In-Depth Interpretation of the Seven QC Tools · Stratification

Introduction

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

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

It is not complicated: it involves separating data according to different dimensions. However, its most critical aspect is: if you do not stratify, the conclusions you draw may be entirely wrong.

This is known as "Simpson's Paradox" — a trend observed in the overall data may be completely reversed in each stratum.

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: classify collected data according to different sources, characteristics, conditions, etc., and then analyze each stratum separately.

Mathematical Essence:
  Decompose the overall data into several non-overlapping subsets (strata),
  Analyze each subset separately,
  Then compare and validate 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:

Quality data of two work teams in a factory:

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

→ The nonconforming rates of both teams are 10%, which looks exactly the same.

But what if we stratify by product model?

Stratification by product model:

         Team A                Team B
  ┌───────────────────────────────────────
  Product X │ Inspected 90 Nonconforming 6(6.7%)   Inspected 20 Nonconforming 2(10.0%)
  Product Y │ Inspected 10 Nonconforming 4(40.0%)  Inspected 30 Nonconforming 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 completely different conclusions depending on whether it is stratified or not.

1.3 Three Major Functions of Stratification

Chapter 2: Common Stratification Dimensions

2.1 Classic Stratification Dimensions

4M1E Stratification Method (Man, Machine, Material, Method, Environment):
  ── Man (人): By operator, shift, skill level
  ── Machine (机): By equipment number, production line, tooling
  ── Material (料): By supplier, batch, material type
  ── Method (法): By process parameters, work methods, SOP version
  ── Environment (环): By temperature zone, season, cleanliness level

2.2 Time Dimension Stratification

Time Stratification:
  ── By shift: Day shift vs Night shift
  ── By time period: Hourly/Shiftly/Daily/Weekly/Monthly
  ── By season: Differences in different seasons
  ── By cycle: Beginning of the month vs End of the month

2.3 Product/Client Dimension Stratification

Product-related:
  ── By product model
  ── By production batch
  ── By product line

Client-related:
  ── By client 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 issues → Stratify by shift

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

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

  Principle 4: From Coarse to Fine
    → Start with broad dimensions and then delve into finer dimensions
    → For example: First stratify by production line → Then by equipment → Then by operator

Chapter 3: Stratification Operation Process (Standard 5-Step Method)

Step 1 — Clarify Analysis Purpose

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

Step 2 — Determine Stratification Dimensions

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

Step 3 — Collect and Organize Data

Data collection considerations:
  ── 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 validation)

Step 4 — Stratified Comparative Analysis

Analysis methods:
  ── Table 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 validation:
  ── Are the differences after stratification significant?
  ── Do the differences have practical significance?
  ── Can the conclusions be repeatedly validated?

Action plan:
  ── Develop improvement measures for the strata with differences
  ── Re-collect data after improvement to validate

Chapter 4: Practical Cases of Stratification

Case 1: Manufacturing — Stratification by Equipment

Background: The nonconforming rate in a machining workshop has been rising for three consecutive months
Summary data: Nonconforming rate 2.8%

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

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

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

Case 2: Manufacturing — Stratification by Supplier

Background: High incoming nonconforming rate at an electronics factory
Summary data: Incoming nonconforming rate 1.5%

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

Stratify by nonconforming type (Supplier A):
  Nonconforming Type      Batches
  Dimensional tolerance    3     ← Main issue
  Surface oxidation         2
  Packaging damage           1

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

Case 3: Service Industry — Stratification by Time Period

Background: Increase in customer complaints at a restaurant
Summary 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 high
  Afternoon Tea (14-17) 1500             30            2.0%
  Dinner (17-21)    2500                75            3.0%

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

Action:
  ── Check the raw materials and cooking process of the Signature Beef Noodles
  ── Discover that the beef supplier has 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
Summary data: Shrinkage nonconforming rate 4.2%

Stratify by shift:
  Shift    Inspection Number    Nonconforming Number    Nonconforming Rate
  Day shift  5000                120                    2.4%
  Night shift 5000                300                    6.0%  ← Significantly high

Stratify by operator (Night shift):
  Operator    Inspection Number    Nonconforming Number    Nonconforming Rate
  Zhang        1500                 25                     1.7%
  Li           2000                 180                    9.0%  ← Key issue
  Wang          1500                 95                     6.3%

Action:
  ── Observe Li's operation and discover that the mold is not preheated according to the SOP
  ── Retrain and certify, and the subsequent nonconforming rate dropped to 2.8%

Chapter 5: Common Misconceptions in Stratification

Misconception 1: Incorrect Selection of Stratification Dimensions

× Incorrect: Choose dimensions based on feelings, without evidence
  → For example: Nonconforming rate increase → "Stratify by color"

✓ Correct: Choose dimensions based on process knowledge and data analysis
  → For example: Nonconforming rate increase → "Stratify by equipment" (dimensional issues are usually related to equipment)

Misconception 2: Overly Fine 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 "Others"

Misconception 3: Drawing Conclusions After Only One Layer of Stratification

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

✓ Correct: Stratification analysis should go from coarse to fine
  → First layer: Stratify by production line → Discover major issues in Line A
  → Second layer: Stratify by equipment → Discover major issues in Machine 2 of Line A
  → Third layer: Stratify by operator → Discover that the night shift operator is the root cause

Misconception 4: Ignoring "Interaction Effects"

× Incorrect: Assume each stratification dimension is independent

✓ Correct: Consider the interaction effects between dimensions
  → For example: The nonconforming rate of Machine A is low during the day shift but high during the night shift
  → This indicates an interaction effect between "equipment × shift"
  → Cross-stratification analysis is required

Chapter 6: Combining Stratification with Other Tools

6.1 Stratification + Pareto Chart

Best partner:
  First, use stratification to identify the dimensions where the problem lies
  Then, use the Pareto chart to focus on the critical few in that dimension

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

6.2 Stratification + Fishbone Diagram

Combination use:
  Step 1: List all possible cause dimensions using a fishbone diagram
  Step 2: Validate the most important dimensions using stratification
  Step 3: Data validation to determine which dimension indeed has differences
  Step 4: In-depth analysis of the dimensions with 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 dimensions
  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):
  ── Clarify the purpose before stratifying
  ── Select dimensions according to 4M1E
  ── Stratify from coarse to fine, layer by layer
  ── Cross-analysis for validation

Way (Why to stratify):
  ── Not just breaking down data
  ── To "prevent summary data from deceiving you"
  ── To "precisely locate the true source of the problem"

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

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

And stratification is that light for you.

Knowledge code: 5.2.4 Document Version: v1.0 Generated Date: 2026-05-03 Author: Quality Think Tank

Issue 2: Stratification (Stratification / 分层法)