8.2 DOE Design Principles: Randomization, Blocking, Replication, and Resolution

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1 Chapter 1: Introduction & CSSBB Exam Strategy

1.1 CSSBB Exam Format, Scoring, and Testing Windows 1.2 Eligibility, Project Affidavits, Application, and Recertification 1.3 Open-Book Strategy, Reference Materials, and a 16-Week Study Plan

2 Chapter 2: Organization-Wide Planning and Deployment

2.1 Fundamentals of Six Sigma and Lean Methodologies 2.2 Selecting the Right Methodology: DMAIC, DFSS, and Lean 2.3 Business Systems, Processes, and Stakeholder Relationships 2.4 Strategic Planning and Deployment of Six Sigma Initiatives 2.5 Six Sigma Roles and Responsibilities 2.6 Organizational Barriers and Common Causes of Six Sigma Failure 2.7 Change Management: Stakeholder Analysis, Readiness, and Communication

3 Chapter 3: Organizational Process Management and Measures

3.1 Impact of Six Sigma Projects on Customers, Suppliers, and Stakeholders 3.2 Benchmarking Types and Performance Goal Setting 3.3 Performance Measures: Balanced Scorecard, KPIs, KBIs, OKRs, and Line of Sight 3.4 Leading and Lagging Indicators and Performance Dashboards 3.5 Financial Measures: Revenue Growth, Margin, NPV, ROI, and Cost-Benefit Analysis 3.6 Cost of Poor Quality and Hard versus Soft Savings

4 Chapter 4: Team Management

4.1 Team Types and Constraints 4.2 Team Roles, Responsibilities, and Member Selection 4.3 Team Success Factors and Ground Rules 4.4 Motivational Techniques and Overcoming Demotivators 4.5 Stages of Team Development and Conflict Resolution 4.6 Team Communication Plans 4.7 Team Leadership Models: Direct, Coach, Support, and Delegate 4.8 Group Behaviors, Conflict Resolution, and Meeting Management 4.9 Facilitation Techniques and Team Decision-Making Methods 4.10 Team Training: Needs Assessment, Delivery, and Evaluation

5 Chapter 5: Define Phase

5.1 Customer Identification and Segmentation 5.2 Customer Data Collection: Methods, Validity, and Reliability 5.3 Customer Requirements: CTX, CTQ Trees, and Operational Definitions 5.4 The Kano Model and Quality Function Deployment 5.5 SIPOC and Process Mapping 5.6 Business Case Justification 5.7 The Project Charter and the Problem Statement 5.8 Project Scope and Boundaries 5.9 SMART Goals and Project Performance Measurements 5.10 Project Charter Reviews and Toll-Gate Governance 5.11 Project Management Tools: Gantt Charts, Toll-Gate Reviews, WBS, and RACI 5.12 Analytical Tools Used Throughout the DMAIC Cycle

6 Chapter 6: Measure Phase

6.1 Process Flow Metrics and the Hidden Factory 6.2 Process Analysis Tools and Value Stream Mapping 6.3 Types of Data and Measurement Scales 6.4 Sampling Concepts, Methods, and Sample Size for Estimation 6.5 Data Collection Plans and Common Pitfalls 6.6 Gage R&R for Variable Measurement Systems 6.7 Attribute Agreement Analysis and Audit MSA 6.8 Measurement Systems Across the Organization, and Metrology 6.9 Population Parameters, Sample Statistics, and Valid Statistical Conclusions 6.10 Descriptive Statistics: Central Tendency, Dispersion, and Shape 6.11 Graphical Methods for Exploratory Data Analysis 6.12 Probability Concepts, Common Distributions, and the Central Limit Theorem 6.13 Additional Distributions: Hypergeometric, Exponential, Lognormal, Weibull, and Bivariate 6.14 Process Capability and Performance Indices 6.15 Capability Studies, Attributes Capability, Yield Metrics, and Long-Term Capability

7 Chapter 7: Analyze Phase

7.1 The Correlation Coefficient, Its Confidence Interval, and Causation 7.2 Linear Regression and Residual Analysis 7.3 Multivariate Tools: Factor Analysis, Discriminant Analysis, and MANOVA 7.4 Hypothesis Testing Terminology, Errors, and Single-Sample Tests 7.5 Statistical Versus Practical Significance 7.6 Sample Size for Hypothesis Tests 7.7 Point Estimates, Confidence, Prediction, and Tolerance Intervals 7.8 Tests for Means, Variances, and Proportions 7.9 Analysis of Variance 7.10 Chi-Square Goodness-of-Fit and Tests of Independence 7.11 Types of Risk and Failure Mode and Effects Analysis 7.12 Gap Analysis and Root Cause Analysis 7.13 Waste Analysis: The Seven Classic Wastes and Resource Under-Utilization

