5.12 Analytical Tools Used Throughout the DMAIC Cycle

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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

5.12 Analytical Tools Used Throughout the DMAIC Cycle

Key Takeaways Explain This Topic AI

The seven tools are affinity diagram, tree diagram, matrix diagram, prioritization matrix, activity network diagram, process decision program chart, and interrelationship digraph.

The affinity diagram groups unstructured verbal data into natural themes and is normally performed silently to prevent anchoring.

The interrelationship digraph identifies drivers and outcomes by counting arrows out versus arrows in for each node.

The process decision program chart maps what could go wrong at each step and pre-plans countermeasures.

The prioritization matrix scores options against weighted criteria to produce a defensible ranked list.

Last updated: August 2026

Why these seven
These are the classic seven management and planning tools , developed to handle the verbal,
relational, and planning problems that the seven basic quality tools (histogram, Pareto, control
chart, and so on) cannot. They appear in the Define chapter of the Body of Knowledge but are used

across all five DMAIC phases, and ASQ tags them at the Apply level.

Tool Handles Typical DMAIC use
Affinity diagram Large volumes of unstructured verbal data Grouping VOC statements, brainstorm output
Tree diagram Decomposition of a goal into means CTQ flowdown, WBS, why-why analysis
Matrix diagram Relationships between two or more lists QFD, cause-to-CTQ mapping, tool selection
Prioritization matrix Ranking options against weighted criteria Project selection, solution selection
Activity network diagram Task sequence and dependency Implementation planning, critical path
Process decision program chart What could go wrong and what to do about it Implementation risk planning
Interrelationship digraph Cause-and-effect among many issues Finding the driver among tangled causes
Affinity diagram
Used when the team has 30 to 100 unstructured statements -- VOC verbatims, brainstormed causes, survey

comments -- and needs to find the natural themes.

Procedure: write each idea on its own card; sort silently into groups that feel related; name each
group with a header that states the theme rather than the category; and split or merge until the

groups are stable.

The silence matters. Sorting out loud lets the first speaker's framing anchor the group, and the
resulting themes tend to reproduce the existing organizational structure rather than the structure in

the data. Silent sorting reliably produces different and better groupings.

Output: themes that become stratification factors in Measure, or the top level of a tree diagram.

Tree diagram

Decomposes a general objective into progressively more specific means, level by level.

CTQ tree : customer need to driver to measurable requirement to specification.

Why-why tree : problem to cause to sub-cause.

WBS : deliverable to sub-deliverable to work package.

The test at each level is the necessary and sufficient question: if all the children are achieved,
is the parent achieved? If not, a branch is missing. Stop when the lowest level is directly actionable

or directly measurable.

Matrix diagram
Shows the strength of relationships between two or more lists. Shapes are named by the letter their

layout resembles: L (two lists, the common case), T (one list against two others), Y (three lists in a circle), X (four lists), and C (three lists in three dimensions).

Relationship strengths conventionally use 9 for strong, 3 for moderate, 1 for weak, and blank for none,
which makes the strong relationships dominate row and column sums. The house of quality is the most

elaborate matrix diagram; a cause-to-CTQ matrix is the simplest useful one.

Prioritization matrix

Ranks a set of options against weighted criteria. Procedure:

List the options and the decision criteria.

Weight the criteria so that the weights sum to 1.0 (or to 100).

Score each option against each criterion on a consistent scale.

Compute Score i = ∑ j w j × s i j \text{Score}_i = \sum_j w_j \times s_{ij} Score i = ∑ j w j × s ij and rank.

Solution option Cost (0.3) Speed (0.2) Effectiveness (0.4) Risk (0.1) Weighted total

Automate inspection 3 4 9 5 0.9 + 0.8 + 3.6 + 0.5 = 5.8 0.9 + 0.8 + 3.6 + 0.5 = 5.8 0.9 + 0.8 + 3.6 + 0.5 = 5.8

Error-proof the fixture 8 8 8 9 2.4 + 1.6 + 3.2 + 0.9 = 8.1 2.4 + 1.6 + 3.2 + 0.9 = 8.1 2.4 + 1.6 + 3.2 + 0.9 = 8.1

Add a second inspector 6 9 4 8 1.8 + 1.8 + 1.6 + 0.8 = 6.0 1.8 + 1.8 + 1.6 + 0.8 = 6.0 1.8 + 1.8 + 1.6 + 0.8 = 6.0

Error-proofing wins. Two cautions: weight the criteria before you score the options , or the weights
will be adjusted to justify a preferred answer; and check that every criterion is scored in the same
direction (here higher is better on all four, so "cost" is scored as cost-favourability rather than as

cost).

Activity network diagram
Shows tasks as a network of dependencies and computes the critical path. It answers the same question
as a Gantt chart but emphasizes the dependency logic rather than the calendar, which makes it the
better tool while the sequence is still being designed. The mechanics of critical path and float are

covered in the project management tools section.

Process decision program chart
The PDPC extends a tree diagram by asking, at each planned step, what could go wrong and what we
would do about it . It is the pre-mortem in diagram form and belongs in the Improve phase before
implementation. Implement new torque verification
|
+-- Install torque transducers
| +-- Risk: calibration drifts -> Countermeasure: 30-day calibration interval, verified daily
| +-- Risk: fixture does not fit -> Countermeasure: trial fit on line 4 before rollout
|
+-- Train operators on reaction plan
| +-- Risk: night shift not covered -> Countermeasure: dedicated night-shift session + level-4 trainer
| +-- Risk: knowledge decays -> Countermeasure: 30-day refresher and audit KBI
|
+-- Update SOP and control plan
+-- Risk: change control delay -> Countermeasure: submit 3 weeks ahead; named approver
PDPC differs from FMEA in scope and quantification: FMEA analyzes failure modes of a process or
design with severity, occurrence, and detection ratings; PDPC analyzes risks to a plan and

pre-plans responses without numeric scoring.

Interrelationship digraph
Used when many issues cause one another and the team cannot tell which to attack. Place each issue on a
diagram, then for every pair ask "does A cause or influence B, does B cause or influence A, or

neither?" and draw one arrow in the dominant direction only.

Then count for each node:

Arrows out (drivers). The node with the most outgoing arrows is the root driver -- act here

for maximum leverage.

Arrows in (outcomes). The node with the most incoming arrows is the key outcome -- measure

here to detect improvement.

Issue Arrows out Arrows in Interpretation
Inaccurate demand forecast 5 1 Root driver
Frequent schedule changes 3 2 Intermediate
Excess changeovers 2 3 Intermediate
Late deliveries 0 5 Key outcome
The digraph's advantage over a fishbone diagram is that it captures relationships among causes ,
not just cause-to-effect. A fishbone would list all four of these as causes of a problem; the digraph

shows that fixing the forecast is what moves the other three.