Teaching Statistics In Quality Science Using The R-Package ...Herrm… · ProjectCharter Process Capability Design Of Experiments 4 R esum e Opinions Regarding The Contents Opinions

Introduction To QualityThe qualityTools Package

Contents Of The R-CourseRésumé

Teaching Statistics In Quality Science UsingThe R-Package qualityTools

Thomas Roth, Joachim Herrmann

The Department of Quality Science - Technical University of Berlin

July 21, 2010

Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools



Outline1 Introduction To Quality

Quality And Quality ManagementProcess-Model For Continual ImprovementStatistics In Problem Solving

2 The qualityTools PackageScope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package

3 Contents Of The R-CourseContents And Teaching MethodologyImprovement ProjectA Students Example

ProjectCharterProcess CapabilityDesign Of Experiments

4 RésuméOpinions Regarding The ContentsOpinions Regarding RSummary





A (Very) Short Introduction To Quality Sciences

quality

degree to which a set of inherent characteristics fulfils requirements

management

coordinated activities to direct and control

quality management system

to direct and control an organization with regard to quality





Process-based Quality Management System For ContinualImprovement (EN ISO 9001:2008)

C

u

s

t

o

m

e

r

s

C

u

s

t

o

m

e

r

s

R

e

q

u

i

r

e

m

e

n

t

s

S

a

t

i

s

f

a

c

t

i

o

n

Management

responsibility

Resource

management

Input OutputProduct

Measurement,

analysis and

improvement

Continual improvement of

the quality management system

Product

realization

Value-adding activities

Information flow





The Role Of Statistics In The Field Of Quality

Process Capability

Pareto Chart

Desirabilities

Hypothesis Test

Quality Control Charts

CorrelationMulti Vari Chart Probability Plot

Problem 1: engineers dislike statisticsor engineers fail to see applications

Solution: exchange statistics with dataanalysis and problem solving

Problem 2: statistics comprise tomuch calculations

Solution: Use R with all its favorableaspects

Use R to keep the focus onmethods rather than calculation

Use R as a software that isavailable on all platforms

Use R to visualize important keyconcepts by simulation




Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package

Scope Of The qualityTools Package

Accessibility

give access to the most relevant subset of methods frequently used in industry

DMAIC Driven Toolbox

provide a complete toolbox for the statistical part of the Six Sigma Methodology

Ease of Use

support an intuitive approach to these methods i.e. consequent implementation ofgeneric methods (show, print, plot, summary, as.data.frame, nrow, . . .)

S4 OOP

Accessor and Replacement functions as well as Validity functions i.e. check thevalidity of instances of a class

Powerful Visualization

provide powerful visualization that are easy to accomplish





Visual Representation Of The qualityTools Package

N = 14k = 2p = 0.centerPointsCube: 3Axial: 3





































2 3 4 5 5 6 6 7 7number of factors k

1

2

3

5

9

17

num

ber o

f blo

cks

C = AB

2III(3−1)

D = ABC

2IV(4−1)

E = ACD = AB

2III(5−2)

F = BCE = ACD = AB

2III(6−3)

G = ABCF = BCE = ACD = AB

2III(7−4)

E = ABCD

2V(5−1)

F = BCDE = ABC

2IV(6−2)

G = ACDF = BCDE = ABC

2IV(7−3)

H = ABDG = ABCF = ACDE = BCD

2IV(8−4)

J = ABCDH = ABDG = ACDF = BCDE = ABC

2III(9−5)

K = ABJ = ABCDH = ABDG = ACDF = BCDE = ABC2III

(10−6)

L = ACK = ABJ = ABCDH = ABDG = ACDF = BCDE = ABC

2III(11−7)

F = ABCDE

2VI(6−1)

G = ABDEF = ABCD

2IV(7−2)

H = BCDEG = ABDF = ABC

2IV(8−3)

J = ABCEH = ABDEG = ACDEF = BCDE

2IV(9−4)

