Understanding VariationUnderstanding Variation

Six Sigma FoundationsContinuous Improvement TrainingSix Sigma FoundationsContinuous Improvement Training

Six Sigma Simplicity

Key Learning PointsKey Learning Points

s Variation in the data represents the voice of the process

s Know the two types of variation – common cause and special cause – and the implication of the different causes

s Use appropriate tools to study variation in discrete and continuous situations

s Know how to use and interpret run charts and control charts and to take appropriate action based on the charts

s Variation in the data represents the voice of the process

s Know the two types of variation – common cause and special cause – and the implication of the different causes

s Use appropriate tools to study variation in discrete and continuous situations

s Know how to use and interpret run charts and control charts and to take appropriate action based on the charts

VariationVariation

s All repetitive activities of a process have a certain amount of variation

s Input, process, and output measures will fluctuate

s This fluctuation is called variations Variation is the voice of the process

s All repetitive activities of a process have a certain amount of variation

s Input, process, and output measures will fluctuate

s This fluctuation is called variations Variation is the voice of the process

All processes have variation

From variation to information: 6M’sFrom variation to information: 6M’s

Materials

Machines

Methods

Measurements

Mother Nature

Manpower

P

R

O

C

E

S

S

Two types of variationTwo types of variation

Common cause No undue influence by one of the 6Ms

ExpectedNormalRandom

Special cause Undue influence by one of the 6Ms

UnexpectedNot normalNot random

Type Definition

Variation existsVariation existss All variation is causeds There are two major classifications of causes which

help you select appropriate management actions

s If all variation is due to “common cause,” the result will be a predictable or stable process

s If some variation is from “special causes,” the result is an unstable or unpredictable system

s To improve any process it is useful to understand its variation

s Variation is the “voice of the process” – learn to listen and understand it

s The sources of variation is eventually what we will focus on fixing in the improve stage of DMAIC

s All variation is causeds There are two major classifications of causes which

help you select appropriate management actions

s If all variation is due to “common cause,” the result will be a predictable or stable process

s If some variation is from “special causes,” the result is an unstable or unpredictable system

s To improve any process it is useful to understand its variation

s Variation is the “voice of the process” – learn to listen and understand it

s The sources of variation is eventually what we will focus on fixing in the improve stage of DMAIC

Tools for understanding variationTools for understanding variation

Type of data Variation for a period of time

Variation over time

Attribute(Count)

s Pareto Diagrams Bar chartss Pie charts

s Run chartss Control charts

s nP -charts P-charts C-charts U-charts Individual measurements

Variables(Continuous)

s Histogram/Frequency diagramss Box-plotss Multi-vari charts

s Run chartss Control charts

s Individual measurementss X-R chartss X-s charts

Control Charts Control Charts

“The use of control charts should start with management, not on the shop floor.”

-W. Edwards Deming

“The use of control charts should start with management, not on the shop floor.”

-W. Edwards Deming

“Management takes a major step forward when they stop asking you to explain random variation.”

-F. Timothy Fuller

“Management takes a major step forward when they stop asking you to explain random variation.”

-F. Timothy Fuller

Types of Control Charts Types of Control Charts

s For continuous (variables) data:s Xbar (average) & R (range) charts, An Xbar chart measures the central

tendency of Y over time. R charts measure the gain or loss of uniformity within sub-groups, which represents the variability in Y over time. R charts are based on the range of values within each sub-group.

s or Xbar & s (s- std deviation): is the same but track the variability based on the standard deviation within sub-group, not the range.

s For continuous (variables) data:s Xbar (average) & R (range) charts, An Xbar chart measures the central

tendency of Y over time. R charts measure the gain or loss of uniformity within sub-groups, which represents the variability in Y over time. R charts are based on the range of values within each sub-group.

s or Xbar & s (s- std deviation): is the same but track the variability based on the standard deviation within sub-group, not the range.

