Six Sigma professionals should be familiar with normally distributed processes: the characteristic bell-shaped curve that is symmetrical about the mean, with tails approaching plus and minus infinity (Figure 1). When data fits a normal distribution, practitioners can make statements about the population using common analytical techniques, including control charts and capability indices (such as sigma…
Most processes, particularly those involving life data and reliability, are not normally distributed. Most Six Sigma and process capability tools, however, assume normality. Only through verifying data normality and selecting the appropriate data analysis method will the results be accurate. This article discusses the non-normality issue and helps the reader understand some options for analyzing…
Normally distributed data is a commonly misunderstood concept in Six Sigma. Some people believe that all data collected and used for analysis must be distributed normally. But normal distribution does not happen as often as people think, and it is not a main objective. Normal distribution is a means to an end, not the end…
Normally distributed data is needed to use a number of statistical analysis tools, such as individuals control charts, Cp/Cpk analysis, t-tests and analysis of variance (ANOVA). When data is not normally distributed, the cause for non-normality should be determined and appropriate remedial actions should be taken. (An introduction to remedial actions for non-normal data can…
The paired t-test is used to check whether the average differences between two samples are significant or due only to random chance. In contrast with the “normal” t-test, the samples from the two groups are paired, which means that there is a dependency between them. The following example illustrates the difference between the regular t-test…
Some practitioners mistakenly believe that it is not necessary to transform data before creating an individuals control chart when the underlying process distribution response is not normal. An individuals control chart, however, is not robust to non-normally distributed data. Therefore, it is important to use an alternate control charting approach. Necessary Transformation Consider a hypothetical…
During a Six Sigma project, the defect rate of the business process is calculated twice, first during the Define phase to show the impact of the problem and again during the Control phase to show how the process has improved. Although effective analysis of data that is not distributed normally is possible, completing one of…
Peter J. Sherman
Shree Phadnis
Arne Buthmann
Forrest W. Breyfogle III
Alastair Muir