In-Depth Analysis of the Seven QC Tools · Stratification

Introduction

"Data does not lie, but those who only look at aggregated data may deceive themselves."

Stratification — the most underestimated weapon among the Seven QC Tools.

It is not complicated: it involves breaking down data into different dimensions for analysis. However, its most critical aspect is: if you do not stratify, the conclusions you draw might be entirely wrong.

This is known as "Simpson's Paradox" — a trend that appears in the overall data can be completely reversed when the data is stratified.

Chapter 1: The Essence of Stratification

1.1 What is Stratification?

Stratification (Stratification), also known as layering, is one of the most fundamental and often overlooked tools among the Seven QC Tools.

Its core idea is very simple: collect data and classify (stratify) it according to different sources, characteristics, conditions, etc., and then analyze each category separately.

Mathematical Essence:
  Break down the overall population into several non-overlapping subsets (strata),
  Analyze each subset separately,
  Then compare the analysis results of the subsets with the overall analysis results.

1.2 Why Stratify — Simpson's Paradox

Let's look at a classic example:

Defect rate data for two teams in a factory:

         Team A        Team B       Total
  ┌───────────────────────────────────
  Inspection │ 100         50          150
  Defects │ 10           5           15
  Defect Rate │ 10.0%       10.0%       10.0%

→ The defect rates for both teams are 10%, making them appear identical.

But what if we stratify by product model?

Stratifying by product model:

         Team A                Team B
  ┌───────────────────────────────────────
  Product X │ Inspection 90 Defects 6 (6.7%)   Inspection 20 Defects 2 (10.0%)
  Product Y │ Inspection 10 Defects 4 (40.0%)  Inspection 30 Defects 3 (10.0%)

→ Stratified truth:
  Product X: Team A 6.7% < Team B 10.0% → Team A is better
  Product Y: Team A 40.0% > Team B 10.0% → Team B is better

→ In reality, both teams have their strengths and weaknesses, rather than being "the same"!

This is the power of stratification — the same set of data can lead to entirely different conclusions when stratified versus when not stratified.

1.3 Three Major Functions of Stratification

Chapter 2: Common Stratification Dimensions

2.1 Classic Stratification Dimensions

4M1E Stratification (Man, Machine, Material, Method, Environment):
  ── Man (Personnel): By operator, shift, skill level
  ── Machine (Equipment): By machine number, line, tooling
  ── Material (Materials): By supplier, batch, material type
  ── Method (Process): By process parameters, work methods, SOP version
  ── Environment (Environment): By temperature zone, season, cleanliness level

2.2 Time Dimension Stratification

Time Stratification:
  ── By Shift: Day shift vs. Night shift
  ── By Time Period: Hourly, per shift, daily, weekly, monthly
  ── By Season: Differences across seasons
  ── By Cycle: Beginning of the month vs. End of the month

2.3 Product/Customer Dimension Stratification

Product-Related:
  ── By Product Model
  ── By Production Batch
  ── By Product Line

Customer-Related:
  ── By Customer Type
  ── By Regional Market
  ── By Sales Channel

2.4 Principles for Selecting Stratification Dimensions

Principles for Selecting Stratification Dimensions:

  Principle 1: Relevance
    → Choose dimensions most likely related to the problem
    → For example: Dimensional tolerance issues → stratify by equipment; Appearance defects → stratify by shift

  Principle 2: Measurability
    → Ensure the data for the dimension can be accurately obtained
    → Not "I think," but "the data shows"

  Principle 3: Actionability
    → After stratification, if differences are found, actions can be taken
    → For example: Stratify by supplier → can replace or negotiate with the supplier

  Principle 4: From Coarse to Fine
    → Start with broad dimensions and then drill down to finer dimensions
    → For example: Start by line → then by equipment → then by operator

Chapter 3: The Standard 5-Step Process for Stratification

Step 1 — Define the Analysis Objective

Ask yourself three questions:
  ① What problem do I need to solve?
  ② What factors do I think might be related to the problem?
  ③ What data do I have available?

