4-8 variables data spc

7/27/2019 4-8 Variables Data SPC

1/60

2001 ConceptFlow 0

Statistical Process Control for Variables Data(SPC)


2/60

2001 ConceptFlow 1

Module Objectives

By the end of this module, the participant will be able to:Apply SPC rules

Interpret run and trend patterns in control charts

Create and interpret

Xbar-R Charts

I-MR charts

Target I-MR charts


3/60

2001 ConceptFlow 2

Why Learn About SPC for Variables?

SPC for variable data will: Keep process centered

Minimize variation

Reduce excursions

Validate improvements

Focus Six Sigma process activity


4/60

2001 ConceptFlow 3

What is SPC for Variables?

SPC for variable data is Industry standard control language

Reliable, easy method of determining

Common cause variation

Special cause variation

Graphical communication

Set of statistical tools for analyzing variables performance data


5/60

2001 ConceptFlow 4

Introduction to SPC


6/60

2001 ConceptFlow 5

SPM and SPC

Statistical Process Control before six sigma Stat ist ical Process Monitor in g

Usual focus of SPC tools

Looks at output

Corrective action after output is out of control

Statistical Process Control after Six Sigma

Same tools, additional focus

Focus on inputs

Corrective action on inputs prior to output out of control


7/60 2001 ConceptFlow 6

Sources of Variation

KPOVsKPIVs

ProcessControl

Process

Materials

Methods

OperatorsMeasurements

Machines

Policies

Procedures

People

Places

EnvironmentStatistical

Process

Control

Statistical

Process

Monitor



SPC Defined

Statistical Process Control Is application of statistical tools and methods to provide feedback

Sets limits of variation

Provides trigger for action



SPC Function

SPC Charts Used to monitor and control process under local responsibility

Require process owners to

take measurements

Plot and interpret data

Take action

Provide a history of the process



Components of a Control Chart

10

9

8

7

6

5

4

3

2

1

0

0 5 10 15 20

Upper Control

Limit

Lower Control

Limit

Mean

Nonrandom Variation Region

Observation number

Observationval

ue

Random Variation RegionObservation 10



Statistics of a Control Chart

10

9

8

7

6

5

4

3

2

1

0

0 5 10 15 20

Nonrandom Variation Region

Observation number

Observationvalue

Random Variation Region

LCL

- 3s

UCL

+ 3s

Mean

99.73%

area



Establishing Process Control Limits

Control limits areAre statistical limits set +/- 3 standard deviations from the mean

Set when process is in control

Fixed at baseline value

Adjusted for improvements

Never widened

Control limits are not related to specification limits

Control Limits arenotspecification limits


13/60

2001 ConceptFlow 12

Definition of Control

In c ontro lis A statistical term for process variation

Within three standard deviations of the mean

That is random without cause

That does not show run patterns

That does not show trend patterns

No assignable cause variation


14/60

2001 ConceptFlow 13

Western Electric Rules for ControlOverview

Any point outside control limits 7 consecutive points on same side of

centerline

7 consecutive points increasing or

decreasing

2 of 3 points in same zone A or

beyond

4 of 5 points in same zone B or

beyond

14 consecutive points alternating up

and down

14 consecutive points in either zoneC

2 s4 s6 s

A

C

CB

B

A

LCL

UCL

Established rules for

run and trend

analysis


15/60

2001 ConceptFlow 14

Nelson Tests for Special Causes

2 s4 s6 s

A

C

CB

B

A

LCL

UCL 1. Any point outside control limits

2. 9 consecutive points on same

side of centerline

3. 6 consecutive points increasing

or decreasing

4. 2 of 3 points in same zone A or

beyond

5. 4 of 5 points in same zone B or

beyond

6. 14 consecutive points

alternating up and down

7. 15 consecutive points in either

zone C

8. 8 points in a row outside zone

C, same side of centerline

Tests proposed by Lloyd

Nelson (1984) and used by

MINITAB for run and trend

analysis


16/60

2001 ConceptFlow 15

Which Tests are Better?

