Now that we have data obtained in the Measure Phase of DMAIC, let’s use it to identify the root causes that are at the heart of what we want to fix.

## Analysis Phase of DMAIC Overview

- List Potential Causes
- Value Added / Non Value Added Analysis
- Root Cause Analysis
- Brainstorm potential causes
- Organize the potential causes to show relationships
- Check the logic
- Prioritize final list

- Data Analysis & Results
- This is where we use various methods and mathematical tools to verify our assumptions. We can also use the advanced techniques to compare data against each other and even to make predictions.

- Mathematical Tools
- Central Limit Theorem
- Distribution Types
- Normal Probability
- F Distribution
- Hypergeometric Distribution
- Binomial Probability Distribution
- Analyzing Bivariate Data:
- Income Example
- Cost vs. Billed Hours Example

- Exponential Distribution
- Coffee Example
- Reliability Example

- Lognormal Distribution
- Poisson Distribution
- Cumulative Poisson Distribution

- Student’s t Distribution

- Data Tests
- F Test for Variance
- Paired t-Test
- Two-sample t-test
- Test for Equal Variances
- Chi-Square
- Graphical Analysis
- Box and Whiskers Plot
- Radar Chart
- Linear Regression

- Hypothesis Testing
- Decision Tree
- Type I and Type II Errors in Hypothesis Testing
- P-Values
- ANOVA
- ANOVA: One-Way
- One-Way Manufacturing Example
- One-Way Service Example
- One-Way Productivity Example

- ANOVA: Two-Way

- ANOVA: One-Way

- Design of Experiments
- Design of Experiments (DOE) Terminology
- Designed Experiment
- Response Variable
- Factors and Levels
- Design Matrix
- Effect
- Interaction
- Randomization and Replication

- Plots
- Main Effects Plot
- Interaction Plot

- Factorial Designs
- DOE Strategy for Experimentation: Full Factorial
- Illustration
- Full Factorial Example

- DOE: Determining Statistical Significance
- Fractional Factorial Designs
- Example

- Strategy for Experimentation: Screening Designs
- Blocking
- Design Resolution
- Standard Order of Design Matrix
- DOE: Illustration of F Ratio Test
- DOE: Taguchi Loss Function
- DOE: Evolutionary Operations (EVOP)
- DOE: Graeco-Latin Square Design
- DOE: Hyper-Graeco-Latin Square
- DOE: Latin Square
- Finding a Z Score
- Weibull Analysis

- Design of Experiments (DOE) Terminology

- Process Capability
- Cpk and Ppk Process Capability Indices
- Cp and Cpk: Formulas
- Cpk to DPMO Conversion Chart
- Pp and Ppk: Example
- Pp and Ppk: Formulas
- Sigma to Ppk Conversion Chart
- Ppk to PPM/DPMO Conversion Chart

- Deliverables
- List of potential causes
- Data Analysis and results
- “Vital few” x’s

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