K = BCDEJ = ACDEH = ABDEG = ABCEF = ABCD

2IV(10−5)

L = ADEFK = AEFJ = ACDH = CDEG = BCDF = ABC2IV

(11−6)

G = ABCDEF

2VII(7−1)

H = ABEFG = ABCD

2V(8−2)

J = CDEFH = ACEFG = ABCD

2IV(9−3)

K = ABCEJ = ABDEH = ACDFG = BCDF

2IV(10−4)

L = ADEFK = BDEFJ = ABFH = ABCDG = CDE

2IV(11−5)

H = ABCDEFG

2VIII(8−1)

J = BCEFGH = ACDFG

2VI(9−2)

K = ACDFJ = BCDEH = ABCG

2V(10−3)

L = ABCDEFGK = ACDFJ = BCDEH = ABCG

2V(11−4)

num

ber o

f run

s N

number of variables k3 4 5 6 7 8 9 10 11

48

1632

6412

80.

81.

0

Half-Normal plot for effects of fdo

A:B:C

A:B

p > 0.1p < 0.05

Lenth Plot of effects

0.6

0.686ABCD

Standardized main effects and interactions

40

50

41.461

ABC

winglengthbodylengthcut


40

50

41.461

ABC


0.0 0.5 1.0

0.0

0.2

0.4

0.6

Effects

Theo

retic

al Q

uant

iles

B

A

B:C

A:C

C

A B C D

A:B

A:C

B:C

y

0.0

0.2

0.4

0.113ME

0.271SME

0.017 0.007 0.023

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

-20

-10

0

10

20

30

-16.503

4.656

-2.719 -1.438

0.653 0.077

-2.228

2.228

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

0

10

20

30

40

-16.503

4.656-2.719

-1.438 0.653 0.077 2.228

A: winglength B: bodylength C: cut

Main Effect Plot for fdo

A

-1

-1 1

A

-1 7.0

-1 1

Interaction plot for fdo

> -2> -1.5> -1

1.5

Filled Contour for yRespone Surface for y

> -2> -1.5> -1

-200 -100 0 100 200 300 400

0.00

00.

002

0.00

40.

006

0.00

8 LSL USLTARGET

Process Capability using normal distribution for x

x = 94.302 Nominal Value = 94.302

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.917

p = 0.017

mean = 94.302

sd = 83.197

-50 50 150 250

050

150

250

0 200 400 600

0.00

00.

002

0.00

40.

006

0.00

80.

010

LSL USLTARGET

Process Capability using weibull distribution for x

x = 94.302 Nominal Value = 302.677

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.249

p = 0.25

shape = 1.022

scale = 95.453

0 100 200 300

050

150

250

-500 0 500 1000 1500 2000 2500 3000

0.00

00.

002

0.00

40.

006

0.00

80.

010

0.01

20.

014

LSL USLTARGET

Process Capability using log-normal distribution for x

x = 94.302 Nominal Value = 1232.359

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.562

p = 0.131

meanlog = 3.968

sdlog = 1.281

0 200 400 600

050

150

250

fligh

ts

- + - + - +

5.5

6.0

6.5

1

A1

5.0

5.5

6.0

6.5

7

A

B-11

5.0

5.5

6.0

6.5

7.0

B

C

> -0.5> 0> +0.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

A

B

A-1

0

1B

-1

0

1

y

-1.5

-1.0

-0.5

0.0

> -0.5> 0> +0.5

0.8

1.0

Desirability function for y

scale = 0.5

composite (overall) desirability: 0.58

A B Ccoded 0 0 0 136 -0 816

Components of Variation

component

totalRR repeatability reproducibility PartToPart

0.0

0.4

0.8

VarCompContribStudyVarContrib

Measurement by Part

Part

Mea

sure

men

t

2 4 6 8 10

0.34

650.