Step 2 — Determine Stratification Dimensions

Identify 1-3 stratification dimensions based on the analysis objective
  → Most common: Stratify by "Man, Machine, Material, Method, Environment" first
  → For complex situations: Cross-stratify by multiple dimensions

Step 3 — Collect and Organize Data

Data Collection Precautions:
  ── Ensure data completeness (no missing key fields)
  ── Ensure data accuracy (no erroneous records)
  ── Ensure sufficient sample size (at least 30 samples per stratum)
  ── Retain original data (for easy traceability and verification)

Step 4 — Stratified Comparative Analysis

Analysis Methods:
  ── Tabular Comparison: Stratified statistical tables (most basic)
  ── Graphical Comparison: Stratified Pareto charts/stratified histograms
  ── Statistical Testing: Chi-square test (to determine if differences are significant)
  ── Cross-Analysis: Stratify by multiple dimensions

Step 5 — Draw Conclusions and Take Action

Conclusion Verification:
  ── Are the differences in the stratified data significant?
  ── Do the differences have practical significance?
  ── Can the conclusions be repeatedly verified?

Action Plan:
  ── Develop improvement measures for the strata with differences
  ── Re-collect data after improvements to verify

Chapter 4: Practical Cases of Stratification

Case 1: Manufacturing — Stratification by Equipment

Background: The defect rate in a machining workshop has been increasing for 3 consecutive months
Aggregated Data: Defect rate 2.8%

Step 1: Stratify by equipment number
  Equipment        Inspection Count    Defect Count    Defect Rate
  CNC-01          2000      82        4.1%  ← Significantly higher
  CNC-02          2000      48        2.4%
  CNC-03          2000      38        1.9%

Step 2: In-depth analysis of CNC-01
  → Found that the spindle bearing of the equipment was worn out
  → Preventive maintenance records show that the last maintenance was over 6 months ago

Action:
  ── Immediately replace the spindle bearing
  ── Adjust the maintenance cycle of the equipment from 12 months to 6 months
  ── The defect rate dropped to 1.8% in the following two months

Case 2: Manufacturing — Stratification by Supplier

Background: High incoming defect rate at an electronics factory
Aggregated Data: Incoming defect rate 1.5%

Stratify by supplier:
  Supplier    Inspection Batches    Defective Batches    Defect Rate
  Supplier A     120         6          5.0%  ← Significantly higher
  Supplier B     150         1          0.7%
  Supplier C     180         2          1.1%

Stratify by defect type (Supplier A):
  Defect Type      Batches
  Dimensional Tolerance       3     ← Primary
  Surface Oxidation       2
  Packaging Damage       1

Action:
  ── Communicate with Supplier A, discovering that their mold has exceeded its lifespan
  ── Require Supplier A to replace the mold and enhance final inspection
  ── The defect rate of subsequent batches dropped to 1.2%

Case 3: Service Industry — Stratification by Time Period

Background: Increase in customer complaints at a restaurant
Aggregated Data: Customer complaint rate 3.5%

Stratify by time period:
  Time Period      Customer Traffic    Complaints    Complaint Rate
  Lunch (11-14)   3000       150      5.0%  ← Significantly higher
  Afternoon Tea (14-17) 1500        30      2.0%
  Dinner (17-21)   2500        75      3.0%

In-depth analysis of the lunch period:
  Stratify by dish:
    Dish        Sales    Complaints    Complaint Rate
    Signature Beef Noodles   800      65      8.1%  ← Key
    Braised Pork Rice   600      40      6.7%
    Others         1600     45      2.8%

Action:
  ── Inspect the raw materials and cooking process of the signature beef noodles
  ── Found that the beef supplier had been changed, leading to a change in taste
  ── Restore the original supplier, and the complaint rate dropped to 3.0%

Case 4: Stratification by Shift

Background: Increase in shrinkage defects in an injection molding workshop
Aggregated Data: Shrinkage defect rate 4.2%

Stratify by shift:
  Shift    Inspection Count    Defect Count    Defect Rate
  Day Shift     5000       120      2.4%
  Night Shift     5000       300      6.0%  ← Significantly higher

