A. Process Analysis and Documentation
 Tools
Develop and review process maps, written procedures, work instructions, flowcharts, etc. (Analysis)
 Process Inputs and Outputs
Identify process input variables and process output variables and document their relationship through causeandeffect diagrams, relational matrices, etc. (Evaluation)
B. Probability and Statistics
 Drawing valid statistical conclusions
Distinguish between enumerative (descriptive) and analytical (inferential) studies, and distinguish between a population parameter and sample statistic. (Evaluation)
 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)
 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
 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)
 Measurement Scales
Define and apply nominal, ordinal, interval and ratio measurement scales. (Application)
 Methods for collecting data
Define and apply methods for collecting data such as check sheets, coding data, automatic gauging etc. (Evaluation)
 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)
 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]
 Graphical methods
Depict relationships by constructing, applying and intereting diagrams and charts such as stemandleaf plots, boxandwhisker 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
 Distributions commonly used by black belts
Describe and apply binomial, Poisson, normal, chisquare, Student's t, and F Distributions. (Evaluation)
 Other distributions
Recognize when to use hypergeometric, bivariate, exponential, lognormal and Weibull distributions. (Application)
E. Measurement Systems
 Measurement Methods
Describe and review measurement methods such as attribute screens, gauge blocks, calipers, micrometers, optical comparators, tensile strength, titration, etc. (Comprehension)
 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)
 Metrology
Understand traceability to calibration standards, measurement error, calibration systems, control and integrity of standards and measurement devices. (Comprehension)
F. Analyzing Process Capability
 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)
 Calculating process performance vs. specification
Distinguish between natural process limits and specification limits and calculate process performance metrics such as percent defective. (Evaluation)
 Process capability indices
Define, select and calculate Cp, Cpk, and assess process capability. (Evaluation)
 Process performance indices
Define, select, and calculate Pp, Ppk, Cpm, and assess process performance. (Evaluation)
 Shortterm vs. longterm capability
Understand the assumptions and conventions appropriate when only shortterm 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 longterm and shortterm capability as it relates to technology and/or control problems. (Evaluation)
 Nonnormal data transformations (process capability for nonnormal data)
Understand the cause of nonnormal data and determine when it is appropriate to transform. (Application)
 Process capability for attributes data
Compute sigma level and understand its relationship to Ppk. (Application)
