A. Process Analysis and Documentation

1. Tools
   Develop and review process maps, written procedures, work instructions, flowcharts, etc. (Analysis)
2. Process Inputs and Outputs
   Identify process input variables and process output variables and document their relationship through cause-and-effect diagrams, relational matrices, etc. (Evaluation)

B. Probability and Statistics

1. Drawing valid statistical conclusions
   Distinguish between enumerative (descriptive) and analytical (inferential) studies, and distinguish between a population parameter and sample statistic. (Evaluation)
2. Central limit theorem and sampling distribution of the mean
   Define the central limit theorem and understand its significance in the application of inferential statistics for confidence intervals, control charts, etc. (Application)
3. Basic probability concepts
   Describe and apply concepts such as independence, mutually exclusive, multiplication rules, complementary probability, joint occurrence of events, etc. (Application)

C. Collecting and Summarizing Data

1. Types of Data
   Identify, define, classify, and compare continuous (variables) and discrete (attributes) data, and recognize opportunities to convert attributes data to variables measures. (Evaluation)
2. Measurement Scales
   Define and apply nominal, ordinal, interval and ratio measurement scales. (Application)
3. Methods for collecting data
   Define and apply methods for collecting data such as check sheets, coding data, automatic gauging etc. (Evaluation)
4. Techniques for assuring data accuracy and integrity
   Define and apply techniques for assuring data accuracy and integrity such as random sampling, stratified sampling, sample homogeneity etc. (Evaluation)
5. Descriptive statistics
   Define, compute and interpret measures of dispersion and central tendency, and construct and interpret frequency distributions and cumulative frequency distributions. (Evaluation) [NOTE: Measures of the geometric and harmonic mean will not be tested]
6. Graphical methods
   Depict relationships by constructing, applying and intereting diagrams and charts such as stem-and-leaf plots, box-and-whisker plots, run charts, scatter diagrams, etc. and depict distributions by constructing, applying and interpreting diagrams such as histograms, normal probability plots, Weibull plots, etc. (Evaluation)

D. Properties and Applications of Probability Distributions

1. Distributions commonly used by black belts
   Describe and apply binomial, Poisson, normal, chi-square, Student's t, and F Distributions. (Evaluation)
2. Other distributions
   Recognize when to use hypergeometric, bivariate, exponential, lognormal and Weibull distributions. (Application)

E. Measurement Systems

1. Measurement Methods
   Describe and review measurement methods such as attribute screens, gauge blocks, calipers, micrometers, optical comparators, tensile strength, titration, etc. (Comprehension)
2. Measurement Systems Analysis
   Calculate, analyze, and interpret measurement system capability using repeatability and reproducibility, measurement correlation, bias, linearity, percent agreement, precision/tolerance (P/T), precision/total variation (P/TV), and use both ANOVA and control chart methods for nondestructive, destructive and attribute systems. (Evaluation)
3. Metrology
   Understand traceability to calibration standards, measurement error, calibration systems, control and integrity of standards and measurement devices. (Comprehension)

F. Analyzing Process Capability

1. Designing and conducting process capability studies
   Identify, describe, and apply the elements of designing and conducting process capability studies, including identifying characteristics, identifying specifications/tolerances, developing sampling plans and verifying stability and normality. (Evaluation)
2. Calculating process performance vs. specification
   Distinguish between natural process limits and specification limits and calculate process performance metrics such as percent defective. (Evaluation)
3. Process capability indices
   Define, select and calculate Cp, Cpk, and assess process capability. (Evaluation)
4. Process performance indices
   Define, select, and calculate Pp, Ppk, Cpm, and assess process performance. (Evaluation)
5. Short-term vs. long-term capability
   Understand the assumptions and conventions appropriate when only short-term data are collected and when only attributes data are available; understand the changes in relationships that occur when long term data are used; interpret relationships between long-term and short-term capability as it relates to technology and/or control problems. (Evaluation)
6. Non-normal data transformations (process capability for non-normal data)
   Understand the cause of non-normal data and determine when it is appropriate to transform. (Application)
7. Process capability for attributes data
   Compute sigma level and understand its relationship to Ppk. (Application)