8 Chapter 8: Improve Phase

8.1 Design of Experiments: Objectives, Terminology, and Effects 8.2 DOE Design Principles: Randomization, Blocking, Replication, and Resolution 8.3 Planning and Evaluating Designed Experiments 8.4 One-Factor Experiments: Completely Randomized, Randomized Block, and Latin Square Designs 8.5 Full Factorial Experiments and Design Selection 8.6 Two-Level Fractional Factorial Experiments and Confounding 8.7 Response Surface Methodology and Optimization 8.8 Waste Elimination: Pull Systems, Kanban, 5S, and Poka-Yoke 8.9 Cycle-Time Reduction: Continuous Flow, SMED, and Heijunka 8.10 Kaizen, Kaizen Blitz, Theory of Constraints, and OEE 8.11 Implementation Planning, Piloting, and Solution Selection

9 Chapter 9: Control Phase

9.1 SPC Objectives, Variable Selection, and Rational Subgrouping 9.2 Control Charts for Variables Data 9.3 Control Charts for Attributes Data 9.4 Short-Run SPC and Moving Average Charts 9.5 Control Chart Analysis: Common Cause, Special Cause, and Run Rules 9.6 Total Productive Maintenance and Visual Controls 9.7 Measurement System Reanalysis 9.8 Control Plan Development and Process Owner Handoff 9.9 Lessons Learned, Documentation, and Training for Sustainment 9.10 Ongoing Evaluation of the Improved Process

10 Chapter 10: Design for Six Sigma (DFSS)

10.1 DFSS Frameworks: DMADV, DMADOV, and Design Transfer 10.2 Design for X (DFX) 10.3 Robust Design, Parameter Design, and Verification 10.4 Tolerance Design and Statistical Tolerancing

8.2 DOE Design Principles: Randomization, Blocking, Replication, and Resolution

Key Takeaways Explain This Topic AI

Randomization protects against unknown lurking variables; blocking removes the effect of a known nuisance variable.

Replication means repeating an entire experimental run including setup, and it is what provides a valid estimate of experimental error.

Repetition means taking several measurements within one run and estimates measurement and within-run variation only.

Design resolution states which effects are confounded: Resolution III confounds main effects with two-factor interactions, IV confounds two-factor interactions with each other, and V is clean for two-factor interactions.

A balanced design has an equal number of observations at each factor level, which makes effect estimates independent and simplifies analysis.

Last updated: August 2026

The three foundational principles

R. A. Fisher's three principles underpin every valid experiment.

• Principle What it does What it protects against
• Randomization Assigns run order and treatment allocation at random Unknown, unmeasured lurking variables
• Replication Repeats whole runs, including setup Provides an estimate of experimental error; improves precision

Blocking Groups runs so a known nuisance factor is constant within a block Known but uninteresting sources of variation

The division of labour is worth memorizing: block what you know, randomize against what you do not.

• Randomization
• If temperature and pressure runs are performed in a systematic order, and ambient humidity happens to
• rise through the day, the humidity effect is inseparable from whatever factor was varied last. Randomize
• the run order and the humidity effect is distributed unpredictably across all factors, converting a

systematic bias into ordinary experimental error.

Randomization also protects the validity of the statistical tests themselves. The F F F tests in an ANOVA

assume independent errors, and independence is what randomization delivers.

Where full randomization is expensive -- for example when a factor requires a lengthy oven change -- a split-plot design randomizes the hard-to-change factor at the whole-plot level and the easy-to-change

• factors within it. This is a legitimate design, but it has two error terms and must be analyzed
• accordingly. Simply running the hard-to-change factor in convenient order and analyzing as though it

were fully randomized is not.

Replication versus repetition

This distinction is a reliable exam question.

Replication Repetition

What is repeated The entire run , including setup, loading, and adjustment Multiple measurements or units within one run

Variation captured All sources: setup, material, operator, measurement Measurement and within-run variation only

Valid for Estimating experimental error; testing significance Improving the precision of a single run's response

• Effect on df Adds degrees of freedom for error Does not add valid error degrees of freedom
• Treating repetition as replication understates experimental error, which inflates the F F F statistic and
• makes effects appear significant when they are not. If a run's setup is done once and five parts are
• measured, that is repetition; averaging them gives a better estimate of that run's response, but it says

nothing about run-to-run variation.