3475

Measurement by Operator Interaction Operator:Part

s = 84.913n = 25

USL = 349.041LSL = -160.438

s = 84.913n = 25

USL = 605.205LSL = 0.149

s = 84.913n = 25

USL = 2463.585LSL = 1.134

6 8 10 12 14 16 18

0.0

0.2

0.4

0.6

y

Des

irabi

lity

scale = 2

coded 0.0 0.136 -0.816real 1.2 51.361 1.892

y1 y2 y3 y4Responses 130.660 1299.669 456.937 67.980Desirabilities 0.213 0.999 0.569 0.936

Multi Vari Plot for temp[, 1] and temp[, 2]

tem

p[, 3

]

temp[, 1]123

2022

24

1.8

2.0

2.2

2.4

Q-Q Plot for "log-normal" distribution

Qua

ntile

s fo

r x

1.8

2.0

2.2

2.4

Q-Q Plot for "exponential" distribution

Qua

ntile

s fo

r x

Probability Plot for "log-normal" distributionP

roba

bilit

y

0.410.5

0.59

0.68

0.77

0.86

0.95

Probability Plot for "weibull" distribution

Pro

babi

lity

0.23

0.32

0.41

0.50.590.68

0.77

0.86

0.95

Operator

Mea

sure

men

t

A B C

0.34

650.

3475 1

11

1 1

11 1

1

1

0.34

640.

3468

0.34

72

Part

mea

n of

Mea

sure

men

t

22

2

2 2

2

2

2

2

23 3 3

3 3

3 33

3

3

A B C D E F G H I J

123

OperatorABC

Gage R&RVarComp VarCompContrib Stdev StudyVar StudyVarContrib

totalRR 1.06e-07 0.8333 3.25e-04 0.001952 0.913repeatability 6.50e-09 0.0512 8.06e-05 0.000484 0.226reproducibility 9.93e-08 0.7822 3.15e-04 0.001891 0.884Operator 9.37e-08 0.7375 3.06e-04 0.001836 0.859O t P t 5 67 09 0 0446 7 53 05 0 000452 0 211

temp[, 2]

1618

1 2 3 1 2 3 1 2 31.4 1.6 1.8 2.0 2.2 2.4 2.6

1.4

1.6

Quantiles from "log-normal" distribution

1.6

1.8

2.0

2.2

2.4

Q-Q Plot for "normal" distribution

Qua

ntile

s fo

r x

0 1 2 3 4 5 6 7

1.4

1.6

Quantiles from "exponential" distribution

1.6

1.8

2.0

2.2

2.4

Q-Q Plot for "weibull" distribution

Qua

ntile

s fo

r x

C B E G A H D I F

Pareto Chart for defects

Freq

uenc

y

C B E G A H D I F

020

4060

80

00.

250.

50.

751

Cum

ulat

ive

Per

cent

age

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14

0.23

0.32

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14

Probability Plot for "exponential" distribution

Pro

babi

lity

0.320.41

0.50.59

0.68

0.77

0.86

0.95

-2 -1 0 1 2

0.0

0.4

0.8

Stacked dot plot

x

0.0

0.4

0.8

Non stacked dot plot

Operator:Part 5.67e-09 0.0446 7.53e-05 0.000452 0.211Part to Part 2.12e-08 0.1667 1.45e-04 0.000873 0.408totalVar 1.27e-07 1.0000 3.56e-04 0.002138 1.000

1.4 1.6 1.8 2.0 2.2 2.4

1.4

Quantiles from "normal" distribution

1.4 1.6 1.8 2.0 2.2 2.4

1.4

Quantiles from "weibull" distribution Cum. Percentage

Percentage

Cum. Frequency

Frequency 13

13

16

16

10

23

12

29

10

33

12

41

10

43

12

54

9

52

11

65

9

61

11

76

8

69

10

86

6

75

8

94

5

80

6

100 x

1.6 1.8 2.0 2.2 2.4

0.050.140.23 -2 -1 0 1 2

x












































1

2

3

5

9

17

num

ber o

f blo

cks

C = AB

2III(3−1)

D = ABC

2IV(4−1)

E = ACD = AB

2III(5−2)

