Normality

Section 4 Process Capability

Lesson S04-07

Text: Section 4 pages 33 – 44

Duration: 33 minutes

Testing for Normality

So far, we have assumed that the individual data values are normally distributed. In practice, we need to test this assumption before using methods for normal data. Using methods for normal data on non-normal data will produce misleading (often too optimistic) capability estimates.

Here, we briefly describe how to perform a normality test on the data. We hypothesize that our data follows a normal distribution, and only reject this hypothesis if we have strong evidence to the contrary.

Normal Probability Plotting

Normal probability plotting may be used to objectively assess whether data comes from a normal distribution, even with small sample sizes. On a normal probability plot, data that follows a normal distribution will appear linear (follow a fairly straight line). For example, a random sample of 30 data points from a normal distribution results in the normal probability plot below.

Handling Non-normal Data

This introductory course primarily focuses on estimating process capability for normally distributed data. Methods for handling nonnormal data are briefly discussed here.

Transformations

Data transformations may be performed which will cause the transformed data to be normally distributed. Taking the log (or natural log) of the data is a common choice. This transformation tends to make skewed data appear more bell-shaped because the log function takes large numbers and brings them back “into the pack.” The smaller numbers are also transformed but they are not affected as much as the larger numbers.

Distribution Fitting

Another method for handling nonnormal data is to try to find a distribution that describes or “fits” the data. Practically speaking, this approach requires statistical software that allows multiple distributions to be fit to the data.

If a reasonable fit is found for a known distribution, then we can utilize the software to compute the required percentiles for our procedure. Some distributions are very flexible and can assume a wide variety of shapes depending on the specified parameters. For example, the Weibull distribution is a commonly used distribution due to its flexibility.