Black Belt Course Outline

Here is our complete course outline for the Black Belt course. Why do we display to all of our competitors our intellectual property? Because we believe that when you are making a decision to choose a supplier for your training, you should know what you are getting for your money. Our training course provides the depth and breadth necessary to be successful in many different industries when you run into common real-world situations not covered in other "follow the recipe" training approaches. We provide you with sufficient background and understanding of the tools in order to avoid catastrophic decisions made because something in the real world happened to be different from the ivory tower assumptions you might find elsewhere.

We encourage you to compare what you get from our training to any other Black Belt course (if you can even get them to give you an outline of what they are selling). This doesn't make our training the easiest Black Belt course out there.

It just makes it the best.

Background and General Skills

What is Six Sigma?
Six Sigma as a business initiative
Importance of customers
Customer satisfaction, dissatisfaction, complaints
Design and Conformance quality
Drivers of Business Performance
Continuous improvement vs. breakthroughs
Plan-Do-Check-Act
Importance of financial analysis of improvements
Concepts of Design for Six Sigma

Define Opportunity / Measure Current State

Effective teaming tools
Using data
- Data and measurement
- Research questions
- QCDISME measures
- Defining CTQ, CTC, CTD, CTP
- Yield measures (TY, RTY, normalized yield)
- Key performance indicators (KPIs)
- Balanced scorecard concepts
- Process vs. results measures
- Measurement and measurement scales
  - Nominal
  - Ordinal
  - Interval
  - Ratio
  - Absolute
- Discrete vs. Continuous
Introduction to statistical methods
- Populations and samples
- Random sampling
- Defining "statistic" and "parameter"
- Sampling error
- Arranging and presenting data
  - Run charts
  - Frequency distributions
  - Frequency polygons
  - Histograms
    - Histogram patterns
- Descriptive statistics
  - Four aspects of data
    - Time
    - Shape
      - Shape statistics
    - Spread
      - Spread statistics
    - Location
      - Location statistics
- Simple probability
  - Probability defined
  - Independent vs. dependent events
- Probability distributions
  - Bernoulli processes
  - Binomial distribution
  - Poisson distribution
  - Normal or Gaussian distribution
  - Exponential distribution
  - Distribution approximation
    - Johnson
    - Weibull (covered further in reliability)
    - Distribution fit testing
      - Normality testing
        
        Anderson-Darling
        
        Shapiro-Wilk
        
        Lin-Mudholkar
        
        Skewness and Kurtosis
      - Exponential testing
      - Poisson testing
    - Transformations
- Estimation
  - Random sampling distributions
  - Criteria for "good" estimators
    - Unbiased
    - Efficient
    - Consistent
    - Sufficient
  - Point estimate
  - Confidence intervals
    - Means (z and t)
    - Standard deviation
    - Proportions (exact binomial)
- Process variation
  - Concept of variability
  - Sources of variability
  - Short- and long-term variability
  - Common cause variability
  - Special cause variability
  - Statistical control
  - Control charts identify special causes
  - Control chart pattern rules (more on control charts later)
  - Process dominance concept
  - Purpose of specifications
  - Product control cycle
  - Taguchi loss function
  - Process control cycle
  - Process control as constrained variation
  - Other process control technologies
- Measurement Systems Analysis (MSA)
  - Measurement as a process
  - Continuous Gages
    - Definitions
      - Reference value
      - Resolution
      - Precision
      - Accuracy
      - Repeatability
      - Reproducibility
      - Linearity
      - Stability
    - Measurement system capability (% R&R or P/T)
    - Types of studies
      - Potential
      - Short-term
      - Long-term
    - Steps to perform MSA
    - Potential study
      - Data collection
      - Data analysis
      - Effect of averaging multiple measures
    - Short-term study
      - Data collection
      - Data analysis
    - Long-term study
      - Data collection
      - Data analysis
    - Destructive tests
      - Effect of Class I, II, and III destructive tests
  - Discrete Gauges
    - Terms
      - Reliability
      - Agreement
      - Internal consistency
      - Concordance
      - Validity
      - Concordance with a standard
    - Measuring Agreement
      - Equality of proportions is not agreement
      - Dependent χ² is not agreement
      - McNemar's Test of Change is disagreement, not agreement
      - Absolute and Relative Agreement
      - Assessing Agreement
      - Kappa (κ) is a coefficient of agreement
      - Notes on κ
    - Procedures for Measurement System Analysis on Discrete Data
      - MSA for Discrete Data
        