F = BCE = ACD = AB

2III(6−3)


2III(7−4)

E = ABCD

2V(5−1)

F = BCDE = ABC

2IV(6−2)


2IV(7−3)


2IV(8−4)


2III(9−5)


(10−6)


2III(11−7)

F = ABCDE

2VI(6−1)

G = ABDEF = ABCD

2IV(7−2)


2IV(8−3)


2IV(9−4)


2IV(10−5)


(11−6)

G = ABCDEF

2VII(7−1)

H = ABEFG = ABCD

2V(8−2)


2IV(9−3)


2IV(10−4)


2IV(11−5)

H = ABCDEFG

2VIII(8−1)

J = BCEFGH = ACDFG

2VI(9−2)


2V(10−3)


2V(11−4)

num

ber o

f run

s N


48

1632

6412

80.

81.

0


A:B:C

A:B

p > 0.1p < 0.05


0.6

0.686ABCD


40

50

41.461

ABC



40

50

41.461

ABC


0.0 0.5 1.0

0.0

0.2

0.4

0.6

Effects

Theo

retic

al Q

uant

iles

B

A

B:C

A:C

C

A B C D

A:B

A:C

B:C

y

0.0

0.2

0.4

0.113ME

0.271SME

0.017 0.007 0.023

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

-20

-10

0

10

20

30

-16.503

4.656

-2.719 -1.438

0.653 0.077

-2.228

2.228

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

0

10

20

30

40

-16.503

4.656-2.719

-1.438 0.653 0.077 2.228



A

-1

-1 1

A

-1 7.0

-1 1


> -2> -1.5> -1

1.5


> -2> -1.5> -1

-200 -100 0 100 200 300 400

0.00

00.

002

0.00

40.

006

0.00

8 LSL USLTARGET


x = 94.302 Nominal Value = 94.302

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.917

p = 0.017

mean = 94.302

sd = 83.197

-50 50 150 250

050

150

250

0 200 400 600

0.00

00.

002

0.00

40.

006

0.00

80.

010

LSL USLTARGET


x = 94.302 Nominal Value = 302.677

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.249

p = 0.25

shape = 1.022

scale = 95.453

0 100 200 300

050

150

250

-500 0 500 1000 1500 2000 2500 3000

0.00

00.

002

0.00

40.

006

0.00

80.

010

0.01

20.

014

LSL USLTARGET


x = 94.302 Nominal Value = 1232.359

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.562

p = 0.131

meanlog = 3.968

sdlog = 1.281

0 200 400 600

050

150

250

fligh

ts

- + - + - +

5.5

6.0

6.5

1

A1

5.0

5.5

6.0

6.5

7

A

B-11

5.0

5.5

6.0

6.5

7.0

B

C

> -0.5> 0> +0.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

A

B

A-1

0

1B

-1

0

1

y

-1.5

-1.0

-0.5

0.0

> -0.5> 0> +0.5

0.8

1.0


scale = 0.5


A B Ccoded 0 0 0 136 -0 816


component


0.0

0.4

0.8


Measurement by Part

Part

Mea

sure

men

t

2 4 6 8 10

0.34

650.

3475


s = 84.913n = 25

USL = 349.041LSL = -160.438

s = 84.913n = 25

USL = 605.205LSL = 0.149

s = 84.913n = 25

USL = 2463.585LSL = 1.134

6 8 10 12 14 16 18

0.0

0.2

0.4

0.6

y

Des

irabi

lity

scale = 2

coded 0.0 0.136 -0.816real 1.2 51.361 1.892



tem

p[, 3

]

temp[, 1]123

2022

24

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

Probability Plot for "log-normal" distribution

Pro

babi

lity

0.410.5

0.59

0.68

0.77

0.86

0.95


Pro

babi

lity

0.23

0.32

0.41

0.50.590.68

0.77

0.86

0.95

Operator

Mea

sure

men

t

A B C

0.34

650.

3475 1

11

1 1

11 1

1

1

0.34

640.

