7.3 Cause-and-Effect (Ishikawa) Diagrams & Scatter Plots

7.3 Cause-and-Effect (Ishikawa) Diagrams & Scatter Plots

Quality improvement requires moving from observing symptoms to isolating root causes and proving relationships. Two essential tools in the ASQ CQIA Body of Knowledge bridge qualitative hypothesis generation and quantitative relationship testing: the Cause-and-Effect (Ishikawa / Fishbone) Diagram and the Scatter Plot. While the fishbone diagram structures team brainstorming around potential cause categories, the scatter plot visually and mathematically evaluates whether an identified input variable correlates with a quality outcome.

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1. Cause-and-Effect (Ishikawa / Fishbone) Diagram Architecture

Developed in 1943 by Dr. Kaoru Ishikawa at the University of Tokyo, the Cause-and-Effect Diagram (also called a Fishbone Diagram due to its skeletal appearance, or an Ishikawa Diagram) is a graphical tool used to brainstorm, organize, and display potential causes of a specific quality problem or effect.

+-------------------------------------------------------------------------+
|                 ISHIKAWA (FISHBONE) DIAGRAM ARCHITECTURE                |
+-------------------------------------------------------------------------+
|                                                                         |
|   [ MACHINE ]          [ METHOD ]           [ MATERIAL ]                |
|        │                   │                    │                       |
|        └──►                └──►                 └──►                    |
|            │                   │                    │                   |
|  ──────────┴───────────────────┴────────────────────┴────────►[ EFFECT ]|
|            │                   │                    │          Problem  |
|        ┌──►                ┌──►                 ┌──►             Box    |
|        │                   │                    │                       |
|   [ MEASUREMENT ]     [ ENVIRONMENT ]       [ MANPOWER ]                |
|                        (Mother Nature)        (People)                  |
+-------------------------------------------------------------------------+

Core Structural Components

1. The Problem Box (Effect / Head): Located on the far right-hand side. It contains a precise, operational definition of the problem being investigated (e.g., "Excessive solder bridge defects on Line 4" or "Customer onboarding cycle time > 5 days").
2. The Central Backbone: A heavy horizontal line pointing directly to the problem box.
3. Primary Category Bones (Major Ribs): Angled lines branching off the backbone representing major taxonomies of potential causes.
4. Secondary and Tertiary Bones (Sub-Ribs): Smaller branches off the primary ribs capturing specific sub-causes and answers to iterative "Why?" questions.

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2. Categorization Frameworks: 6Ms, 4Ps, and 5Ss

To ensure comprehensive brainstorming and prevent teams from fixating on a single cause category (such as blaming operator error), standardized taxonomies are used based on the industry sector.

The Manufacturing 6Ms

Service and Transactional Taxonomies

• The 4Ps (Service / Administrative):
  • Policies: High-level organizational rules, pricing structures, approval limits.
  • Procedures: Step-by-step workflow handoffs, billing protocols, software data entry.
  • People: Staffing levels, training, customer communication skills.
  • Plant / Place: Office layout, physical workspace ergonomics, digital server availability.
• The 5Ss (Transactional / Office): Surroundings, Suppliers, Systems, Skills, and Safety.

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3. Facilitating Fishbone Construction & Integrating the 5 Whys

A fishbone diagram is most effective when constructed through a structured, multi-step facilitation process:

+-------------------------------------------------------------------------+
|               NESTING THE 5 WHYS ON A FISHBONE SUB-BRANCH               |
+-------------------------------------------------------------------------+
|                                                                         |
|  [ METHOD (Primary Rib) ]                                               |
|       │                                                                 |
|       └──► (Why 1?) Solder paste applied too thick                      |
|                 │                                                       |
|                 └──► (Why 2?) Stencil aperture clogged                  |
|                           │                                             |
|                           └──► (Why 3?) Cleaning cycle skipped          |
|                                     │                                   |
|                                     └──► (Why 4?) No visual timer       |
|                                               │                         |
|                                               └──► (Why 5? ROOT CAUSE)  |
|                                                    Missing PM standard  |
|                                                    work procedure       |
+-------------------------------------------------------------------------+

Step-by-Step Construction Protocol

1. Define the Effect: Agree on an objective, measurable problem statement placed in the right-hand box.
2. Identify Major Categories: Draw the backbone and assign the 6Ms or 4Ps to primary branch ribs.
3. Divergent Brainstorming: Engage cross-functional team members (operators, engineers, quality technicians) using silent brainstorming or round-robin ideation to populate causes.
4. Drill Down with the 5 Whys: For every major cause identified, ask "Why does this happen?" iteratively. Draw sub-branches for each layer of inquiry until an actionable, systemic root cause is uncovered.
5. Convergent Prioritization: Use multi-voting (e.g., dot voting) or data collection check sheets to identify the top 2 to 3 vital causes for empirical verification.

