What are the best methods to transform non-normal data for SPC?

1 How to identify non-normal data

The first step to transform non-normal data for SPC is to check whether the data are normal or not. There are several ways to do this, such as plotting a histogram, a box plot, or a normal probability plot of the data, and looking for signs of deviation from the normal shape. Another way is to use a statistical test, such as the Shapiro-Wilk test, the Kolmogorov-Smirnov test, or the Anderson-Darling test, to compare the data with a normal distribution and calculate a p-value. If the p-value is less than a significance level, such as 0.05, then the data are not normal.

2 How to transform non-normal data

The second step to transform non-normal data for SPC is to apply a mathematical function to the data that changes its shape and makes it more normal. There are different types of transformations, such as logarithmic, square root, inverse, power, or Box-Cox transformations, that can be used depending on the nature and direction of the skewness or multimodality of the data. The goal is to find a transformation that minimizes the deviation from normality and preserves the relationship between the data and the process variables. A common way to evaluate the effectiveness of a transformation is to use a normality test or a normal probability plot on the transformed data and compare it with the original data.

3 How to use transformed data for SPC

The third step to transform non-normal data for SPC is to use the transformed data for creating and interpreting the SPC charts and tests. This means that the control limits, the mean, the standard deviation, and the specification limits of the process must be calculated based on the transformed data, not the original data. Moreover, the process capability indices, such as Cp, Cpk, Pp, and Ppk, must be adjusted for the transformation by using a correction factor, such as lambda or zeta, that accounts for the change in variation and location of the data due to the transformation. Finally, the transformed data must be back-transformed to the original scale before reporting or communicating the results of the SPC analysis.

4 How to choose the best transformation method

When transforming non-normal data for SPC, it’s essential to choose the best transformation method that meets the needs and objectives of the process and data. As there is no single best method that works for all situations, different methods may have different advantages and disadvantages. Factors influencing the choice of transformation method include the type and degree of non-normality of the data, the ease and simplicity of applying and interpreting the transformation, the availability and compatibility of software and tools for performing the transformation, the impact and relevance of the transformation on process performance and quality, as well as the preference and experience of the analyst or user.

5 How to avoid transforming non-normal data

When considering whether to transform non-normal data for SPC, one must consider if transforming the data is necessary or desirable. Alternatives to transforming the data may be more appropriate or effective. These alternatives include using non-parametric methods that don't assume normality, distribution-specific methods that fit the data to different distributions, robust methods that reduce the influence of outliers, and investigating and eliminating the causes of non-normality. Examples of these alternatives include run charts, median charts, Weibull distributions, trimmed mean charts, Winsorized charts, and Huber's M-estimator.

6 Here’s what else to consider

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