Western Electric

Any point outside control limits

7 consecutive points on same side of

centerline

7 consecutive points increasing ordecreasing

2 of 3 points in same zone A or beyond

4 of 5 points in same zone B or beyond


and down 14 consecutive points in either zone C

Nelson


9 consecutive points on same side of

centerline

6 consecutive points increasing ordecreasing




and down 15 consecutive points in either zone C

8 points in a row outside zone C, either

side of centerline


17/60

2001 ConceptFlow 16

False Alarm Rates are the Key

Nelson


9 consecutive points on same side of centerline

6 consecutive points increasing or decreasing



14 consecutive points alternating up and down

15 consecutive points in either zone C

8 points in a row outside zone C, either side ofcenterline

False Alarm Rate

.0027

Approx .003

Approx .003

.00305

.0043

Approx .004

Approx .003

Approx .003

The Nelson tests are designed so that the false alarm

rates for all tests are approximately the same. The

Western Electric rules do not have this property.


18/60


19/60

2001 ConceptFlow 18

Nelson Test 2

Rule 2: 9 consecutive points on same side of centerline

A

B

C

C

B

A


20/60

2001 ConceptFlow 19

Nelson Test 3

Rule 3: 6 consecutive points increasing or decreasing

A

B

C

C

B

A


21/60

2001 ConceptFlow 20

Nelson Test 4

Rule 4: 2 of 3 points in same zone A or beyond

A

B

C

C

B

A


22/60

2001 ConceptFlow 21

Nelson Test 5

Rule 5: 4 of 5 points in same zone B or beyond

A

B

C

C

B

A


23/60

2001 ConceptFlow 22

Nelson Test 6

Rule 6: 14 consecutive points alternating up and down

A

B

C

C

B

A


24/60

2001 ConceptFlow 23

Nelson Test 7

Rule 7: 15 consecutive points in either zone C

A

B

C

C

B

A


25/60

2001 ConceptFlow 24

Nelson Test 8

Rule 8: 8 points in a row outside zone C, either side

A

B

C

C

B

A


26/60

2001 ConceptFlow 25

Nelson Tests in MINITAB

Stat>Control Charts>Xbar-R


27/60

2001 ConceptFlow 26

Control Chart Roadmap

Variable

Xbar-R

Chart

I-MR

Chart

Xbar-schart

N


28/60

2001 ConceptFlow 27

Xbar-R: Average, Range Charts


29/60

2001 ConceptFlow 28

Xbar-R Chart Principles

Xbar-R Charts (and Xbar-s) are two separate charts of the samesubgroup data

Xbar chart is a plot of the subgroup means

R chart is a plot of the subgroup ranges (or if s, plot of subgroup

standard deviation)

Most sensitive charts for tracking and identifying assignable cause ofvariation

Based on control chart factors that assume a normal distribution within

subgroups

Establish three sigma process limits


30/60

2001 ConceptFlow 29

Xbar-R and Subgroup Data

X1 X2 X3 X4 X5

SG 1 43.8 43.7 47.2 46.3 44.4

SG 2 44.7 43.2 45.7 45.8 44.4

SG 3 45.3 43.8 44.3 46.2 46.6

SG 4 45.4 44.1 44.6 45.3 45.0

SG 5 43.8 45.6 44.6 44.8 45.0

SG 6 45.7 46.0 45.6 45.9 46.5

SG 7 46.5 45.6 45.7 46.9 45.6SG 8 46.1 45.8 45.5 45.9 45.1

SG 9 44.5 44.0 45.4 45.8 44.7

SG 10 47.8 43.6 44.5 46.0 44.5

SG 11 45.5 45.4 42.8 47.0 45.1

SG 12 46.8 43.5 43.4 46.0 45.0

SG 13 44.2 44.7 46.1 44.5 45.8

SG 14 44.6 44.7 45.2 43.0 45.5

SG 15 46.0 46.0 45.0 44.5 47.2

SG 16 46.3 43.7 44.8 46.0 45.4

SG 17 43.2 43.0 45.6 44.8 45.4

SG 18 45.2 45.1 46.9 45.0 44.8

SG 19 44.6 44.5 44.6 43.7 45.1

SG 20 45.6 44.2 46.0 43.5 45.9

You measure the revenue per FA

earned from 20 complexes over five

days.

