|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.
- Short-term vs. long-term capability
- Describe the assumptions and conventions that are appropriate when only short-term data are collected and when only attributes data are available. Describe the changes in relationships that occur when long-term data are used, and interpret the relationship between long- and short-term 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
- Multi-vari studies
- Create and interpret multi-vari 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 (p-value); recognize the difference between correlation and causation. Interpret the linear regression equation and determine its statistical significance (p-value). Use regression models for estimation and prediction.
F. Hypothesis testing
- 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.
- Paired-comparison tests
- Define and describe paired-comparison parametric hypothesis tests.
- Single-factor analysis of variance (ANOVA)
- Define terms related to one-way 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, multi-vari studies, FMEA, measurement system capability re-analysis, and post-improvement capability analysis to identify, implement, and validate solutions through F-test, t-test, etc .
J. Control plan
- Assist in developing a control plan to document and hold the gains, and assist in implementing controls and monitoring systems.