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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 Goal Distribution Requirement or Test ANOVA Mean F-Statistic Measurement variation Normal Gage R&R Measurement Variation Kappa Analysis Repeatability & Reproducibility K-Statistic Test measurement error None Anderson-Darling Normality Test Normal distribution A-Squared p-Value Do samples conform to a normal distribution Tests against normality Binomial 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 F-Test Variance F-Statistic Valuable when deviating from normality F Distribution Mann-Whitney Test Medians W-Statistic Z-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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