• Blocking
• A block is a group of experimental units expected to be more homogeneous within than between: one
• raw material lot, one day, one operator, one machine. Assign a complete set of treatments within each

block, and the block-to-block variation is estimated and removed from the error term.

The result is a more sensitive experiment. The cost is one or more degrees of freedom, and the

assumption that the blocking factor does not interact with the treatment factors.

• Balance, order, and efficiency
• Balance. A design is balanced when each factor level appears the same number of times and each
• combination appears equally often. Balanced designs make the effect estimates orthogonal -- estimated

independently of one another -- so removing a term from the model does not change the other estimates.

Unbalanced designs can still be analyzed but the estimates are correlated and interpretation is harder.

• Order. Standard order (Yates order) is a canonical listing of runs used for constructing and
• analyzing the design. Run order must be randomized. Never confuse the two: the design matrix is

written in standard order, and the experiment is executed in random order.

• Efficiency. The information obtained per experimental run. Factorial designs are efficient because
• every run contributes to the estimate of every effect; one-factor-at-a-time experimentation is

inefficient because each run informs only one comparison, and it cannot detect interactions at all.

• Power and sample size in DOE
• Power is the probability of detecting a real effect of a given size. In a two-level factorial, the

number of runs required to detect an effect δ \delta δ with power 1 − β 1-\beta 1 − β depends on δ / σ \delta/\sigma δ / σ and

on the number of replicates. Effect estimate = y ˉ + − y ˉ − , S E effect = 2 σ N \text{Effect estimate} = \bar{y}_{+} - \bar{y}_{-}, \qquad SE_{\text{effect}} = \frac{2\sigma}{\sqrt{N}} Effect estimate = y ˉ ​ + ​ − y ˉ ​ − ​ , S E effect ​ = N ​ 2 σ ​

where N N N is the total number of runs. Because every run contributes to every effect estimate, adding

one replicate of a 2 4 2^4 2 4 design (16 more runs) reduces the standard error of every effect by a factor of 2 \sqrt{2} 2 ​ .

• Two practical rules: an unreplicated two-level factorial has no degrees of freedom for error unless
• higher-order interactions are pooled into error or a normal probability plot of effects is used; and
• adding centre points provides both an error estimate and a test for curvature without disturbing the

factorial structure.

• Interaction and confounding
• An interaction exists when the effect of one factor depends on the level of another. Interaction
• plots with non-parallel lines indicate interaction; crossing lines indicate a strong one. Interactions

are the main reason factorial designs beat one-factor-at-a-time work, because OFAT cannot detect them.

• Confounding (aliasing) occurs when two effects cannot be separately estimated because they are
• calculated from the same contrast. It is the price of fractional designs: reduce the number of runs and

some effects merge.

Resolution

Design resolution states which effects are confounded, and it is written as a Roman numeral.

Resolution Confounding pattern Use

III Main effects confounded with two-factor interactions Screening many factors cheaply; risky if interactions are likely

IV Main effects clear of two-factor interactions; two-factor interactions confounded with each other Common screening choice; identifies important main effects safely

V Main effects and two-factor interactions clear of each other; two-factor interactions confounded with three-factor interactions Characterization; usually adequate for a final model

A useful mnemonic: the resolution number is the length of the shortest word in the defining relation,

and an effect of order p p p is confounded with effects of order R − p R - p R − p . In Resolution III, a main effect

( p = 1 p=1 p = 1 ) is confounded with 3 − 1 = 2 3-1 = 2 3 − 1 = 2 -factor interactions; in Resolution V, a main effect is clear of

two-factor interactions and two-factor interactions ( p = 2 p=2 p = 2 ) are confounded with 5 − 2 = 3 5-2 = 3 5 − 2 = 3 -factor

interactions.

Because three-factor and higher interactions are usually negligible in physical processes -- the sparsity of effects principle -- Resolution V designs are treated as effectively unconfounded.

• A design checklist
• Have the response, factors, levels, and ranges been defined, with the response measured by a

validated measurement system?

Are the factor ranges wide enough to produce a detectable effect, but inside safe operating

limits?

Is the design balanced , and what is its resolution?

Which effects are confounded , and is that acceptable given what is known about the process?

Is the run order randomized , and if not, is a split-plot analysis planned?

Are there replicates (not merely repetitions) to estimate error, or centre points?

Are known nuisance factors blocked ?

Has the power to detect the practically important effect been computed before running?