QLTY07006 2009 Six Sigma 2 - Statistical Control

Perform basic probability calculations by applying the probability rules and concepts

Describe and interpret the common probability distributions

Calculate, analyse and interpret measurement systems

Perform process capability and process perfromance analysis and interpret the results.

Perform exploratory data analysis using multi-vari charts, correlation and simple regression

Perform basic hypothesis testing eg. Hypothesis testing of means

Perform one way analysis of variance

Describe the experimental design terms and process

Develop control charts for variable and attribute data and interpret the results

Develop control charts with Minitab

Use the six sigma tools to implement control and monitoring systems

Assessments will be through a series of continuous assessments and a final written exam

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

• 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.
• 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.