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)
