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Continuous Improvement Toolkit

Scatter Diagram

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The Continuous Improvement Map

Multivariate

Brainstorming

IDEF0

Document control

Check Sheets**

Flowcharting

Flow Process Charts**

KPIs

SCAMPER***

Pugh Matrix

Lateral Thinking

Reliability

Service Blueprints

Affinity Diagrams

Mind Mapping*

Attribute Analysis

Morphological Analysis

How-How Diagram***

Control Charts

Waste Analysis**

Time Value Map**

Value Stream Mapping**

Value Analysis**

Suggestion Systems

Histograms

Activity NetworksRACI Matrix

Stakeholder Analysis

Improvement Roadmaps

DMAIC

SWOT Analysis

Policy Deployment

Project Charter

PDCA Gantt Charts

MOST

PERT/CPMDaily Planning

Delphi MethodPayoff Matrix

Relations Mapping

Data Mining

Just in Time

Automation

Product Family Matrix Flow

Spaghetti**

Multi-vari Studies

Decision Tree

FMEA

PDPC

RAID Log*

Fault Tree Analysis

Paired Comparison

Traffic Light Assessment

TPN AnalysisRisk Analysis*

Run Charts

Scatter Diagram

A3 Thinking

Importance Urgency Matrix

Four Field Matrix

Critical-to X Portfolio MatrixForce Field Analysis

Decision Balance Sheet

Break-even Analysis

Voting

Quality Function Deployment

Pick Chart

Gap Analysis*

Bottleneck Analysis

Cost Benefit Analysis

Kaizen Events Control Planning

Standard Work

Mistake Proofing

Quick Changeover Visual Management

Simulation

TPM

5S

Health & Safety

Best PracticesPareto Analysis

5 Whys

Prioritization Matrix

Hypothesis

SIPOC*

Matrix Diagram

Fishbone Diagrams

Tree Diagram*

Root Cause Analysis

Correlation

DOEANOVA

NonparametricChi-Square

Regression

Observations

KanoLean Measures

Benchmarking***

Interviews

Graphical Methods

Data collection planner*

Questionnaires

Probability Distributions

MSA

Descriptive Statistics

Cost of Quality*

Sampling

Focus Groups

Capability Indices

Process Yield

Project KPIs

Normal Distribution

DataCollection

UnderstandingPerformance**

ImplementingSolutions***

Planning & Project Management*ManagingRisk

UnderstandingCause & Effect

Designing & Analyzing ProcessesGroup Creativity

Selecting & Decision Making

Five Ws

Process Redesign

Pull

Process Mapping

OEE

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Scatter Diagram

Many situations require the investigating whether a relationship exists between two or more variables

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Scatter Diagram

A line manager may want to check the relationship between the number of training hours and employee productivity

Or if the number of defects is a function of the experience of the person causing it

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Scatter Diagram

Other Examples

The relationship between equipment downtime and its cost of maintenance

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Scatter Diagram

Other Examples

The relationship between driving speed and fuel consumption

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Scatter Diagram

Other Examples

The relationship between the number of people working on a shift and the average answer time in a call center

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Scatter Diagram

Other Examples

The relationship between the number of years of education someone has and the annual income of that person

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Scatter Diagram

A diagram that shows whether two variables are correlated or related to each other

It shows patterns in the relationship that cannot be seen by just looking at the data

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Scatter Diagram

It works with both continuous and count data

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Scatter Diagram

Primarily used to visually investigate the relationship between two variables

Often an output and an input variables

Y0 1 0 0 1 1 0 1 0 0 11 0 0 0 1 1 0 1 0 1 0X

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Scatter Diagram

This is useful to verify that a change in one variable can affect the other variable

It helps detecting the primary factors that are really causing a problem and hence eliminating non-critical factors from consideration

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Scatter Diagram

Often used as a first step when analyzing and communicating the correlation between pairs of variables

Before conducting advanced statistical techniques

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Scatter Diagram

Often used with statistical tools (such as regression) to support or reject hypotheses about the data

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Scatter Diagram

Where do scatter diagrams fit?

Graph the data Scatter diagram

Check the correlations Use Pearson Coefficient

1st regression Linear / Multiple regression

Evaluate regression R-squared and analyze residuals

Re-run regression (If necessary)

Simple: With different model (Cubic)Multiple: Remove unnecessary items

Use the resultsControl critical process inputs and select best operating levels

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Scatter Diagram

The input variable is normally placed on the horizontal axis while the output variable is placed on the vertical axis

Input or explanatory or independent variable

Output orresponse ordependent

variable

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Scatter Diagram

You may also compare two input or output variables to each other

In this case, it doesn’t matter which variable goes on the horizontal axis and which goes on the vertical axis

X1 X2& Y1 Y2&

X Y&

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Scatter Diagram

Scatter diagrams can indicate several types of correlationX

X X

X

X X

XX

XX

XNo correlation when the datapoints are scattered randomlywithout showing any particularpattern.

