A matrix diagram is a visual representation that shows the connection between various groups of data. It is a planning tool that essentially displays the existence and strength of relationships between pairs of items from two or more data sets. It aims to help in problem-solving, decision making, and process improvement efforts.
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A Matrix Diagram
A visual representation that shows the connection between various groups
of data.
They are essential tools in . . .
Matrix Diagram 2
Decision Making
Problem-solving
Planning
Process Improvement
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A Matrix Diagram
It is a planning tool that essentially displays the existence and strength of
relationships between pairs of items from two or more data sets.
Matrix Diagram 3
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Problem-Solving
One of its main applications is in problem-solving scenarios where the
relationship between a problem and potential solutions or causes needs to
be explored.
Matrix Diagram 4
Problem
Causes
Problem Solutions
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Used by Other Tools
Several advanced problem-solving tools make use of the matrix diagram concept.
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Cause and Effect Matrix Quality Function Deployment
Whats
Hows
Inputs
Outputs
The application extends to situations ranging from requirement-specification matching to
alternative solution significance comparison and improvement opportunity identification.
Matrix Diagram
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Examples of Applications
Matrix Diagram 6
A marketing team
may use a matrix
diagram to identify
and select the
most effective
sales tools from
various options.
Alternatives
significance
comparison
A quality team may
use a matrix
diagram to
determine the
most suitable
inspection
methods.
Alternatives
significance
comparison
A manufacturing
team may apply a
matrix diagram to
identify causes
that affect
materials
consumption.
Cause and
effect
analysis
An HR team may
use a matrix
diagram to select
social activities that
enhance employee
loyalty.
Alternatives
significance
comparison
A restaurant team
may use a matrix
diagram to
enhance customer
experience and
satisfaction.
Improvement
opportunity
identification
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Benefits
Matrix Diagram 7
Provides visual representation
which helps the team to
understand complex information.
Supports continuous improvement
by adapting to evolving
requirements.
Facilitates a structured approach
to planning, problem-solving, and
decision-making.
Helps in prioritizing items based
on their importance and impact.
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Data Sets
The data sets can be any collection of . . .
Matrix Diagram 8
Requirements and measures
Specifications and features
Characteristics and attributes
Problems, issues and causes
Factors and criteria
Methods, tools and techniques
Ideas and solutions
Functions and tasks
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Types of Matrix Diagrams
Matrix diagrams come in various shapes.
Each shape has a descriptive letter name which indicate its shape.
Matrix Diagram 9
An L-shaped matrix diagram allows the comparison of two data sets
T-shaped, X-shaped, and Y-shaped matrices allow the comparison of more than two lists
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L-Shaped Matrix Diagram
Matrix Diagram 10
A B C D
1 ⚫
2 ⚫ ⚫
3 ⚫ ⚫
4 ⚫
Represented as a two-dimensional table.
Particularly useful in comparing only two lists.
The most basic and commonly used.
The left-hand column lists items from the first set.
For example, a problem and its potential causes.
The top row contains items from the second set.
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Basic Structure
In any matrix diagram . . .
• The relationship between any two items is
indicated in the cell where they intersect.
• At each intersection point, the relationship is
either present or absent.
• When it is present, the strength of the
relationship can be indicated using numerical
values or symbols placed at the intersection
point.
Matrix Diagram 11
A B C D
1
2 ⚫
3
4
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Numerical Values vs. Symbols
Matrix Diagram 12
A B C D
1 1
2 1 3
3 5 1
4 3
A B C D
1
2
3
4
For numerical values, a scale from
1 to 5 can be used where 1
indicates a weak relationship and 5
indicates a strong relationship.
Each symbol corresponds to a
specific numerical value or level of
strength, such as weak, moderate,
and strong.
Symbols are preferred over numbers as they enhance clarity and simplify interpretation.
Strength of Relationships
Strong 9
Moderate 3
Weak 1
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Weighting and Weighted Scores
Weighting can be applied in the matrix to
assign relative importance to specific items
within the data sets.
Weighted scores will later be calculated to
identify, prioritize, and select the most
favorable options.
Matrix Diagram 13
A B C D
1 ⚫
2 ⚫ ⚫
3 ⚫ ⚫
4 ⚫
A B C D
1 ⚫
2 ⚫ ⚫
3 ⚫ ⚫
4 ⚫
Weights
Weighted
scores
Overall relationship strength score
Ranks
Additional information can be displayed on the matrix:
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Constructing an L-Shaped Matrix Diagram
Matrix Diagram 14
In your team, clearly explain the purpose for building the matrix diagram
• Select and collect the two sets of data to be compared.
