Lean Six Sigma Black Belt Course

Based on the comprehensive list you've provided, it appears that you are outlining a curriculum for a statistical process improvement program, which covers a wide range of statistical and quality control topics. This curriculum is likely designed to prepare individuals for roles in quality assurance, data analysis, Six Sigma certification, or similar positions where strong statistical understanding and application skills are necessary.

Here's a breakdown of the curriculum:

1. Linear Correlation - Understanding the correlation coefficient (r), its interpretation, and how to calculate it for linear relationships between variables.

2. Non-linear Correlation - Discussing Spearman's rank correlation coefficient (rho) and its application when dealing with non-linear or monotonic relationships.

3. Partial Correlation - Learning how to control for the influence of one or more independent variables on another pair of variables to isolate the direct relationship between them.

4. Regression Analysis - Covering multi-linear regression, including how to interpret the results and build models that can predict outcomes based on multiple independent variables.

5. Confidence and Prediction Bands - Understanding the construction of confidence intervals for predictions and how to use prediction bands to estimate future observations.

6. Residual Analysis - Learning how to analyze the residuals from a regression model to check for violations of assumptions and to improve the model's predictive power.

7. Logistic Regression - Understanding logistic regression, particularly for binary outcomes, and its interpretation in the context of probability, odds, and log-odds.

8. Dealing with Non-normal Data - Identifying non-normal distributions and transforming data (e.g., Box-Cox, Johnson) to normalize it when necessary.

9. Process Capability Analysis - Assessing the capability of a process to produce products within specification limits, considering both normal and non-normal distributions (e.g., Weibull, Binomial, Poisson).

10. Non-Parametric Tests - Learning about statistical tests that do not assume a particular distributional form for the data, such as Mann-Whitney U, Kruskal-Wallis, Mood's Median Test, and Wilcoxon signed-rank test.

11. Experimental Design (DOE) - Understanding the principles of design of experiments (DOE), including types of designs, factors, levels, and how to plan, conduct, and evaluate experiments.

12. Advanced Control Charts - Learning about advanced control chart techniques like X-S charts, cumulative sum (CumSum) charts, and exponential weighted moving average (EWMA) charts for monitoring processes over time.

This curriculum is extensive and covers both theoretical understanding and practical application of statistical methods. It is designed to equip individuals with the skills needed to analyze data, improve processes, and make informed decisions based on statistical evidence. The program also touches upon concepts relevant to certification exams from organizations like ASQ® and IASSC®, although it's important to note that this curriculum is independent of these organizations.