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
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Quality And Quality ManagementProcess-Model For Continual ImprovementStatistics In Problem Solving
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Quality And Quality ManagementProcess-Model For Continual ImprovementStatistics In Problem Solving
Process-based Quality Management System For ContinualImprovement (EN ISO 9001:2008)
C
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Management
responsibility
Resource
management
Input OutputProduct
Measurement,
analysis and
improvement
Continual improvement of
the quality management system
Product
realization
Value-adding activities
Information flow
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Quality And Quality ManagementProcess-Model For Continual ImprovementStatistics In Problem Solving
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package
Visual Representation Of The qualityTools Package
N = 14k = 2p = 0.centerPointsCube: 3Axial: 3
N = 8k = 2p = 0.centerPointsCube: 0Axial: 0
N = 20k = 3p = 0.centerPointsCube: 2Axial: 2
N = 18k = 3p = 0.centerPointsCube: 2Axial: 2
N = 14k = 3p = 0.centerPointsCube: 0Axial: 0
N = 34k = 4p = 0.centerPointsCube: 2Axial: 2
N = 30k = 4p = 0.centerPointsCube: 2Axial: 2
N = 28k = 4p = 0.centerPointsCube: 2Axial: 2
N = 24k = 4p = 0.centerPointsCube: 0Axial: 0
N = 62k = 5p = 0.centerPointsCube: 2Axial: 4
N = 54k = 5p = 0.centerPointsCube: 2Axial: 4
N = 50k = 5p = 0.centerPointsCube: 2Axial: 4
N = 48k = 5p = 0.centerPointsCube: 2Axial: 4
N = 42k = 5p = 0.centerPointsCube: 0Axial: 0
N = 53k = 5p = 1.centerPointsCube: 6Axial: 1
N = 41k = 5p = 1.centerPointsCube: 6Axial: 1
N = 35k = 5p = 1.centerPointsCube: 6Axial: 1
N = 28k = 5p = 1.centerPointsCube: 0Axial: 0
N = 98k = 6p = 0.centerPointsCube: 1Axial: 6
N = 90k = 6p = 0.centerPointsCube: 1Axial: 6
N = 86k = 6p = 0.centerPointsCube: 1Axial: 6
N = 84k = 6p = 0.centerPointsCube: 1Axial: 6
N = 83k = 6p = 0.centerPointsCube: 1Axial: 6
N = 76k = 6p = 0.centerPointsCube: 0Axial: 0
N = 80k = 6p = 1.centerPointsCube: 4Axial: 2
N = 64k = 6p = 1.centerPointsCube: 4Axial: 2
N = 56k = 6p = 1.centerPointsCube: 4Axial: 2
N = 52k = 6p = 1.centerPointsCube: 4Axial: 2
N = 46k = 6p = 1.centerPointsCube: 0Axial: 0
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 161k = 7p = 0.centerPointsCube: 1Axial: 11
N = 157k = 7p = 0.centerPointsCube: 1Axial: 11
N = 155k = 7p = 0.centerPointsCube: 1Axial: 11
N = 154k = 7p = 0.centerPointsCube: 1Axial: 11
N = 142k = 7p = 0.centerPointsCube: 0Axial: 0
N = 92k = 7p = 1.centerPointsCube: 1Axial: 4
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
Standardized main effects and interactions
40
50
41.461
ABC
winglengthbodylengthcut
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package
Visual Representation Of The qualityTools Package
N = 14k = 2p = 0.centerPointsCube: 3Axial: 3
N = 8k = 2p = 0.centerPointsCube: 0Axial: 0
N = 20k = 3p = 0.centerPointsCube: 2Axial: 2
N = 18k = 3p = 0.centerPointsCube: 2Axial: 2
N = 14k = 3p = 0.centerPointsCube: 0Axial: 0
N = 34k = 4p = 0.centerPointsCube: 2Axial: 2
N = 30k = 4p = 0.centerPointsCube: 2Axial: 2
N = 28k = 4p = 0.centerPointsCube: 2Axial: 2
N = 24k = 4p = 0.centerPointsCube: 0Axial: 0
N = 62k = 5p = 0.centerPointsCube: 2Axial: 4
N = 54k = 5p = 0.centerPointsCube: 2Axial: 4
N = 50k = 5p = 0.centerPointsCube: 2Axial: 4
N = 48k = 5p = 0.centerPointsCube: 2Axial: 4
N = 42k = 5p = 0.centerPointsCube: 0Axial: 0
N = 53k = 5p = 1.centerPointsCube: 6Axial: 1
N = 41k = 5p = 1.centerPointsCube: 6Axial: 1
N = 35k = 5p = 1.centerPointsCube: 6Axial: 1
N = 28k = 5p = 1.centerPointsCube: 0Axial: 0
N = 98k = 6p = 0.centerPointsCube: 1Axial: 6
N = 90k = 6p = 0.centerPointsCube: 1Axial: 6
N = 86k = 6p = 0.centerPointsCube: 1Axial: 6
N = 84k = 6p = 0.centerPointsCube: 1Axial: 6
N = 83k = 6p = 0.centerPointsCube: 1Axial: 6
N = 76k = 6p = 0.centerPointsCube: 0Axial: 0
N = 80k = 6p = 1.centerPointsCube: 4Axial: 2
N = 64k = 6p = 1.centerPointsCube: 4Axial: 2
