4-9 Attribute Data SPC

7/27/2019 4-9 Attribute Data SPC

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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

np-charts

p-charts

c-charts

u-charts


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2001 ConceptFlow 2

Why Learn About SPC for Attribute?

SPC for variable data will Keep process centered

Minimize variation

Reduce excursions

Validate improvements

Focus Six Sigma process activity


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2001 ConceptFlow 3

What is SPC for Attributes?

SPC for attribute 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


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2001 ConceptFlow 4

Attribute Control Charts


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2001 ConceptFlow 5

Control Chart Roadmap

Attribute

u-chartp-chart

Defects ordefective?

Defects

Constant area of

opportunityn = const

Defectives

np-chart c-chart

YesNo YesNo


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np-chart Principles

np-charts Measure the proportion non-conforming

uses binomial distribution

good/bad, accept/reject, yes/no

Each proportion is a subgroup of samples

large subgroups required (50 minimum)

Subgroup size must be constant

Control limits will be constant

20 or more subgroups suggested for analysis



np-charts and Uniform Subgroup Size

The sourcing department

measures 125 purchase orders

daily and records the number of

entry errors.

Is the order entry process in

control?

Since the data has a constantsubgroup size (orders processed) of

defectives (error/no error) an np-chart

will be used

Day Orders Errors

1 125 14

2 125 5

3 125 7

4 125 17

5 125 4

6 125 3

7 125 148 125 5

9 125 10

10 125 6

11 125 5

12 125 26

13 125 6

14 125 14

15 125 6

16 125 7

17 125 8

18 125 11

19 125 13

20 125 10



Constructing an np-chart Graph

Day Orders Errors Prop np1 125 14 0.112 14

2 125 5 0.040 5

3 125 7 0.056 7

4 125 17 0.136 17

5 125 4 0.032 4

6 125 3 0.024 3

7 125 14 0.112 14

8 125 5 0.040 5

9 125 10 0.080 10

10 125 6 0.048 6

11 125 5 0.040 5

12 125 26 0.208 26

13 125 6 0.048 6

14 125 14 0.112 14

15 125 6 0.048 616 125 7 0.056 7

17 125 8 0.064 8

18 125 11 0.088 11

19 125 13 0.104 13

20 125 10 0.080 10

Total 191

pbar 0.076

npbar 9.55

Out of

control point



Defining the np-chart UCL and LCL

Control limits are constant; subgroup size mustalso be constant

1 1

3 (1 )

3 (1 )

n p

n p

k k

i i

i i

UCL n p n p p

LCL n p n p p

where n is subgroup size

X X

p n pnk k

where k is number of subgroups



Calculated valuesagree with MinitabTM

Calculating the np-chart UCL and LCL

Manual calculations may differ slightly

from Minitab due to rounding and

binomial estimates

1910.0764

125*20

125* 0.0764 9.550

p

n p

9.55 3 9.55(1 0.0764)

18.46

9.55 3 (1 0.0764)

0.640

n p

n p

UCL

LCL n p



np-charts in MinitabStep 1

Copy or enter the data by subgroupsinto the worksheet

Open file SPC Attribute np-chart.MPJ

Stat>Control Charts>np

Either 125 orColumn
http://d/SPC%20Attribute%20np-chart.MTWhttp://d/SPC%20Attribute%20np-chart.MTWhttp://d/SPC%20Attribute%20np-chart.MTWhttp://d/SPC%20Attribute%20np-chart.MTW


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2001 ConceptFlow 13

np-charts in MinitabStep 2


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2001 ConceptFlow 14

np-chart Class Exercise

Using np-chart Data tab of file SPC At tr ibu te Class Exercises.xls For Shipment Number subgroups

1. Calculate UCL and LCL

2. Copy the data into Minitab

3. Verify your calculations

4. Determine if process is in control

5. Run an I-MR chart on this data

What does I-MR show?

Why is it wrong?

6. Prepare for discussion


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2001 ConceptFlow 15

p-charts

Varying Subgroup Size


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2001 ConceptFlow 16

p-chart Principles

p-charts Measure the proportion non-conforming

Uses binomial distribution

Good/bad, accept/reject, yes/no

Each proportion is a subgroup of samples

Large subgroups required (50 minimum)

Subgroup size does not have to be constant

Control limits may vary from subgroup to subgroup based upon

subgroup size



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2001 ConceptFlow 17

p-charts and Varying Subgroup Size

The sourcing department

measures the number of entry

errors on a daily basis.

Is the order entry process in

control?