3468

0.34

72

Part

mea

n of

Mea

sure

men

t

22

2

2 2

2

2

2

2

23 3 3

3 3

3 33

3

3

A B C D E F G H I J

123

OperatorABC



temp[, 2]

1618

1 2 3 1 2 3 1 2 31.4 1.6 1.8 2.0 2.2 2.4 2.6

1.4

1.6


1.6

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

0 1 2 3 4 5 6 7

1.4

1.6


1.6

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

C B E G A H D I F


Freq

uenc

y

C B E G A H D I F

020

4060

80

00.

250.

50.

751

Cum

ulat

ive

Per

cent

age

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14

0.23

0.32

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14


Pro

babi

lity

0.320.41

0.50.59

0.68

0.77

0.86

0.95

-2 -1 0 1 2

0.0

0.4

0.8

Stacked dot plot

x

0.0

0.4

0.8



1.4 1.6 1.8 2.0 2.2 2.4

1.4


1.4 1.6 1.8 2.0 2.2 2.4

1.4


Percentage

Cum. Frequency

Frequency 13

13

16

16

10

23

12

29

10

33

12

41

10

43

12

54

9

52

11

65

9

61

11

76

8

69

10

86

6

75

8

94

5

80

6

100 x

1.6 1.8 2.0 2.2 2.4

0.050.140.23 -2 -1 0 1 2

x












































1

2

3

5

9

17

num

ber o

f blo

cks

C = AB

2III(3−1)

D = ABC

2IV(4−1)

E = ACD = AB

2III(5−2)

F = BCE = ACD = AB

2III(6−3)


2III(7−4)

E = ABCD

2V(5−1)

F = BCDE = ABC

2IV(6−2)


2IV(7−3)


2IV(8−4)


2III(9−5)


(10−6)


2III(11−7)

F = ABCDE

2VI(6−1)

G = ABDEF = ABCD

2IV(7−2)


2IV(8−3)


2IV(9−4)


2IV(10−5)


(11−6)

G = ABCDEF

2VII(7−1)

H = ABEFG = ABCD

2V(8−2)


2IV(9−3)


2IV(10−4)


2IV(11−5)

H = ABCDEFG

2VIII(8−1)

J = BCEFGH = ACDFG

2VI(9−2)


2V(10−3)


2V(11−4)

num

ber o

f run

s N


48

1632

6412

80.

81.

0


A:B:C

A:B

p > 0.1p < 0.05


0.6

0.686ABCD


40

50

41.461

ABC



40

50

41.461

ABC


0.0 0.5 1.0

0.0

0.2

0.4

0.6

Effects

Theo

retic

al Q

uant

iles

B

A

B:C

A:C

C

A B C D

A:B

A:C

B:C

y

0.0

0.2

0.4

0.113ME

0.271SME

0.017 0.007 0.023

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

-20

-10

0

10

20

30

-16.503

4.656

-2.719 -1.438

0.653 0.077

-2.228

2.228

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

0

10

20

30

40

-16.503

4.656-2.719

-1.438 0.653 0.077 2.228



A

-1

-1 1

A

-1 7.0

-1 1


> -2> -1.5> -1

1.5


> -2> -1.5> -1

-200 -100 0 100 200 300 400

0.00

00.

002

0.00

40.

006

0.00

8 LSL USLTARGET


x = 94.302 Nominal Value = 94.302

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.917

p = 0.017

mean = 94.302

sd = 83.197

-50 50 150 250

050

150

250

0 200 400 600

0.00

00.

002

0.00

40.

006

0.00

80.

010

LSL USLTARGET


x = 94.302 Nominal Value = 302.677

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.249

p = 0.25

shape = 1.022

scale = 95.453

0 100 200 300

050

150

250

-500 0 500 1000 1500 2000 2500 3000

0.00

00.

002

0.00

40.

006

0.00

80.

010

0.01

20.

