram to help you determine whether the transformation was effective in making the data follow a normal distribution.
Nonnormal capability
• Uses actual data units for the histogram.
• Calculates only overall capability.
• Draws the chosen nonnormal distribution curve on the histogram to help you determine whether the data fits the specified distribution.