Is the process in control?

Since the data is subgroup data an

Xbar-R chart will be used


31/60

2001 ConceptFlow 30

Constructing an Xbar-R Chart Graph

X1 X2 X3 X4 X5 Xbar Range

SG 1 43.8 43.7 47.2 46.3 44.4 45.1 3.5

SG 2 44.7 43.2 45.7 45.8 44.4 44.8 2.6

SG 3 45.3 43.8 44.3 46.2 46.6 45.2 2.8

SG 4 45.4 44.1 44.6 45.3 45.0 44.9 1.3

SG 5 43.8 45.6 44.6 44.8 45.0 44.8 1.8

SG 6 45.7 46.0 45.6 45.9 46.5 45.9 0.9

SG 7 46.5 45.6 45.7 46.9 45.6 46.1 1.3

SG 8 46.1 45.8 45.5 45.9 45.1 45.7 1.0SG 9 44.5 44.0 45.4 45.8 44.7 44.9 1.8

SG 10 47.8 43.6 44.5 46.0 44.5 45.3 4.2

SG 11 45.5 45.4 42.8 47.0 45.1 45.2 4.2

SG 12 46.8 43.5 43.4 46.0 45.0 44.9 3.4

SG 13 44.2 44.7 46.1 44.5 45.8 45.1 1.9

SG 14 44.6 44.7 45.2 43.0 45.5 44.6 2.5

SG 15 46.0 46.0 45.0 44.5 47.2 45.7 2.7

SG 16 46.3 43.7 44.8 46.0 45.4 45.2 2.6

SG 17 43.2 43.0 45.6 44.8 45.4 44.4 2.6

SG 18 45.2 45.1 46.9 45.0 44.8 45.4 2.1

SG 19 44.6 44.5 44.6 43.7 45.1 44.5 1.4

SG 20 45.6 44.2 46.0 43.5 45.9 45.0 2.5

45.13 2.36Average


32/60

2001 ConceptFlow 31

Defining the Xbar-R UCL and LCL

2

2

X

X

UCL X A R

LCL X A R

4

3

R

R

UCL D R

UCL D R

A2, D3 and D4 are Shewhart control constants


33/60

2001 ConceptFlow 32

n D4 D3 A2

2 3.27 0.00 1.88

3 2.57 0.00 1.02

4 2.28 0.00 0.73

5 2.11 0.00 0.58

6 2.00 0.00 0.48

7 1.92 0.08 0.428 1.86 0.14 0.37

9 1.82 0.18 0.34

Shewhart Control Chart Constants

n is the subgroup size

2

2

45.13 * 2.355 46.49

45.

0.5

13 * 2.355 4

8

0.5 78 3. 6

X

X

UCL X A R

LCL X A R

4

3

* 2.355 4.97

*2.355

.

0

2 11

0

R

R

UCL D R

UCL D R

Calculated valuesagree with Minitab

Calculating the Xbar-R UCL and LCL


34/60

2001 ConceptFlow 33

Xbar-R Charts in MinitabStep 1

Copy or enter the data by subgroups into the worksheet Open file SPC VARIABLE XBAR.MTW
http://localhost/var/windows/TEMP/SPC%20VARIABLE%20XBAR.MTWhttp://localhost/var/windows/TEMP/SPC%20VARIABLE%20XBAR.MTW