Types of Control Charts Types of Control Charts

s For attribute (count) data:s nP charts: A simple chart used to track the number

of non-conforming units (percentage of defective parts) assuming the sample size is constant.

s P charts: A simple chart used to track the number of non-conforming units (percentage of defective parts) assuming the sample size is NOT constant.

s C charts: A simple chart used to track the number of defects per units produced (not the % defective) assuming the sample size is constant.

s U charts: A simple chart used to track the number of defects per units produced (not the % defective) assuming the sample size is NOT constant.

s For attribute (count) data:s nP charts: A simple chart used to track the number

of non-conforming units (percentage of defective parts) assuming the sample size is constant.

s P charts: A simple chart used to track the number of non-conforming units (percentage of defective parts) assuming the sample size is NOT constant.

s C charts: A simple chart used to track the number of defects per units produced (not the % defective) assuming the sample size is constant.

s U charts: A simple chart used to track the number of defects per units produced (not the % defective) assuming the sample size is NOT constant.

Control ChartsControl Charts

Why use it?s To monitor, control and improve process performance over time by

studying variation in its source

What does it do?s Focuses attention on detecting and monitoring process variation

over times Distinguishes special from common cause of variation, as a guide

to local management actions Serves as a tool for ongoing control of a processs Helps improve a process to perform consistently and predictably

for higher quality, lower cost and higher effective capacitys Provides a common language for discussing process performance

Why use it?s To monitor, control and improve process performance over time by

studying variation in its source

What does it do?s Focuses attention on detecting and monitoring process variation

over times Distinguishes special from common cause of variation, as a guide

to local management actions Serves as a tool for ongoing control of a processs Helps improve a process to perform consistently and predictably

for higher quality, lower cost and higher effective capacitys Provides a common language for discussing process performance

Recognizing source of variation

VariationVariation

Variation types and StrategiesInterpreting Run or

control chart

Stable?

Special cause

strategy

Common cause

strategy

Unstable Stable

Variation: what to do nextVariation: what to do nextSpecial cause Common cause

Waste time Increase variation

Gain a betterunderstand

of the system

Reducevariation

Gain useful information

Reducevariation

Lose time in responding tothe problem

Waste time

Look for what was different between individual points

Take actionbased on thereporteddifference

Study all the data

Make basicchanges to the process

Typ

e o

f va

riat

ion

Spe

cial

cau

seC

omm

on c

ause

3020100

7

6

5

4

3

2

1

0

-1

Sample Number

Sam

ple

Mea

n

Xbar Chart for C3

1

1

11

1

1

11

X = 1.283

3.0SL = 2.945

-3.0SL =- 0.3793

Out of Control

In Control

Variation and Control ChartsVariation and Control Charts

SAMPLE NUMBER

Region of Non-Random Variation

Region of Non-Random Variation

Region of Random Variation

UpperControlLimit

ProcessAverage

LowerControlLimit

VariationVariationDetermining if your process is “out of control”

Zone A

Zone A

Zone B

Zone C

Zone C

Zone B

Upper control limit(UCL)

Average

Lower control limit(LCL)

VariationVariationTime plot

What is this graph telling you?

% on time shipment Roosendaal 2001

0%10%20%30%40%50%60%70%80%90%

100%

Month

pe

rce

nt

on

tim

e

VariationVariation

% on time shipment

70%

75%

80%

85%

90%

95%

100%

Month

pe

rce

nt

on

tim

eTime plot

What is this graph telling you?

VariationVariation

% on time shipment

70%

75%

80%

85%

90%

95%

100%

Month

per

cen

t on

tim

e

Median

Run Chart

VariationVariationRun Chart

4 14 24

0,75

0,85

0,95

Observation

On

time

rate

Number of runs about median:Expected number of runs:

Longest run about median:Approx P-Value for Clustering:

Approx P-Value for Mixtures:

Number of runs up or down:Expected number of runs:

Longest run up or down:Approx P-Value for Trends:

Approx P-Value for Oscillation:

8,000013,0000

5,0000 0,0184

0,9816

13,000015,6667

5,0000 0,0897

0,9103

Run Chart for On time rate

VariationVariationIndividual control chart

0 5 10 15 20 25

0,8

0,9

1,0

Observation Number

Indi

vidu

al V

alue

I Chart for On time

1

1

Mean=0,8745

UCL=0,9686

LCL=0,7803

VariationVariationl & MR chart

252015105Subgroup 0

1,0

0,9

0,8

Indi

vid

ual V

alu

e

11

Mean=0,8745

UCL=0,9686

LCL=0,7803

0,15

0,10

0,05

0,00

Movin

g R

ange

1

R=0,03540

UCL=0,1157

LCL=0

I and MR Chart for On time rate

VariationVariationP chart

2520151050

0,25

0,15

0,05

Sample Number

Prop

ortio

n

P Chart for Late

P=0,1253

UCL=0,1549

LCL=0,09570

VariationVariationStrategy for eliminating Special cause of variation

Timely data • Work to get special causes signaled quickly – use early warning indicators throughout your operation