Since the data has varying subgroupsizes (orders processed) of defectives

(error/no error) a p-chart will be used

Day Orders Errors

1 123 14

2 102 5

3 87 7

4 119 17

5 88 4

6 72 3

7 100 148 94 5

9 111 10

10 103 6

11 92 5

12 155 26

13 47 6

14 116 14

15 97 6

16 102 7

17 117 8

18 101 11

19 89 13

20 103 10


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2001 ConceptFlow 18

Constructing a p-chart Graph

Day Orders Errors Prop

1 123 14 0.114

2 102 5 0.049

3 87 7 0.080

4 119 17 0.143

5 88 4 0.045

6 72 3 0.042

7 100 14 0.140

8 94 5 0.053

9 111 10 0.090

10 103 6 0.058

11 92 5 0.054

12 155 26 0.168

13 47 6 0.128

14 116 14 0.121

15 97 6 0.062

16 102 7 0.069

17 117 8 0.068

18 101 11 0.109

19 89 13 0.146

20 103 10 0.097

Total 2018 191 0.09465

Out of

control point


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2001 ConceptFlow 19

Defining the p-chart UCL and LCL

Control limits are dependent upon subgroup sizeand are individually calculated for each point

(1 )3

(1 )3

p

p

p pUCL p

p pL

n

pn

CL

(1 )3

(1 )3

i

i

p

p

p pUCL p

p pL

n

p nCL


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2001 ConceptFlow 20

Calculating the p-chart UCL and LCL

Average over subgroups

Calculated valuesagree with Minitab

0.09465(1 0.09465)0.09465 3

0.1821

0.09465(1 0.09465)0.0

2018/ 20

2018/9465 3

0.00720

2

p

p

UCL

LCL

13

13

0.9465(1 0.09465)0.9465 3

0.223

0.9465(1 0.09465)0.9465 3

0.0335

47

47

0.0

p

p

UCL

UCL

Individual subgroup

Manual calculations may differ slightlyfrom Minitab due to rounding and

binomial estimates


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2001 ConceptFlow 21

p-charts in MinitabStep 1


Open file SPC Attribute p-chart.MPJ

Stat>Control Charts>p
http://d/SPC%20Attribute%20p-chart.MTWhttp://d/SPC%20Attribute%20p-chart.MTWhttp://d/SPC%20Attribute%20p-chart.MTWhttp://d/SPC%20Attribute%20p-chart.MTW


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2001 ConceptFlow 22

p-charts in MinitabStep 2


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2001 ConceptFlow 23

p-chart Class Exercise

Using p-chart Data tab of file SPC Att r ibu te Class Exercises.xls For Daily Tests subgroups

1. Calculate UCL and LCL for overall Pbar

2. Calculate UCL and LCL for point 11




6. Copy the Is this the same? data in Minitab?




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2001 ConceptFlow 24

c-charts

Constant Area of Opportunity


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2001 ConceptFlow 25

c-chart Principles

c-charts Measure the count of non-conforming defects

uses Poisson distribution

good/bad, accept/reject, yes/no

Each count is a subgroup of samples

Area of opportunity must be constant

lot, unit, invoice

Control limits will be constant



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2001 ConceptFlow 26

c-chart Subgroups

A BB measures the number of non-

suppressed confirms on consults

accounts for 100 account lots from 20

complexes.

Is the process in control?

Cmplx Non-Surpr

1 31

2 39

3 38

4 5

5 22

6 34

7 108 23

9 11

10 36

11 25

12 4

13 4

14 11

15 2516 4

17 38

18 36

19 36

20 17

Average 22.45


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2001 ConceptFlow 27

Constructing a c-chart Graph

Cmplx Non-Surpr

1 31

2 39

3 38

4 5

5 22

6 34

7 108 23

9 11

10 36

11 25

12 4

13 4

14 11

15 2516 4

17 38

18 36

19 36

20 17

Average 22.45

One out of

control point

Non-Surpressed


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2001 ConceptFlow 28

Defining the c-chart UCL and LCL

3

3

c

c

UCL c c

LCL c c

Control limits are constant; subgroup size mustalso be constant, i.e. piece, lot, shipment etc.