• Agree on symbols and their values.
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Constructing an L-Shaped Matrix Diagram
Matrix Diagram 15
Draw a two-dimensional table on a flipchart or whiteboard
• Insert the first data set in the left-hand column and the second set in the top row.
• Assign weighted scores to show relative importance of items.
A B C D
1
2
3
4
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Constructing an L-Shaped Matrix Diagram
Matrix Diagram 16
Work through the matrix and discuss the relationships between every pair of items
• Place the appropriate numerical value or symbol in the intersecting cell.
• Calculate the final weighted scores for each item in either or both data sets.
A B C D
1 ⚫ ⚫ ⚫
2 ⚫
3 ⚫
4 ⚫ ⚫
## ## ## ##
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Constructing an L-Shaped Matrix Diagram
Matrix Diagram 17
Review the completed matrix with the team to make informed decisions
Explore opportunities to combine the best aspects of different options.
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Example – Making a Better Cup of Tea
This diagram represents a cause-and-effect analysis.
Cause
Taste Volume Temperature
Score
The boil kettle 6
Adding water 13
Adding tea 9
Adding sugar 3
Adding milk 11
Stirring 3
Score 25 7 13
Strong 9
Medium 3
Weak 1
Matrix Diagram 18
Effect
Water appears to be the most significant factor influencing taste, volume, and temperature.
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Example – Assigning Human Resources to Multiple Projects
Matrix Diagram 19
Score 12 22 15 10 3 5 Score
SPC 17
5S 4
SOP 42
Sampling 4
FMEA 0
Employee Harvey Sami Emir Zakaria Chadi Peter Score
Energy usage 1
Spoilage reduction 4
Safety management 3
Visual Management 3
Score 2 2 2 3 1 1
Skills
Projects
Strong 9
Medium 3
Weak 1
Involved
For example, it is
important for
those working on
the spoilage
reduction project
to have basic
knowledge of
statistical process
control (SPC).
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Example – Application of Improvement Tools
Matrix Diagram 21
Graphical
Analysis
SPC KPIs
Data
Collection
Methods
Cause
and
Effect
Process
Mapping
Kaizen 5S
HR 18 4
Finance 9 7
Purchasing 8 8
IT 14 6
Quality 32 3
Marketing 16 5
Maintenance 34 2
Production 38 1
Store 8 8
29 18 23 32 21 21 17 18
2 6 3 1 4 4 8 6
What do columns with
low scores indicate?
What do columns with
high scores indicate?
What do rows with low
scores indicate?
What do rows with high
scores indicate?
This example illustrates
the workshops attended
or conducted by each
department in an
organization during a
change management
process.
Workshops in their
initial stages.
Workshops in their
final stages.
Departments with
minimal progress.
Departments with
significant progress.
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Correlation Matrix
It is also possible to compare the same items
together by using a triangular half-matrix
called the correlation matrix.
For example, this adjacency matrix is created
in a facility to analyze and reorganize rooms
and areas in a way that supports workflow
efficiency and enhances teams' collaboration.
1st aid
Utility area
Shop
Shop
Walk Way
Meeting
Offices
Stairs
Switch
Gr
Workshop QC
Prayer Tool
room
Store&W/H Canteen
Elecrical
Adjacent
Nearby
Far away
Adjacency
Matrix
Workshop
QC room
Electrical shop
Canteen
First aid room
Offices & meeting rooms
Store and W/H
Tool room
Utility area
Space
planning
matrix
Matrix Diagram 22
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Further Information
One of the challenges when using a matrix diagram is in the number of
comparisons that you need to apply.
For example, a ten-by-ten matrix requires 100 comparisons.
Matrix Diagram 23
L-Matrix
Item A Item B Item C
Item 1 1st 2nd 3rd
Item 2 4th 5th 6th
Item 3 7th 8th 9th
Item 1
Item 2
Item 3
Item A
Item B
Item C
3 X 3
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Further Information – Tree Diagrams
Tree diagrams can be used to collect and organize the sets of data for
comparison in the matrix, particularly when the categorization of items is
required.
Matrix Diagram 24
Variable
costs
Fixed
costs
Admin
costs
Breakdowns
Changeovers
Idling and minor stoppages
Reduced speed
Scrap and rework
Start-up losses
Downtime
losses
Speed
losses
Quality
losses
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Further Information – Matrix Diagram Templates
There are many
templates available to
help in creating matrix
diagrams.
Examples are also
provided to illustrate
the practical use of
these formats and
shapes.
Matrix Diagram 25