Full Title Six Sigma 2 Statistical Control

Short Title Six Sigma 2 Statistical Contro

Code QLTY07022
Level 07
Credit 05

Department Mech and Manufact Eng

Subject Area Quality
Attendence N/A%


This module aims to provide learners with the statistical tools associated with the six sigma DMAIC philosophy specifically in the areas of Measure, Improve and control consistent with the ASQ and Quality America Green Belt Body of Knowledge. The student will be able to perform basic statistical analysis, develop and plots control charts, determine process and measurement capability. Minitab statistical software will be used to demonstrate and apply these statistical techniques.

Indicative Syllabus

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); recognise 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.
  • Determine appropriate sample size for various test. .
  • Tests for means, and proportions
  • Define, compare, and contrast statistical and practical significance.
  • 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, 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.


Learning Outcomes
On completion of this module the learner will/should be able to
  1. Perform basic probability calculations by applying the probability rules and concepts

  2. Describe and interpret the common probability distributions

  3. Calculate, analyse and interpret measurement systems

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

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

  6. Perform basic hypothesis testing eg. Hypothesis testing of means

  7. Perform one way analysis of variance

  8. Describe the experimental design terms and process

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

  10. Develop control charts with Minitab

  11. Use the six sigma tools to implement control and monitoring systems

Assessment Strategies

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

Assessment Facilitites


Module Dependencies
Pre Requisite Modules
Co Requisite Modules
Incompatible Modules

Coursework Assessment Breakdown %
Course Work / Continuous Assessment 20 %
End of Semester / Year Formal Examination 80 %

Coursework Assessment Breakdown

Description Outcome Assessed % of Total Assessment Week
Multiple Choice Quizzes 1,2,3,4,5,6,8,9,11 10 OnGoing
Assignment Work 4,7,9,10 10 OnGoing

End Exam Assessment Breakdown

Description Outcome Assessed % of Total Assessment Week
Final Exam One 2.5 hour written paper 1,2,3,4,5,6,7,8,9,11 80 End of Term

Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload
Lecture Not Specified Lecture 2 Weekly 2.00
Tutorial Not Specified Tutorial 2 Weekly 2.00
Independent Learning UNKNOWN Independent Learning 4 Weekly 4.00

Total Average Weekly Learner Workload 4.00 Hours

Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload
Lecture Distance Learning Suite Online Lecture 2.5 Weekly 2.50
Tutorial Not Specified Tutorial 0 Weekly 0.00
Independent Learning UNKNOWN Independent Learning 4 Weekly 4.00

Total Average Weekly Learner Workload 2.50 Hours

Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload

Total Average Weekly Learner Workload 0.00 Hours

Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload

Total Average Weekly Learner Workload 0.00 Hours

Book Resources





Keller, Paul A.

Six Sigma Demystified 2nd Ed

ISBN: 007174679X

McGraw-Hill Professional


Oakland, John

Statistical Process Control



Roderick A. Munro, Matthew J. Maio, and Mohamed B. Nawaz The Certified Six Sigma Green Belt Handbook 2nd











Other Resources


Url Resources


Additional Info

ISBN BookList

Book Cover Book Details
Quentin Brook 2017 Lean Six Sigma & Minitab - The Complete Toolbox Guide for Business Improvement Opex Resources Ltd