Search for cause • Immediately search for cause when control chart gives a signal that a special cause has occurred

• Find out what was different on that occasion• Keep asking “why?, why?, why?” …

Take corrective action

• Immediate remedy to contain the damage• Do not make fundamental changes in that

process

Prevent and retain • Seek ways to prevent that special cause from recurring (mistake-proof), or, if results are good, retain the lesson

VariationVariationStrategy for improvement of a statistically stable system

All the data • All the data are relevant, not just high points or low points – not just the points we don’t like

More complex• Improving a stable process is more complex that

identifying a special cause – more time and more resources are generally needed

Management lead • Management should initiate and lead change effort to improve a system of common cause

High & low difference

• Common cause of variation can hardly ever be reduced by attempts to explain the difference between high and low points when a process is in statistical control

Process change • Processes in statistical control usually require fundamental changes in the system

Case Study 1

“Status Change” Requests

BackgroundBackgrounds A manager comes to you and states that they need your help

because their change request process is “totally out of control” and the number of change requests are going up. Department costs are skyrocketing because of all the manual processing that is needing to be done.

s This process handles employee’s who have a status change, for example, change in marital status, number of dependents change, etc.

s You decide to meet with the manager to obtain data and discuss with the manager the reasons why they feel there is a problem.

s Upon meeting in the office, the manager hands you the data and states that one look at the data and you can see the most recent point is a sign of major problems. Nothing about the process has changed, so the manager doesn’t know why things are getting worse. The data is on the next page….

Month # Status Changes Year

Jan 56 2000

Feb 82 2000

Mar 71 2000

Apr 74 2000

May 78 2000

Jun 63 2000

Jul 99 2000

Aug 95 2000

Sep 79 2000

Oct 127 2000

Nov 75 2000

Dec 54 2000

Month # Status Changes Year

Jan 50 2001

Feb 71 2001

Mar 32 2001

Apr 58 2001

May 43 2001

Jun 76 2001

Jul 54 2001

Aug 70 2001

Sep 45 2001

Oct 51 2001

Nov 53 2001

Dec 100 2001

How is the process?How is the process?s 2 Years worth of data are below…how are we doing? Can you tell from the

data below? Manager says much worse compared to the past. Are we?

s 2 Years worth of data are below…how are we doing? Can you tell from the data below? Manager says much worse compared to the past. Are we?

Let’s chart it out…Let’s chart it out…s What do you think our chart tells us?s What do you think our chart tells us?

# of Change Requests

0

20

40

60

80

100

120

140

20

00

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20

01

Year

# o

f R

eq

ue

sts

Num. of StatusChanges

Point of concern??

Some ConsiderationsSome Considerationss While graphically showing our data is better than

looking at raw data, the previous chart is still weak, and leaves conclusions more open to opinion

s Each person may interpret data and/or graphs based on their personal biases and experience.

s While graphically showing our data is better than looking at raw data, the previous chart is still weak, and leaves conclusions more open to opinion

s Each person may interpret data and/or graphs based on their personal biases and experience.

“No data have meaning apart from their context.” --- Dr. Donald Wheeler

How do we give “context” to data?

# of Change Requests

0

20

40

60

80

100

120

140

20

00

20

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20

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# o

f R

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sts

Num. of StatusChanges

Context Attempt #1

The Chart…The Chart…s How do you interpret the chart now?

Think this point is abnormal now?

How about this point?

How about this point?

What can we do?What can we do?s Statistical Process Control (SPC) is a way of bringing

out the “context” of the data.s Statistical Process Control charts have also been

called Process Behavior Charts.s Process Behavior Charts utilize all the data to

develop historical “context” to allow evaluation within context rather than single point comparison to another point.

s This “context” is more than comparing differences between one point and another, rather, it takes into consideration the variation of the data in the process under investigation.

s Statistical Process Control (SPC) is a way of bringing out the “context” of the data.

s Statistical Process Control charts have also been called Process Behavior Charts.

s Process Behavior Charts utilize all the data to develop historical “context” to allow evaluation within context rather than single point comparison to another point.

s This “context” is more than comparing differences between one point and another, rather, it takes into consideration the variation of the data in the process under investigation.