014

LSL USLTARGET


x = 94.302 Nominal Value = 1232.359

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.562

p = 0.131

meanlog = 3.968

sdlog = 1.281

0 200 400 600

050

150

250

fligh

ts

- + - + - +

5.5

6.0

6.5

1

A1

5.0

5.5

6.0

6.5

7

A

B-11

5.0

5.5

6.0

6.5

7.0

B

C

> -0.5> 0> +0.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

A

B

A-1

0

1B

-1

0

1

y

-1.5

-1.0

-0.5

0.0

> -0.5> 0> +0.5

0.8

1.0


scale = 0.5


A B Ccoded 0 0 0 136 -0 816


component


0.0

0.4

0.8


Measurement by Part

Part

Mea

sure

men

t

2 4 6 8 10

0.34

650.

3475


s = 84.913n = 25

USL = 349.041LSL = -160.438

s = 84.913n = 25

USL = 605.205LSL = 0.149

s = 84.913n = 25

USL = 2463.585LSL = 1.134

6 8 10 12 14 16 18

0.0

0.2

0.4

0.6

y

Des

irabi

lity

scale = 2

coded 0.0 0.136 -0.816real 1.2 51.361 1.892



tem

p[, 3

]

temp[, 1]123

2022

24

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x


Pro

babi

lity

0.410.5

0.59

0.68

0.77

0.86

0.95


Pro

babi

lity

0.23

0.32

0.41

0.50.590.68

0.77

0.86

0.95

Operator

Mea

sure

men

t

A B C

0.34

650.

3475 1

11

1 1

11 1

1

1

0.34

640.

3468

0.34

72

Part

mea

n of

Mea

sure

men

t

22

2

2 2

2

2

2

2

23 3 3

3 3

3 33

3

3

A B C D E F G H I J

123

OperatorABC



temp[, 2]

1618

1 2 3 1 2 3 1 2 31.4 1.6 1.8 2.0 2.2 2.4 2.6

1.4

1.6


1.6

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

0 1 2 3 4 5 6 7

1.4

1.6


1.6

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

C B E G A H D I F


Freq

uenc

y

C B E G A H D I F0

2040

6080

00.

250.

50.

751

Cum

ulat

ive

Per

cent

age

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14

0.23

0.32

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14


Pro

babi

lity

0.320.41

0.50.59

0.68

0.77

0.86

0.95

-2 -1 0 1 2

0.0

0.4

0.8

Stacked dot plot

x

0.0

0.4

0.8



1.4 1.6 1.8 2.0 2.2 2.4

1.4


1.4 1.6 1.8 2.0 2.2 2.4

1.4


Percentage

Cum. Frequency

Frequency 13

13

16

16

10

23

12

29

10

33

12

41

10

43

12

54

9

52

11

65

9

61

11

76

8

69

10

86

6

75

8

94

5

80

6

100 x

1.6 1.8 2.0 2.2 2.4

0.050.140.23 -2 -1 0 1 2

x












































1

2

3

5

9

17

num

ber o

f blo

cks

C = AB

2III(3−1)

D = ABC

2IV(4−1)

E = ACD = AB

2III(5−2)

F = BCE = ACD = AB

2III(6−3)


2III(7−4)

E = ABCD

2V(5−1)

F = BCDE = ABC

2IV(6−2)


2IV(7−3)


2IV(8−4)


2III(9−5)


(10−6)


2III(11−7)

F = ABCDE

2VI(6−1)

G = ABDEF = ABCD

2IV(7−2)


2IV(8−3)


2IV(9−4)


2IV(10−5)


(11−6)

G = ABCDEF

2VII(7−1)

H = ABEFG = ABCD

2V(8−2)


2IV(9−3)


2IV(10−4)


2IV(11−5)

H = ABCDEFG

2VIII(8−1)

J = BCEFGH = ACDFG

2VI(9−2)


2V(10−3)


2V(11−4)

num

ber o

f run

s N


48

1632

6412

80.

81.