35/60

2001 ConceptFlow 34


Stack the data


36/60

2001 ConceptFlow 35


Stat>Control Charts>Xbar-R


37/60

2001 ConceptFlow 36

Xbar-R Charts in Minitab

Step 4


38/60

2001 ConceptFlow 37

Xbar-R Charts in Minitab

Step 5


39/60

2001 ConceptFlow 38

Xbar-R Class Exercise

Using Xbar Charts Data tab of file SPC Variable Class Exercises.xls

1. Find Xbars, Xdbar and Rbar

2. Determine applicable Shewhart constants

3. Calculate UCL and LCL for Xbar and R

4. Copy the data into Minitab

5. Stack the data

6. Verify your calculations

7. Determine if process is in control
http://localhost/var/windows/TEMP/SPC%20Variable%20Class%20Exercises.xlshttp://localhost/var/windows/TEMP/SPC%20Variable%20Class%20Exercises.xls


40/60


41/60

2001 ConceptFlow 40

I-MR Chart Principles

I-MR Charts are two separate charts of the same data

I chart is a plot of the individual data

MR chart is a plot of the moving range of the previous individuals

I-MR charts are sensitive to trends, cycles and patterns

Used when subgroup variation is zero or no subgroups exist

Destructive testing

Batch processing


42/60

2001 ConceptFlow 41

I-MR and Individual Data

Revenue2.38

2.06

2.46

1.96

2.22

2.44

2.16

2.13

1.97

2.29

2.07

1.97

2.09

2.16

2.57

2.83

2.04

2.13

2.55

2.39

Once a day the office measures

the revenue generated by its FAs.

Is the process in control?

Since the data is individual data an I-MR

chart will be used.


43/60

2001 ConceptFlow 42

Constructing an I-MR ChartGraph

Revenue MR (2)1 2.38

2 2.06 0.32

3 2.46 0.40

4 1.96 0.50

5 2.22 0.26

6 2.44 0.22

7 2.16 0.28

8 2.13 0.03

9 1.97 0.16

10 2.29 0.32

11 2.07 0.22

12 1.97 0.10

13 2.09 0.12

14 2.16 0.07

15 2.57 0.41

16 2.83 0.26

17 2.04 0.7918 2.13 0.09

19 2.55 0.42

20 2.39 0.16

Ave 2.244 0.270

Note: calculated for a

moving range of 2

Revenues


44/60

2001 ConceptFlow 43

E2, D3 and D4 are Shewhart control constants

Defining the I-MR UCL and LCL

2

2

X

X

UCL X E R

LCL X E R

4

3

MR

MR

UCL D R

UCL D R

Revenues


45/60

2001 ConceptFlow 44

n D4 D3 A2 E2

2 3.27 0.00 1.88 2.66

3 2.57 0.00 1.02 1.77

4 2.28 0.00 0.73 1.46

5 2.11 0.00 0.58 1.29

6 2.00 0.00 0.48 1.18

7 1.92 0.08 0.42 1.11

8 1.86 0.14 0.37 1.05

9 1.82 0.18 0.34 1.01

n is the data or moving range subgroup size

Shewhart Control Chart Constants

4

3

*0.270 0.88

*0.270

3

0

.27

0

MR

MR

UCL D R

UCL D R

2

2

2.244 * 0.270 2.96

2.244 * 0.270 1.52

2.66

2.66

X

X

UCL X E R

LCL X E R

Calculated valuesagree with Minitab

Calculating the I-MR UCL and LCL

Revenues


46/60

2001 ConceptFlow 45

I-MR Charts in MinitabStep 1

Copy or enter the data by subgroups into the worksheet

Open file SPC VARIABLE IM.MTW

Revenues
http://localhost/var/windows/TEMP/SPC%20VARIABLE%20IMR.MTWhttp://localhost/var/windows/TEMP/SPC%20VARIABLE%20IMR.MTW


47/60

2001 ConceptFlow 46

I-MR Charts in Minitab

Step 2

Stat>Control Charts>I-MR

Revenues


48/60

2001 ConceptFlow 47

I-MR Charts in Minitab

Step 3

Revenues


49/60

2001 ConceptFlow 48

I-MR Charting an Improvement in Process

A process improvement has been made to increaserevenues. Is it real?