Stratify by operator (Night Shift):
  Operator    Inspection Count    Defect Count    Defect Rate
  Zhang       1500       25       1.7%
  Li       2000      180       9.0%  ← Key
  Wang       1500       95       6.3%

Action:
  ── Observe Li's operation and find that the mold is not preheated according to the SOP
  ── Retrain and re-certify, and the defect rate dropped to 2.8% in subsequent batches

Chapter 5: Common Pitfalls in Stratification

Pitfall 1: Incorrect Selection of Stratification Dimensions

× Incorrect: Choose dimensions based on intuition without evidence
  → For example: Defect rate increase → "stratify by color"

✓ Correct: Select dimensions based on process knowledge and data analysis
  → For example: Defect rate increase → "stratify by equipment" (dimensional issues are often related to equipment)

Pitfall 2: Over-Stratification, Insufficient Sample Size

× Incorrect: Stratify into more than 20 layers, with only a few samples per layer
  → Statistically meaningless

✓ Correct: Ensure at least 30 samples per layer
  → If a layer has too few samples, combine it with an adjacent layer or "other"

Pitfall 3: Drawing Conclusions After Only One Layer

× Incorrect: Stratify one layer, find differences → draw conclusions directly

✓ Correct: Stratification analysis should go from coarse to fine
  → First Layer: By line → find major issues with Line A
  → Second Layer: By equipment → find major issues with Line A's Machine 2
  → Third Layer: By operator → find that the night shift operator is the root cause

Pitfall 4: Ignoring "Interaction Effects"

× Incorrect: Assume each stratification dimension is independent

✓ Correct: Consider interaction effects between dimensions
  → For example: Machine A has a lower defect rate during the day shift but a higher defect rate during the night shift
  → This indicates an interaction effect between "Machine × Shift"
  → Cross-stratification analysis is required

Chapter 6: Combining Stratification with Other Tools

6.1 Stratification + Pareto Chart

Best Partner:
  Use stratification to identify the dimension where the problem lies
  Then use a Pareto chart to focus on the critical few within that dimension

Example:
  Step 1: Stratify by line → find that Line A has the highest defect rate
  Step 2: Draw a Pareto chart for all defect types on Line A
  Step 3: Identify the critical few on Line A → welding defects
  Step 4: Analyze the root cause of welding defects

6.2 Stratification + Fishbone Diagram

Combination Use:
  Step 1: Use a fishbone diagram to list all possible cause dimensions
  Step 2: Validate the most important dimensions using stratification
  Step 3: Data validation to confirm which dimensions have significant differences
  Step 4: In-depth analysis of the dimensions with significant differences

→ The fishbone diagram provides "hypotheses"
→ Stratification provides "validation"

6.3 Stratification + Histogram

Combination Use:
  After stratifying by different dimensions, draw histograms for each stratum
  Compare the histograms of each stratum:
  ├── Whether the central position (mean) is different
  ├── Whether the dispersion (standard deviation) is different
  └── Whether the distribution shape is different

6.4 Stratification + Control Chart

Combination Use:
  Step 1: Draw an overall control chart → determine if the process is in control
  Step 2: If there are abnormal points → stratify by dimension
  Step 3: Redraw control charts for each stratum
  Step 4: Identify which stratum's process has changed

Chapter 7: Evaluation Criteria for Stratification

Summary: The "Way" and "Technique" of Stratification

Technique (How to Stratify):
  ── Define the purpose before stratifying
  ── Select dimensions according to 4M1E
  ── Stratify from coarse to fine
  ── Cross-analyze to validate

Way (Why to Stratify):
  ── It's not just about breaking down data
  ── It's about "not being deceived by aggregated data"
  ── It's about "precisely identifying the true source of the problem"

The greatest value of stratification is not in "breaking down data," but in "revealing what you otherwise couldn't see."

A quality engineer who does not use stratification is like someone searching for something in the dark with sunglasses on — you see a rough outline, but never the true details.

Stratification is the light that guides you.

Document Version: v1.0 Generated Date: 2026-05-03 Author: Excellence Quality Think Tank

Issue 2: Stratification (Stratification / Layering)