Let’s find out what we can see when statistics are applied:

Applying StatisticsApplying Statisticss There are two charts with limits on them. Also, we are viewing

data by years…However, have there been any process changes? No.

s There are two charts with limits on them. Also, we are viewing data by years…However, have there been any process changes? No.

0Subgroup 5 10 15 20 25

0

50

100

150

Indiv

idual

Val

ue

Mean=58.58

UCL=119.5

LCL=-2.345

2000 2001

01020304050607080

Mov

ing R

ange

R=22.91

UCL=74.85

LCL=0

2000 2001

I and MR Chart for # of Requests by Year1

2

Now what do you think?

0Subgroup 5 10 15 20 25

0

20

40

60

80

100

120

140

Indiv

idual

Val

ue 1

Mean=69

UCL=125.9

LCL=12.11

01020304050607080

Mov

ing R

ange

R=21.39

UCL=69.89

LCL=0

I and MR Chart for # of Requsts

Applying StatisticsApplying Statisticss If there have been no process changes, then this view of

the data may be appropriate:

s If there have been no process changes, then this view of the data may be appropriate:

Now what do you think?

Conclusion?Conclusion?

s October 2000 (point 10) indicated an unusually “high” number of requests (manager couldn’t remember why the number was so high). Otherwise, the process has “behaved” predictably…including the last data point.

s If the manager doesn’t like the current levels of requests, perhaps there are opportunities for reducing such manual intensive changes.

s These changes might involve a major change in the system.

s October 2000 (point 10) indicated an unusually “high” number of requests (manager couldn’t remember why the number was so high). Otherwise, the process has “behaved” predictably…including the last data point.

s If the manager doesn’t like the current levels of requests, perhaps there are opportunities for reducing such manual intensive changes.

s These changes might involve a major change in the system.

“Managing a company by means of the monthly report is like trying to drive a car by watching the yellow line in the rear-view mirror.”

Dr. Myron Tribus

Case Study 2

Percentage On-Time Delivery

BackgroundBackground

s In a plant monthly report, the line with the smallest percent differences is percentage of on-time shipments.

s In the data following, it would seem the level is at an expected level by management, and would get only a “cursory glance.”

s In July, 91.0% of the shipments were shipped on time. This is 0.3% below the historic average and 0.9% below the value last July.

s By traditional comparisons, the on-time shipments performance is slightly lower, but essentially unchanged from last year.

InformationInformation

s Monthly Report:s Monthly Report:

Monthly Report for July Dept July Act. Monthly Avg. % Diff. % Diff July Year to Date Plan % Diff.

Value Value Last Year Avg.

20 91.0 91.3 -0.3 -0.9 90.8 91.3 -0.5

Monthly Report for July Dept July Act. Monthly Avg. % Diff. % Diff July Year to Date Plan % Diff.

Value Value Last Year Avg.

20 91.0 91.3 -0.3 -0.9 90.8 91.3 -0.5OnTime

Ship.

DataData

s Percentage On-time shipments for Department 20:

92.1 199991.6 199991.8 199991.5 199991.1 199991.1 199990.1 199989.2 199989.9 199990.8 199991.2 199991.2 199991.2 200091.1 200090.4 2000

90.7 200090.7 200091.3 200091.8 2000

92 200091.5 200091.9 200091.6 200091.4 200091.7 200191.1 200190.9 200190.2 200189.7 200190.8 2001

91 2001

% Year % Year

% On-Time Chart

87.5

88

88.5

89

89.5

90

90.5

91

91.5

92

92.5

19

99

19

99

19

99

19

99

19

99

19

99

20

00

20

00

20

00

20

00

20

00

20

00

20

01

20

01

20

01

20

01

Year

% Series1

Let’s chart it out…Let’s chart it out…s What do you think our chart tells us? Any concerns?

% On-Time Chart

87.5

88

88.5

89

89.5

90

90.5

91

91.5

92

92.5

19

99

19

99

19

99

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% Series1

The Chart…The Chart…s How do you interpret the chart now?