Non-Surpressed


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2001 ConceptFlow 29


Calculating the c-chart UCL and LCL

22.45 3 22.45

36.66

22.45 3 22.45

8.236

c

c

UCL

LCL


from Minitab due to rounding andPoisson estimates

Non-Surpressed


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2001 ConceptFlow 30

c-charts in MinitabStep 1


Open file SPC Attribute Data c-chart.MPJ

Stat>Control Charts>c

Non-Surpressed

Cmplx NonSurpr

NonSurprCmplx
http://d/SPC%20Attribute%20c-chart.MTWhttp://d/SPC%20Attribute%20c-chart.MTWhttp://d/SPC%20Attribute%20c-chart.MTWhttp://d/SPC%20Attribute%20c-chart.MTWhttp://d/SPC%20Attribute%20c-chart.MTW


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2001 ConceptFlow 31

c-charts in Minitab

Step 2

Non-Surpressed


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2001 ConceptFlow 32

c-chart Class Exercise

Using c-chart Data tab of fileSPC At tr ibu te Class Exercises.xls

For CSR subgroups of complaints

1. Calculate UCL and LCL






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2001 ConceptFlow 33

u-charts

Varying Area of Opportunity


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2001 ConceptFlow 34

u-chart Principles

u-charts

Measure the count of non-conforming defects

Uses Poisson distribution

Good/bad, accept/reject, yes/no

Each count is a subgroup of samples

Area of opportunity may vary

Lot, unit, invoice

Control limits may vary



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2001 ConceptFlow 35

u-chart Subgroups

A group of FAs track their trades

through the system to determine how

many defects are found in the process

over the week. It is possible to have

more than 1 defect per trade.

Is the process in control?

FA Trades

Count of

Defects

1 159 17

2 138 6

3 120 9

4 148 21

5 127 5

6 98 4

7 136 178 134 6

9 139 12

10 127 7

11 125 6

12 161 23

13 75 7

14 161 17

15 139 7

16 143 9

17 163 10

18 192 32

19 119 16

20 134 12

Total 2738 243

Ubar 0.08875


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2001 ConceptFlow 36

FA Trades

Count of

Defects

Percent

age

1 159 17 0.107

2 138 6 0.043

3 120 9 0.075

4 148 21 0.142

5 127 5 0.039

6 98 4 0.041

7 136 17 0.125

8 134 6 0.045

9 139 12 0.086

10 127 7 0.055

11 125 6 0.048

12 161 23 0.143

13 75 7 0.093

14 161 17 0.106

15 139 7 0.050

16 143 9 0.063

17 163 10 0.061

18 192 32 0.167

19 119 16 0.134

20 134 12 0.090

Total 2738 243

Ubar 0.088751

Constructing a u-chart Graph

Out of

control point


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2001 ConceptFlow 37

Defining the u-chart UCL and LCL

Control limits are dependent upon subgroup areaand are individually calculated for each point

3

3

u

u

uUCL u

a

uLCL u

a

3

3

i

i

u

i

u

i

uUCL u

a

u

LCL u a


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2001 ConceptFlow 38

Calculating the u-chart UCL and LCL


from Minitab due to rounding andPoisson estimates


Individual subgroup

Average over subgroups0.08875

0.08875 3136.9

0.165

0.088750.08875 3

136.90.012

u

u

UCL

LCL

12

12

0.088750.08875 3

161

0.159

0.088750.08875 3

161

0.0183

u

u

UCL

LCL


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2001 ConceptFlow 39

u-charts in MinitabStep 1


Open file SPC Attribute Data u-chart.MPJ

Stat>Control Charts>c

FA Trades

Trades

TradesFA
http://d/SPC%20Attribute%20u-chart.MTWhttp://d/SPC%20Attribute%20u-chart.MTWhttp://d/SPC%20Attribute%20u-chart.MTWhttp://d/SPC%20Attribute%20u-chart.MTWhttp://d/SPC%20Attribute%20u-chart.MTW


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2001 ConceptFlow 40

u-charts in MinitabStep 2


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2001 ConceptFlow 41

u-chart Class Exercise

Using u-chart Data tab of file SPC Att r ibu te Class Exercises.xls

For errors from line items ordered

1. Calculate overall UCL and LCL

2. Calculate UCL and LCL for point 3






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2001 ConceptFlow 42

Departing Note on SPC and Control Charts

Clearly the last class exercise for u-charts showed the process is in

control. Bu t is con trol an acceptable level of performance?

Certainly not in this case.

SPC and control charting will point the Black Belt in the right direction

to solve the problem. The u-chart shows that focus should be applied

to the systemic common cause variation. The process random

variation is the culprit.


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2001 ConceptFlow 43

Module Key Learning Points


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2001 ConceptFlow 44

Objectives Review

The participant will be about to:

Apply SPC rules

Interpret run and trend patterns in control charts

Create and interpret

np-charts

p-charts

c-charts

u-charts


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4-9 Attribute Data SPC

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