Note that the width of the scattered pattern reflects the strength of the relationship

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Scatter Diagram

A positive correlation occurswhen the values of one variableincrease as the values of theother also increase.

XX

X

X

X

X

X X

XX

X

Scatter diagrams can indicate several types of correlation

The fitted line slopes from bottom left to top right

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Scatter Diagram

Scatter diagrams can indicate several types of correlation

A negative correlation occurswhen the values of one variableincrease as the values of theother decrease.

XX X X

XX

XXX

X

X

X

The fitted line slopes from upper left to lower right

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Scatter Diagram

Scatter diagrams can indicate several types of correlation

Scatter diagrams can also indicate nonlinear relationships between variables.

XX X

XX X

XX

X

XX

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Scatter Diagram

Example – Forest Trees

Both are output variables

20.01 7.51 5.01 2.51 0.0

80

70

60

50

40

30

20

1 0

0

Diameter

Volume

Shows the relationship between the volume and the diameter of sample trees in a forest.

Data source: Minitab

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Scatter Diagram

Example – Presence of Diabetes at a Workplace

An analysis that was conducted for diagnosing the presence of diabetes at a workplace.

The population was generally young (75.8% were below thirty).

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Scatter Diagram

Example – Presence of Diabetes

This scatter diagram illustrates that there is no obvious relationship between age and glucose levels.

High glucose levels are found in all ages, and normal glucose levels are found in higher ages.

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Scatter Diagram

Example – The amount of sales per month generated at two locations

Location A

Loca

tio

n B

The plotted points form a negative slope.

The sales at location B is inversely related to the sales at location A.

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Scatter Diagram

Example – The amount of sales per month generated at two locations

Location A

Loca

tio

n B

Does this mean that location A caused the decrease in sales at location B, or vice versa?

Answer: Not necessarily,unless the two locations aredirect competitors.

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Scatter Diagram

How to Construct a Scatter Diagram

Collect the two paired sets of data

C r e a t e a s u m m a r y t a b l e o f t h e d a t a

Variable 1 Variable 2

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Scatter Diagram

How to Construct a Scatter Diagram

Draw and label the horizontal and vertical axes withvariable names and scale values

Xxxx

Xxxx

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Scatter Diagram

How to Construct a Scatter Diagram

Plot the data pairs on the diagram by placing a dot at the intersection of each data pair

L o o k a t h o w t h e p a t t e r n a p p e a rs a n d h o w t h e t w o va r i a b l e s va r y t o g e t h e r

Y

X

XX

XXX

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Scatter Diagram

Matrix Plots

Summarizes the relationship between pairs of multiple variables in one graph

Allows to visually assess the variables that might be related

3 variables

X1 X2& Y&

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Scatter Diagram

Matrix Plots

Produces a scatter diagram for every combination of variables

Potential correlations between pairs of variables can then be identified

X

X X

X

XX

X

X

X

X

X

X

XX X

X

XX X

XX

X

X

X

XX

X X

XX

X

XX

X

X XX

X X X

X

X

X

X

X

X

X

X XXX

X

X XX

X X

X

X X

X

XXX

X

X

X

X

X

X

X

X

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Scatter Diagram

Matrix Plots – Example

1 00

80

60

201 00

963

9

6

3

1 008060

20

1 0

0

Salary

Publication

Years

There may be a relationship between the years of experience and salaries

# of publications doesn't appear to be correlated with the years of experience

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Scatter Diagram

Matrix Plots – Example

1 00

80

60

201 00

963

9

6

3

1 008060

20

1 0

0

Salary

Publication

Years

Is there a correlation between the number of publication and salaries?

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Scatter Diagram

Further Information – One of the 7 Basic Tools of Quality

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Scatter Diagram

Further Information

When the relationship is not so clear, Correlation can be used to help validate if a relationship exists between the variables

Regression techniques go a step further by defining the relationship in a mathematical format

# of Defects

Years of experience

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Scatter Diagram

Further Information

Be careful before concluding that there is a direct cause-and-effect relationship between the variables

There might be a third factor that is causing the change in the two variables

Y = f ( x )

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Scatter Diagram

Further Information

You can also illustrate a stratification factor in scatter diagrams

For example, the relationship between a process outputand a process input for two different settings