Consider a production process that produced 10,000 widgets in January and experienced a total of 112 rejected widgets after a quality control inspection (i.e., failure rate = 1.12%). A Six Sigma project was deployed to fix this problem and by March the improvement plan was in place. In April, the process produced 8,000 widgets and experienced a total of 63 rejects (failure rate = 0.79%). Did the process indeed improve?
The appropriate hypothesis test for this question is the two-proportions test. …

Linear regression is one of the most commonly used hypothesis tests in Lean Six Sigma work. Linear regression offers the statistics for testing whether two or more sets of continuous data correlate with each other, i.e. whether one drives another one.…

Three methods for dissolving a powder in water show a different time (in minutes) it takes until the powder dissolves fully. The results are summarised in Figure 1.

There is an assumption that the population means of the three methods Method 1, Method 2 and Method 3 are not all equal (i.e., at least one method is different from the others). How can we test this?

One way is to use multiple two-sample t-tests and compare Method 1 with Method 2, Method 1 with Method 3 and Method 2 with Method 3 (comparing all the pairs). But if each test is 0.05, the probability of making a Type 1 error when running three tests would increase.
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In some situations, Lean Six Sigma practitioners find a Y that is discrete and Xs that are continuous. How can we apply regression in these cases? Black Belt training indicated that the correct technique is something called b inary logistic regression or binary regression. But this tool is often not well understood.…

The two-sample t-test is one of the most commonly used hypothesis tests in Data Analytics or Lean Six Sigma work. The two-sample t-test offers the statistics for comparing average of two groups and identify whether the groups are really significantly different or if the difference is due instead to random chance.…

Measurement error is unavoidable. There will always be some measurement variation that is due to the measurement system itself.

Most problematic measurement system issues come from measuring attribute data in terms that rely on human judgment such as good/bad, pass/fail, etc. This is because it is very difficult for all testers to apply the same operational definition of what is “good” and what is “bad.”…