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4. Scatter Plots: Visualizing Bivariate Relationships

While a fishbone diagram generates qualitative hypotheses about potential causes, a Scatter Plot (or Scatter Diagram) provides the graphical tool to examine the mathematical relationship between two continuous variables.

A scatter plot displays paired bivariate data $(x_i, y_i)$ on a Cartesian coordinate system:

• Horizontal Axis ($X$-Axis): Represents the independent variable (the hypothesized cause, input factor, or process parameter under control, such as furnace temperature, chemical concentration, or training hours).
• Vertical Axis ($Y$-Axis): Represents the dependent variable (the effect, output response, or quality characteristic, such as tensile strength, defect count, or processing time).

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5. Interpreting Scatter Plot Correlation Patterns

Visual analysis of the scatter plot's point cloud reveals the nature, direction, and strength of the relationship between variables.

+-------------------------------------------------------------------------+
|                   SCATTER PLOT CORRELATION TAXONOMY                     |
+-------------------------------------------------------------------------+
|                                                                         |
|   1. STRONG POSITIVE            2. STRONG NEGATIVE                      |
|   Y ▲         •                 Y ▲ •                                   |
|     │       • •                   │   • •                               |
|     │     • •                     │     • •                             |
|     │   • •                       │       • •                           |
|     │ • •                         │         • •                         |
|     └─────────────► X             └─────────────► X                     |
|     r ≈ +0.90                     r ≈ -0.90                             |
|                                                                         |
|   3. NO CORRELATION             4. CURVILINEAR (Non-Linear)             |
|   Y ▲  •    •   •               Y ▲       • •                           |
|     │    •   •   •                │     •     •                         |
|     │  •   •   •                  │   •         •                       |
|     │    •   •   •                │ •             •                     |
|     │  •   •   •   •              │•               •                    |
|     └─────────────► X             └─────────────► X                     |
|     r ≈ 0.00                      r ≈ 0.00 (Strong physical link!)      |
|                                                                         |
+-------------------------------------------------------------------------+

Pattern Classification

• Strong Positive Correlation ($r \to +1.0$): As $X$ increases, $Y$ increases in a tight linear band (e.g., increased machine speed directly increases operating temperature).
• Strong Negative Correlation ($r \to -1.0$): As $X$ increases, $Y$ decreases in a tight linear band (e.g., increased preventive maintenance hours decreases machine breakdown frequency).
• Weak / Moderate Correlation ($0.3 < |r| < 0.7$): Points show a general upward or downward slope but with wide scatter, indicating that other confounding variables are influencing $Y$.
• Zero / No Correlation ($r \approx 0$): Points form a random circular or shotgun cloud; changes in $X$ have no apparent linear impact on $Y$.
• Curvilinear (Non-Linear) Relationship: The point cluster follows a distinct mathematical curve (such as an inverted U-shape or quadratic curve). In an inverted U-shape, tensile strength increases with temperature up to an optimum point, after which higher heat degrades material strength. Crucial CQIA Exam Concept: The linear correlation coefficient $r$ for a symmetrical parabolic curve may equal 0.00, despite a perfect deterministic physical relationship existing between the variables.

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6. The Pearson Correlation Coefficient ($r$) vs. Causation

The Pearson Product-Moment Correlation Coefficient ($r$) quantifies the strength and direction of a linear relationship between two continuous variables:

$r = \frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^n (x_i - \bar{x})^2 \sum_{i=1}^n (y_i - \bar{y})^2}}$

Properties of $r$

• Boundaries: $-1.0 \le r \le +1.0$.
• Direction: Positive values denote a direct relationship; negative values denote an inverse relationship.
• Coefficient of Determination ($r^2$): Represents the proportion of total variation in $Y$ that is explained by the linear relationship with $X$ (e.g., if $r = 0.80$, $r^2 = 0.64$, meaning 64% of the variation in $Y$ is explained by $X$).

Correlation Does Not Equal Causation

[!WARNING] A high correlation coefficient ($|r| > 0.90$) proves only that two variables move together mathematically; it does not prove that $X$ causes $Y$. The observed relationship may be driven by:

1. A Lurking / Confounding Variable ($Z$): Both ice cream sales ($X$) and drowning incidents ($Y$) correlate strongly ($r = 0.85$), but both are driven by a third confounding variable: summer ambient temperature ($Z$).
2. Reverse Causation: $Y$ may actually be causing $X$.
3. Spurious Coincidence: Statistical chance in finite datasets.

To establish true causality, quality teams must combine statistical correlation with physical engineering subject-matter expertise, controlled Design of Experiments (DoE), and confirmatory pilot runs.