        Sample sizes
        
        Potential study
        
        Long-term study
      - Subjective analysis is insufficient
      - Assumptions for discrete gauges
      - Sample considerations
      - MSA procedure for discrete gauges
      - MSA guidelines for discrete gauges
    - Two inspectors, two categories
      - κ_max
      - Assessing internal consistency
    - Two inspectors, more than two categories
      - Post-hoc for more than two categories
      - Assessing internal consistency for more than two categories
    - Testing for significance of κ
      - Testing for κ = 0
      - Testing for κ = κ'
    - Validity analysis for discrete data
      - Agreement vs. validity
      - Light's G
    - More than two appraisers
      - Random or Fixed?
    - Long-term control of discrete gauges
      - Generating control chart limits for κ
    - Capability of discrete gauges
      - Calculating κ_critical
- Process Characterization
  - Process capability for variable data
    - Steps to perform a capability analysis
    - C_p
    - C_pk
    - C_pm
    - What to do if the process is not capable
  - Process capability for attribute data
  - Process performance analysis
    - When to use
    - P_p
    - P_pk
    - P_pm
    - C_p(potential)
    - Variance components
  - Sigma measures
    - Strengths and weaknesses
    - Calculate sigma from:
      - z-score
      - Defects per million opportunities
      - P_pm
    - Other Six Sigma measures
      - Total opportunities
      - Defects per unit
      - Defects per unit opportunity
      - Defects per million opportunities
      - Yield relations
        
        Throughput yield
        
        Defects per unit
        
        Rolled throughput yield
        
        Total defects per unit
        
        Normalized yield
        
        Defects per normalized unit
  - Other measures
    - Cycle time
    - Uptime
    - Mean time between failures
    - Asset utilization

Analyze Current State

Scientific hypotheses
Sources of industrial mythology
Plan-Do-Check-Act cycle (PDCA)
Problems, Causes, and Solutions
- Understanding Problems
  - Performance improvement
    - Location
    - Stability
    - Variability
  - Solving incidents
    - Recurrence rate
    - Duration without intervention
- Understanding Causes
  - Level of cause
    - Nominal
    - Countable
    - Continuous
  - Multiple causes
    - Additive
    - Interactive
    - Primary
  - Causal chains
  - Root causes
  - Certain vs. probabilistic causes
  - Common vs. special causes
- Elimination and improvement
  - Knowledge of the causes
    - Self-evident
    - Trouble-shooting
    - Trial and error
    - Analytical methods
    - Knowledge of the causal mechanism
    - Benefit of taking action on deeper causes
- Process improvement stages
  - Chaos
  - Sporadic
  - Control
  - Incremental improvement
  - Breakthrough
- Integrate with Prevention Planning and Analysis (PPA) more on this in reliability
Basic hypothesis testing
- Definitions
  - Statistical vs. scientific hypothesis
  - Hypothesis test
  - Statistical significance
  - Null hypothesis
  - Alternative hypothesis
  - Directional / one-tail hypothesis
  - Non-directional / two-tail hypothesis
  - Alpha (α) error and risk
  - Population
  - Sample
  - Statistic
  - Test statistic
  - p-value of test statistic
- Type I (α) and Type II (β) error, power, and confidence
  - Strategies for deciding Type II (β) error
  - Calculating Type II (β) error and power
  - Power curves
- Hypothesis testing procedure
- How to choose the appropriate statistical test for a data set
Sample size calculations
- Importance of sample size calculations
- Parameters needed for sample size calculations
  - α - Type I
  - β - Type II
  - σ - Standard deviation
  - Δ - Delta
- Calculation of sample size for:
  - Means
  - Variance
  - Proportion
  - Rates
  - ANOVA
  - Correlations
One-sample hypothesis tests
- Definition
- Hypothesis testing steps
- z-test
- t-test
- Variance (χ²)
- Exact binomial
- Sign test for location
Correlation and regression
- Definitions
- Product moment coefficient (r)
- Coefficient of determination (r²)
- Tests of correlation
  - r=0
  - Spearman's rank order correlation (r_s)
  - Other measures (r_bi, φ, Cramer's v)
- Simple regression
  - Linear
  - Curve fitting
  - Confidence and prediction
- Two independent sample hypothesis tests
  - Independence vs. dependence
  - Two independent sample test for means
    - Variance known (z)
    - Variance unknown (t)
      - Presumed equal
      - Presumed unequal
  - Testing hypothesis for variance and dispersion
    - Levene test (ADA)
    - ADM_(n-1)
  - Two independent sample proportion test
    - Fisher's Exact
    - χ²
    - Normal approximation (discouraged)
  - Wilcoxon-Mann-Whitney Test (U)
- Two dependent sample hypothesis tests
  - Dependent by nature and design
  - Iso-plot
  - Paired t-test for means
  - Matched pair t-test for variances
  - Two-sample sign test
  - McNemar's test of change
Foundations of experimental design
- Purpose of research
- The scientific method
- Types of research studies
  - Non-experimental
  - Experimental
- Experimental design definitions
  - Variable
  - Dependent variable
  - Criterion measure
  - Independent variable
  - Level of a treatment factor
  - Single factor experiment
  - Factorial experiment
  - Fractional factorial experiment
  - Experimental unit or test unit
  - Population
  - Research population
  - Inference space
  - Sample
  - Replication
  - Repetition
  - Randomization
  - Experimental or sampling error
  - Statistical inference
  - Confounding
  - Internal validity
  - External validity
- Developing proper experimental designs
  - Planning
  - Confidence
  - Power
  - Threats to internal validity
  - Designs resisting threats to external validity
  - Threats to external validity
- Steps to conduct an experiment
  - State the Problem or Research Purpose
  - State the research question
  - State the dependent variable(s)
  - Select the associated criterion measure(s)
  - Identify and classify all independent variables
  - Perform measurement systems studies as appropriate
  - Select levels of the incorporated treatment variables
  - Select an appropriate experimental design
  - Develop the experimental plan
  - Run the experiment
  - Analyze the results
  - Run confirmation studies as required
  - Report the findings

