A. Probability and statistics  Drawing valid statistical conclusions
 Distinguish between enumerative (descriptive) and analytical (inferential) studies, and distinguish between a population parameter and a sample statistic.
 Central limit theorem and sampling distribution of the mean
 Define the central limit theorem and describe its significance in the application of inferential statistics for confidence intervals, control charts, etc.
 Basic probability concepts
 Describe and apply concepts such as independence, mutually exclusive, multiplication rules, etc.
B. Probability distributions  Describe and interpret normal, binomial, and Poisson, chi square, Student's t, and F distributions.
C. Measurement system analysis  Calculate, analyze, and interpret measurement system capability using repeatability and reproducibility (GR&R), measurement correlation, bias, linearity, percent agreement, and precision/tolerance (P/T).
D. Process capability and performance  Process capability studies
 Identify, describe, and apply the elements of designing and conducting process capability studies, including identifying characteristics, identifying specifications and tolerances, developing sampling plans, and verifying stability and normality.
 Process performance vs. specification
 Distinguish between natural process limits and specification limits, and calculate process performance metrics such as percent defective.
 Process capability indices
 Define, select, and calculate Cp and Cpk, and assess process capability.
 Process performance indices
 Define, select, and calculate Pp, Ppk, Cpm, and assess process performance.
 Shortterm vs. longterm capability
 Describe the assumptions and conventions that are appropriate when only shortterm data are collected and when only attributes data are available. Describe the changes in relationships that occur when longterm data are used, and interpret the relationship between long and shortterm capability as it relates to a 1.5 sigma shift.
 Process capability for attributes data
 Compute the sigma level for a process and describe its relationship to Ppk.
E. Exploratory data analysis  Multivari studies
 Create and interpret multivari studies to interpret the difference between positional, cyclical, and temporal variation; apply sampling plans to investigate the largest sources of variation.
 Simple linear correlation and regression
 Interpret the correlation coefficient and determine its statistical significance (pvalue); recognize the difference between correlation and causation. Interpret the linear regression equation and determine its statistical significance (pvalue). Use regression models for estimation and prediction.
F. Hypothesis testing  Basics
 Define and distinguish between statistical and practical significance and apply tests for significance level, power, type I and type II errors. Determine appropriate sample size for various test. .
 Tests for means, variances, and proportions
 Define, compare, and contrast statistical and practical significance.
 Pairedcomparison tests
 Define and describe pairedcomparison parametric hypothesis tests.
 Singlefactor analysis of variance (ANOVA)
 Define terms related to oneway ANOVAs and interpret their results and data plots.
 Chi square
 Define and interpret chi square and use it to determine statistical significance.
G. Design of experiments (DOE)  Basic terms
 Define and describe basic DOE terms such as independent and dependent variables, factors and levels, response, treatment, error, repetition, and replication.
 Main effects
 Interpret main effects and interaction plots.
H. Statistical process control (SPC)  Objectives and benefits
 Describe the objectives and benefits of SPC, including controlling process performance, identifying
 special and common causes, etc.
 Rational subgrouping
 Define and describe how rational subgrouping is used.
 Selection and application of control charts
 Identify, select, construct, and apply the following types of control charts: R, s, individuals and moving range (ImR / XmR), median, p, np, c, and u.
 Analysis of control charts
 Interpret control charts and distinguish between common and special causes using rules for determining statistical control.
I. Implement and validate solutions  Use various improvement methods such as brainstorming, main effects analysis, multivari studies, FMEA, measurement system capability reanalysis, and postimprovement capability analysis to identify, implement, and validate solutions through Ftest, ttest, etc .
J. Control plan  Assist in developing a control plan to document and hold the gains, and assist in implementing controls and monitoring systems.