0


A:B:C

A:B

p > 0.1p < 0.05


0.6

0.686ABCD


40

50

41.461

ABC



40

50

41.461

ABC


0.0 0.5 1.0

0.0

0.2

0.4

0.6

Effects

Theo

retic

al Q

uant

iles

B

A

B:C

A:C

C

A B C D

A:B

A:C

B:C

y

0.0

0.2

0.4

0.113ME

0.271SME

0.017 0.007 0.023

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

-20

-10

0

10

20

30

-16.503

4.656

-2.719 -1.438

0.653 0.077

-2.228

2.228

A B C

A:B

B:C

A:B

:C

A:C

fligh

ts

0

10

20

30

40

-16.503

4.656-2.719

-1.438 0.653 0.077 2.228



A

-1

-1 1

A

-1 7.0

-1 1


> -2> -1.5> -1

1.5


> -2> -1.5> -1

-200 -100 0 100 200 300 400

0.00

00.

002

0.00

40.

006

0.00

8 LSL USLTARGET


x = 94.302 Nominal Value = 94.302

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.917

p = 0.017

mean = 94.302

sd = 83.197

-50 50 150 250

050

150

250

0 200 400 600

0.00

00.

002

0.00

40.

006

0.00

80.

010

LSL USLTARGET


x = 94.302 Nominal Value = 302.677

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.249

p = 0.25

shape = 1.022

scale = 95.453

0 100 200 300

050

150

250

-500 0 500 1000 1500 2000 2500 3000

0.00

00.

002

0.00

40.

006

0.00

80.

010

0.01

20.

014

LSL USLTARGET


x = 94.302 Nominal Value = 1232.359

cp = 1

cpk = 1

cpkL = 1

cpkU = 1

A = 0.562

p = 0.131

meanlog = 3.968

sdlog = 1.281

0 200 400 600

050

150

250

fligh

ts

- + - + - +

5.5

6.0

6.5

1

A1

5.0

5.5

6.0

6.5

7

A

B-11

5.0

5.5

6.0

6.5

7.0

B

C

> -0.5> 0> +0.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1.5

-1.0

-0.5

0.0

0.5

1.0

A

B

A-1

0

1B

-1

0

1

y

-1.5

-1.0

-0.5

0.0

> -0.5> 0> +0.5

0.8

1.0


scale = 0.5


A B Ccoded 0 0 0 136 -0 816


component


0.0

0.4

0.8


Measurement by Part

Part

Mea

sure

men

t

2 4 6 8 10

0.34

650.

3475


s = 84.913n = 25

USL = 349.041LSL = -160.438

s = 84.913n = 25

USL = 605.205LSL = 0.149

s = 84.913n = 25

USL = 2463.585LSL = 1.134

6 8 10 12 14 16 18

0.0

0.2

0.4

0.6

y

Des

irabi

lity

scale = 2

coded 0.0 0.136 -0.816real 1.2 51.361 1.892



tem

p[, 3

]

temp[, 1]123

2022

24

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x


Pro

babi

lity

0.410.5

0.59

0.68

0.77

0.86

0.95


Pro

babi

lity

0.23

0.32

0.41

0.50.590.68

0.77

0.86

0.95

Operator

Mea

sure

men

t

A B C

0.34

650.

3475 1

11

1 1

11 1

1

1

0.34

640.

3468

0.34

72

Part

mea

n of

Mea

sure

men

t

22

2

2 2

2

2

2

2

23 3 3

3 3

3 33

3

3

A B C D E F G H I J

123

OperatorABC



temp[, 2]

1618

1 2 3 1 2 3 1 2 31.4 1.6 1.8 2.0 2.2 2.4 2.6

1.4

1.6


1.6

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

0 1 2 3 4 5 6 7

1.4

1.6


1.6

1.8

2.0

2.2

2.4


Qua

ntile

s fo

r x

C B E G A H D I F


Freq

uenc

y

C B E G A H D I F

020

4060

80

00.

250.

50.