Improve Performance

Oneway ANOVA - fixed factors
- Testing for means
  - Principles of ANOVA
  - Statistical importance
- Testing for homogeneity of variance
  - Levene test
  - ADM_(n-1)
- Post-hoc analysis
  - Fisher's LSD (t-tests)
  - Bonferroni
  - Tukey HSD and Games & Howell
  - Scheffé and Brown-Forsythe
  - Post-hocs for dispersion
Oneway ANOVA - random factors
- Importance of understanding random factors
- Between components variance
- Intraclass correlation coefficient (importance)
Two-way ANOVA models
- 2x2 factorial designs
- Importance
- Post-hoc analysis
  - With interaction
  - Without interaction
- Testing for homogeneity of variance
  - ADA
  - ADM
- JxK designs
- Special topics
  - Random and mixed models
  - Nesting
  - Blocking
  - Unequal n
  - Handling empty cells
  - Nominal data
  - Poisson and count data
  - Ordinal data
Three-way and higher designs
- Three way analysis
- Three way interactions
- Dispersion analysis
- Random, mixed, and nested models
- More than three-way designs
Fractional experimental designs
- Purpose of screening experiments
- Taguchi orthogonal arrays
  - Designing and customizing
  - Confounding
  - Linear graphs
  - Analysis
    - Location
      - Post-hoc
      - Statistical importance
      - % RFC
      - Practical importance
    - Dispersion
    - Pooling
  - Predicting process outputs
    - Discrete vs. continuous factors
    - Building a model
    - Estimating variability
    - Optimizing across continuous factors
  - Unreplicated designs
    - Unassigned columns as primary error
    - Pooling in unreplicated designs
- Additional topics
  - Creating a 4-level factor
  - Creating a 3-level factor
  - Interactions of high level factors
  - Creating an 8-level factor
  - Complex fractional design aids
    - By hand
    - Using software
    - Tsui's Tables
  - 3^N series arrays
  - Proportional data
Confirmation experiments
- Purpose
- Experiments
  - Best Run
  - Tentative Best Combination
  - Worst Run
  - Tentative Worst Combination
  - Current design/configuration
  - Follow-up investigations

Control Improved Process

Prevention planning and analysis
- Defining process control
- Process control methods
- Steps to perform PPA
- Ongoing use
Statistical process control (SPC)
- Tools for process study
- Steps to develop a control chart
  - Select a characteristic
  - Select sampling plan
  - Select chart type
  - Collect data
  - Generate chart
  - Assess control
  - Assess process capability
    - C_p
    - C_pk
    - C_pm
  - Process performance measures
    - P_p
    - P_pk
    - P_pm
  - What to do if the process is not capable
- X-bar and R
- X-bar and s
- X and moving range
  - X & MR concerns
    - Sensitivity
    - Distribution shape
    - Autocorrelation
  - Handling stratified data
- p-charts
- np-charts
- c-charts
- u-charts
Process performance analysis
Principles of robust product and process design
- Optimization
- Variation transmission
- Tooling design
- Raw materials and components
- Process settings
- Operational methods
- Generic technology
Mistake-proofing
- Human error
- Types of errors
- Techniques
  - Successive check
  - Sensors detecting an error
  - Sensors detecting a machine condition before failure
  - Pins or guides preventing an error
  - Correct counts are ensured
  - Alarm is used
  - Machine is automatically shut down
  - Color coding
  - Checklist minimizes chance of error
  - Automatic measurement prevents an error
  - Sequence must be followed in a proper order
  - Fixed number of parts is ensured
  - Wrong part cannot be selected
  - Forcing a part to be oriented correctly
  - Ensuring safety
Automatic control systems
- Dangers of automatic control systems
  - Autocorrelation
  - Run tests
- Types of control systems
- Adjustment charts
Principles of standardization
- PDSA (Plan-Do-Standardize-Act)
- Features of standardization
- Defining standard operating procedure
Reliability methods
- Reliability definitions
  - Reliability
  - Failure
  - Lifetime
  - MTBF
  - MTTF
- Reliability roadmap
  - Improving process for Added Capacity
    - Total productive maintenance
    - Total asset utilization
  - Building New Equipment for Added Capacity
    - Reliability modelling
    - Design specification
    - Design reviews
- Tools
  - FMEAs
  - Growth Analysis
  - Weibull Analysis
  - Fault Tree Analysis
  - Root Cause Analysis

Six Sigma Solutions

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Solving the unsolvable in industry

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