Data transformations for capability analysis

If you use a capability analysis designed for normal data, such as Normal Capability Analysis, your data must follow a normal distribution. If your data are not normal, the results of the analysis will not be accurate. Sometimes you may be able to transform nonnormal data by applying a function to the data that changes its values so that they more closely follow a normal distribution.

For example, suppose you want to perform a capability analysis on the time required to deliver pizzas. Because there is a minimum time that is needed for delivery, but no set maximum amount of time for delivery, the data skews to the right. A transformation can be applied to remove this severe skewness in the data.

The Box-Cox transformation is a power transformation, W = Y**λ, where Minitab determines the best value for λ.

Although the best estimate of lambda (λ) could be any number between −5 and 5, in any practical situation you want a λ value that corresponds to an understandable transformation, such as the square root (λ=0.5) or the natural log (λ=0).

The Johnson transformation uses a different algorithm than the Box-Cox transformation. The Johnson transformation function is selected from three families of functions in the Johnson system. Because the functions cover a wide variety of distributions by changing the parameters, Minitab usually finds an acceptable transformation. The family Minitab selects is called the Best Transformation Type.