We still need more “context”!

Applying StatisticsApplying Statisticss With the Process Behavior charts, we can see times of

unpredictability. It is at these points that we look for an explanation why.

302010Subgroup 0

92

91

90

89

Individ

ual

Val

ue

1

11

Mean=91.05

UCL=92.18

LCL=89.93

1.5

1.0

0.5

0.0

Mov

ing R

ange

R=0.4233

UCL=1.383

LCL=0

I and MR Chart for % On-Time

Conclusion?Conclusion?

s Three of the individual values fall outside the limits. Thus, there is too much variation in this time series to be due to chance alone.

s The three values should be treated as signals, and investigations into the causes the percentage of on-time shipments dropped during these months.

s Since the process is “unpredictable,” it may happen again, only worse.

Case Study 3

Regional Sales

BackgroundBackground

s A sales manager who recently learned about Process Behavior charts decided to utilize this tools to put their regional sales data into “context.”

s The manager has plotted the data for the last 12 month’s and keeps the chart posted on their wall. The manager hopes this will also improve the monthly values over time for the monthly and quarterly reports.

s While more sales are always wanted, the manager is pleased that the sales process is consistent.

s During one of their weekly meetings, you see the chart on the wall and notices something…

Raw DataRaw Datas The manager has the raw sales data posted next to the

chart:

North South West East98180 99850 100110 10146097150 99150 101530 10189098240 98280 100560 10135097320 98680 101200 10222097820 98160 101460 10208098330 98930 100990 10212098210 99190 100750 10241097750 98760 101390 10233097590 98710 100000 10161098020 98900 101640 101740

100830 99490 101890 100850100890 99420 100260 101780

0Subgroup 5 10

97000

98000

99000

100000

101000

102000

103000

Sam

ple M

ean

Mean=100031

UCL=102784

LCL=97277

0

5000

10000

Sam

ple

Ran

ge

R=3780

UCL=8623

LCL=0

Xbar/R Chart for Data

The Sales ChartThe Sales Charts What do you think our chart tells us? Any concerns?

Sales Data

0Subgroup 5 10

97000

98000

99000

100000

101000

102000

103000

Sam

ple M

ean

Mean=100031

UCL=102784

LCL=97277

0

5000

10000

Sam

ple

Ran

ge

R=3780

UCL=8623

LCL=0

Xbar/R Chart for Data

A Second LookA Second Looks What is being plotted:

Sales Data

Notice what was being plotted on the process behavior chart. The

average. There are actually 4 different regions…let’s look at

them individually.

The Sales ChartThe Sales Charts West Region

105Subgroup 0

104000

103000

102000

101000

100000

99000

98000

Indi

vid

ual V

alue

Mean=100982

UCL=103291

LCL=98673

3000

2000

1000

0

Mov

ing

Ran

ge

R=868.2

UCL=2837

LCL=0

I and MR Chart for West

The Sales ChartThe Sales Charts East Region

0Subgroup 5 10

101000

102000

103000

Indi

vid

ual V

alu

e

Mean=101820

UCL=103043

LCL=100597

0

500

1000

1500

Mov

ing

Ran

ge

R=460

UCL=1503

LCL=0

I and MR Chart for East

The Sales ChartThe Sales Charts South Region

0Subgroup 5 10

98000

99000

100000

Indi

vid

ual V

alu

e

Mean=98960

UCL=100133

LCL=97787

0

500

1000

1500

Mov

ing

Ran

ge

R=440.9

UCL=1441

LCL=0

I and MR Chart for South

0Subgroup 5 10

96000

97000

98000

99000

100000

101000

Indi

vid

ual V

alu

e

1 1

Mean=98361

UCL=100317

LCL=96405

0

1000

2000

3000

Mov

ing

Ran

ge

1

R=735.5

UCL=2403

LCL=0

I and MR Chart for North

The Sales ChartThe Sales Charts North Region

What is happening here??

Conclusion?Conclusion?

s The manager shouldn’t be so cozy in the consistency of the regional sales.

s Be careful not to “mix” your data. It could mask potential stability issues in your process.

s The manager needs to investigate and learn the causes of the excessive variation in the sales data of the north region.

s In this case, it may be a good thing…perhaps a new sales or marketing method being used

Understanding VariationUnderstanding Variation

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