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Manufacturing Statistics

Manufacturers run the business using statistics because they give the best metrics for manufacturing performance.  We have listed a summary table of statistical tests here that may be useful for selection of statistical test.  Some are Non-Parametric and others are Parametric.  Some will measure means and others variation.  These are the suite that a Lean Six Sigma Black Belt will use to determine performance.

As manufacturing moves towards Six Sigma levels of performance, different tests become important.  For instance, is your sample distribution even normal? There are another suite of statistical tools used in Statistical Process Control. These tools are mostly used to monitor processes in a constantly degrading environment.  They measure performance against a threshold.

Statistical test summary

Test Name

What is tested

Test Statistic


Distribution Requirement or Test




Measurement variation


Gage R&R

Measurement Variation

Kappa Analysis

Repeatability & Reproducibility K-Statistic Test measurement error None

Anderson-Darling Normality Test

Normal distribution A-Squared


Do samples conform to a normal distribution Tests against normality


Probability of discrete events p-Value Probabilities of discrete events Assigns discrete probabilities

One Sample Proportion Test

Mean Z-Statistic Statistics of discrete events Z Distribution


Variance F-Statistic Valuable when deviating from normality F Distribution

Mann-Whitney Test

Medians W-Statistic


Non-parametric test. Mean of  samples are the same Not Normal Distribution

Levene’s Test

Variances are equal L-Statistic Non-parametric test. Variances are the same. F Distribution

Mood’s Test

Median -Statistic Non-parametric test. Medians are equal. chi2 Distribution

Friedman’s Test

Treatments F-Statistic Treatments are equal  chi2 Distribution

Statistics can go wrong when used incorrectly.  For instance, if assumptions are made but not validated.  Or if sampling is inadequate.  It is best to engage a Lean Six Sigma Black Belt to verify the correct and best tests are completed.

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