751

Cum

ulat

ive

Per

cent

age

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14

0.23

0.32

x

1.6 1.8 2.0 2.2 2.4

0.05

0.14


Pro

babi

lity

0.320.41

0.50.59

0.68

0.77

0.86

0.95

-2 -1 0 1 2

0.0

0.4

0.8

Stacked dot plot

x

0.0

0.4

0.8



1.4 1.6 1.8 2.0 2.2 2.4

1.4


1.4 1.6 1.8 2.0 2.2 2.4

1.4


Percentage

Cum. Frequency

Frequency 13

13

16

16

10

23

12

29

10

33

12

41

10

43

12

54

9

52

11

65

9

61

11

76

8

69

10

86

6

75

8

94

5

80

6

100 x

1.6 1.8 2.0 2.2 2.4

0.050.140.23 -2 -1 0 1 2

x




Contents And Teaching MethodologyImprovement ProjectA Students Example

Contents And Teaching Methodology Of The R-Course

Process Capability

Pareto Chart

Desirabilities

Hypothesis Test

Quality Control Charts

CorrelationMulti Vari Chart Probability Plot

Applied Statistics

Descriptive Statistics

Inductive Statistics

Bivariate Methods

Quality Tools (6σ)

Process Capability

Gage R&R

Design of Experiments

Teaching Methodology

Lectures and Excercise Sheets

Improvement Project

Lecture Notes, Slides and Forum





The (Revised) Helicopter Improvement Project

Problem Statement

Insufficient and unstable helicopter flight times.Come up with a better design. Start byworking out a Project Charter (take intoaccount costs) and standardizing the releaseprocess of the helicopter.

Project Charter

Define the problem, scope, objectiveand participants of the project

Process Capability

Reduce the variation of flight times bystandardizing the release-process ofthe helicopter

Design of Experiments

Devise and run a sequential factorialdesign. Gain knowledge from a model.

Path of steepest ascent

Build and test further prototypes





ProjectCharter - Kick off the improvement project





Standardization - Improving The Process Capability Ratio

> pcr(flights , lsl=mean(flights )-0.3, usl=mean(flights )+0.3)

Anderson Darling Test for normal distribution

data: x[, 1]A = 0.4616 , mean =5.941 , sd=0.062 , p-value =0.2317alternative hypothesis: true distribution is not equal to normal

c(6.122, 5.977, 5.974, 5.917, 5.921, 5.922, 5.945, 5.941, 6, 5.874, 5.881, 5.91, 5.932, 5.925, 5.979, 5.889, 5.846, 5.872, 5.991, 5.993)

Den

sity

5.6 5.8 6.0 6.2

02

46

8

LSL USLTARGET

Process Capability using normal distribution for flights

x = 5.941s = 0.062n = 20

Nominal Value = 5.941USL = 6.241LSL = 5.641

cp = 1.62

cpk = 1.62

cpkL = 1.62

cpkU = 1.62

A = 0.462

p = 0.232

mean = 5.941

sd = 0.06

●

● ●●

●

●●●●

●●

●●

●●●● ●

●

●

Quantiles from distribution distribution

5.85 5.95 6.05

5.85

5.95

6.05


Abwurf.wmvMedia File (video/x-ms-wmv)




Design Of Experiments - Size And Direction Of Effects

> fdo = facDesign(k=3, centerCube = 2, replicates = 2) #factorial design> names(fdo) = c(" winglength", "bodylength", "cut") #optional> lows(fdo) = c(60, 50, 0) #optional> highs(fdo) = c(90, 100, 60) #optional> units(fdo) = c("mm", "mm", "mm") #optional> response(fdo)= flights #generic setter for all designs> summary(fdo)

Information about the factors:A B C

low 60 50 0high 90 100 60name winglength bodylength cutunit mm mm mmtype numeric numeric numeric-----------

StandOrd RunOrd

Documents

Teaching Statistics In Quality Science Using The R-Package ...Herrm… · ProjectCharter Process Capability Design Of Experiments 4 R esum e Opinions Regarding The Contents Opinions