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.