Stack the data

Revenues


50/60

2001 ConceptFlow 49

I-MR Shows Two Populations

Recalculating limits based upon improved

statistics show clearly that old process is

significantly different.


51/60

2001 ConceptFlow 50

I-MR Class Exercise

Using IMR Charts Data tab of file SPC Variable Class Exercises.xls,

1. Find Xbar, Xdbar and Rbar

2. Determine applicable Shewhart constants

3. Calculate UCL and LCL for Xbar and R

4. Copy the data into MINITAB

5. Stack the data

6. Verify your calculations

7. Determine if process is in control
http://localhost/var/windows/TEMP/SPC%20Variable%20Class%20Exercises.xlshttp://localhost/var/windows/TEMP/SPC%20Variable%20Class%20Exercises.xls


52/60

2001 ConceptFlow 51

Target I-MR Charts

T t I MR Ch t P i i l


53/60

2001 ConceptFlow 52

Target I-MR Chart Principles

Target I-MR Charts are two separate charts of the same data

Individuals plotted as difference from target

MR chart is a plot of the moving range of the previous individuals

I-MR charts are sensitive to trends, cycles and patterns

Useful when trying to predict widely varying parent individuals

Inventory levels

Forecasting

T t I MR d A t l D t


54/60

2001 ConceptFlow 53

Target I-MR and Actual Data

The marketing department uses a

demand forecasting process for

weekly revenue forecasting.

Is their demand forecasting process

in control?

Since the data is individual data

an I-MR chart is used.

Actual132

96

127

177

126

120

133185

152

148

189

148

163

139131

111

143

166

134

135

I MR Ch t f A t l d t


55/60

2001 ConceptFlow 54

I-MR Chart of Actual data

Looks like the forecasting is in

control, but dig a little deeper

N d f T t I MR Ch ti


56/60

2001 ConceptFlow 55

Need for Target I-MR Charting

Actual Target Delta132 138 6

96 99 3

127 127 0

177 175 -2

126 128 2

120 123 3

133 135 2185 166 -19

152 154 2

148 154 6

189 186 -3

148 153 5

163 161 -2

139 143 4131 136 5

111 133 22

143 143 0

166 171 5

134 138 4

135 135 0

Demand forecasting does not

produce actual clients do.

Demand forecasting produces a

demand target. The differencebetween the forecast and the

actual is the true measure of the

process.

I-MR chart the difference

T t I MR Ch t


57/60

2001 ConceptFlow 56

Target I-MR Chart

Demand forecasting process is not in control.

Possible area for Six Sigma project work!


58/60

Obj ti R i


59/60

2001 ConceptFlow 58

Objectives Review

The participant will be able to:

Apply SPC rules

Interpret run and trend patterns in control charts

Create and interpret

Xbar-R Charts

I-MR charts

Target I-MR charts

Trademarks and Service Marks


60/60

Trademarks and Service Marks

Six Sigma is a federally registered trademark of Motorola, Inc.

Breakthrough Strategy is a federally registered trademark of Six Sigma Academy.

ESSENTEQ is a trademark of Six Sigma Academy.

METREQ is a trademark of Six Sigma Academy.

Weaving excellence into the fabric of business is a trademark of Six Sigma Academy.

FASTART is a trademark of Six Sigma Academy.

Breakthrough Design is a trademark of Six Sigma Academy.

Breakthrough Lean is a trademark of Six Sigma Academy.

Design with the Power of Six Sigma is a trademark of Six Sigma Academy.

Legal Lean is a trademark of Six Sigma Academy.

SSA Navigator is a trademark of Six Sigma Academy.

SigmaCALC is a trademark of Six Sigma Academy.

SigmaFlowis a trademark of Compass Partners, Inc.

SigmaTRAC is a trademark of DuPont.

MINITAB is a trademark of Minitab, Inc.

4-8 variables data spc

Documents