Black Belt/Quality Engineering Statistics

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1. Collecting and summarizing data
   1. Continuous vs. discrete data
   2. Measurement scales: Nominal, ordinal, interval, and ratio
   3. Data collection methods: Check sheets, coding data, automatic gauging
   4. Effective sampling techniques: Randomized, stratified, systematic, representative
   5. Overview of measurement assurance and fauge R&R analysis
   6. Basic graphical tools: Stem-and-leaf plots, box-and-whisker plots, run charts, scatter diagrams, frequency distributions, histograms, etc.
2. Basic probability and statistics
   1. Descriptive vs. inferential statistics
   2. Sample statistics vs. population parameters
   3. Basic probability concepts
   4. Measures of central rendency: Mean, median, and mode
   5. Measures of dispersion: Range, standard deviation, and variance
3. Properties and applications of probability distributions
   1. Effective use of the normal, binomial, Poisson, chi-square, student's t, and F distributions
   2. Overview of the hypergeometric, bivariate, exponential, lognormal, and Weibull distributions
   3. Testing distribution assumptions: Normal probability plots, skewness and Kurtosis, chi-square goodness-of-fit tests
   4. The central limit theorem and sampling distribution of the mean
4. Confidence intervals and hypothesis testing
   1. Statistical significance issues: Statistical vs. practical Significance, interpreting p-values, type I and Type II (alpha and beta) errors
   2. Point and interval estimation: Confidence intervals for means and proportions, prediction intervals, tolerance intervals
   3. Hypothesis tests for population means, proportions, and variances
   4. Estimating sample sizes for confidence intervals and hypothesis tests
   5. Paired-comparison tests
   6. Contingency tables
   7. Nonparametric tests: Mood's median, Levene's test, Kruskal-Wallis, Mann-Whitney.
   8. Analysis of Variance (ANOVA)
5. Exploratory data analysis
   1. Multi-vari charts: Distinguishing between positional, cyclical, and temporal variation
   2. Simple and multiple least-squares linear regression
   3. Simple linear correlation and correlation vs. causation
   4. Model diagnostics: Evaluating model residuals
      

Course Content/Main Topics	% Of Time Spent on Topic
Collecting and summarizing data	15%
Basic probability and statistics	10%
Properties and applications of probability distributions	25%
Confidence intervals and hypothesis testing	30%
Exploratory data analysis	20%

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