N = 56k = 6p = 1.centerPointsCube: 4Axial: 2
N = 52k = 6p = 1.centerPointsCube: 4Axial: 2
N = 46k = 6p = 1.centerPointsCube: 0Axial: 0
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 161k = 7p = 0.centerPointsCube: 1Axial: 11
N = 157k = 7p = 0.centerPointsCube: 1Axial: 11
N = 155k = 7p = 0.centerPointsCube: 1Axial: 11
N = 154k = 7p = 0.centerPointsCube: 1Axial: 11
N = 142k = 7p = 0.centerPointsCube: 0Axial: 0
N = 92k = 7p = 1.centerPointsCube: 1Axial: 4
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
Standardized main effects and interactions
40
50
41.461
ABC
winglengthbodylengthcut
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" distribution
Pro
babi
lity
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package
Visual Representation Of The qualityTools Package
N = 14k = 2p = 0.centerPointsCube: 3Axial: 3
N = 8k = 2p = 0.centerPointsCube: 0Axial: 0
N = 20k = 3p = 0.centerPointsCube: 2Axial: 2
N = 18k = 3p = 0.centerPointsCube: 2Axial: 2
N = 14k = 3p = 0.centerPointsCube: 0Axial: 0
N = 34k = 4p = 0.centerPointsCube: 2Axial: 2
N = 30k = 4p = 0.centerPointsCube: 2Axial: 2
N = 28k = 4p = 0.centerPointsCube: 2Axial: 2
N = 24k = 4p = 0.centerPointsCube: 0Axial: 0
N = 62k = 5p = 0.centerPointsCube: 2Axial: 4
N = 54k = 5p = 0.centerPointsCube: 2Axial: 4
N = 50k = 5p = 0.centerPointsCube: 2Axial: 4
N = 48k = 5p = 0.centerPointsCube: 2Axial: 4
N = 42k = 5p = 0.centerPointsCube: 0Axial: 0
N = 53k = 5p = 1.centerPointsCube: 6Axial: 1
N = 41k = 5p = 1.centerPointsCube: 6Axial: 1
N = 35k = 5p = 1.centerPointsCube: 6Axial: 1
N = 28k = 5p = 1.centerPointsCube: 0Axial: 0
N = 98k = 6p = 0.centerPointsCube: 1Axial: 6
N = 90k = 6p = 0.centerPointsCube: 1Axial: 6
N = 86k = 6p = 0.centerPointsCube: 1Axial: 6
N = 84k = 6p = 0.centerPointsCube: 1Axial: 6
N = 83k = 6p = 0.centerPointsCube: 1Axial: 6
N = 76k = 6p = 0.centerPointsCube: 0Axial: 0
N = 80k = 6p = 1.centerPointsCube: 4Axial: 2
N = 64k = 6p = 1.centerPointsCube: 4Axial: 2
N = 56k = 6p = 1.centerPointsCube: 4Axial: 2
N = 52k = 6p = 1.centerPointsCube: 4Axial: 2
N = 46k = 6p = 1.centerPointsCube: 0Axial: 0
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 161k = 7p = 0.centerPointsCube: 1Axial: 11
N = 157k = 7p = 0.centerPointsCube: 1Axial: 11
N = 155k = 7p = 0.centerPointsCube: 1Axial: 11
N = 154k = 7p = 0.centerPointsCube: 1Axial: 11
N = 142k = 7p = 0.centerPointsCube: 0Axial: 0
N = 92k = 7p = 1.centerPointsCube: 1Axial: 4
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
Standardized main effects and interactions
40
50
41.461
ABC
winglengthbodylengthcut
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" distribution
Pro
babi
lity
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package
Visual Representation Of The qualityTools Package
N = 14k = 2p = 0.centerPointsCube: 3Axial: 3
N = 8k = 2p = 0.centerPointsCube: 0Axial: 0
N = 20k = 3p = 0.centerPointsCube: 2Axial: 2
N = 18k = 3p = 0.centerPointsCube: 2Axial: 2
N = 14k = 3p = 0.centerPointsCube: 0Axial: 0
N = 34k = 4p = 0.centerPointsCube: 2Axial: 2
N = 30k = 4p = 0.centerPointsCube: 2Axial: 2
N = 28k = 4p = 0.centerPointsCube: 2Axial: 2
N = 24k = 4p = 0.centerPointsCube: 0Axial: 0
N = 62k = 5p = 0.centerPointsCube: 2Axial: 4
N = 54k = 5p = 0.centerPointsCube: 2Axial: 4
N = 50k = 5p = 0.centerPointsCube: 2Axial: 4
N = 48k = 5p = 0.centerPointsCube: 2Axial: 4
N = 42k = 5p = 0.centerPointsCube: 0Axial: 0
N = 53k = 5p = 1.centerPointsCube: 6Axial: 1
N = 41k = 5p = 1.centerPointsCube: 6Axial: 1
N = 35k = 5p = 1.centerPointsCube: 6Axial: 1
N = 28k = 5p = 1.centerPointsCube: 0Axial: 0
N = 98k = 6p = 0.centerPointsCube: 1Axial: 6
N = 90k = 6p = 0.centerPointsCube: 1Axial: 6
N = 86k = 6p = 0.centerPointsCube: 1Axial: 6
N = 84k = 6p = 0.centerPointsCube: 1Axial: 6
N = 83k = 6p = 0.centerPointsCube: 1Axial: 6
N = 76k = 6p = 0.centerPointsCube: 0Axial: 0
N = 80k = 6p = 1.centerPointsCube: 4Axial: 2
N = 64k = 6p = 1.centerPointsCube: 4Axial: 2
N = 56k = 6p = 1.centerPointsCube: 4Axial: 2
N = 52k = 6p = 1.centerPointsCube: 4Axial: 2
N = 46k = 6p = 1.centerPointsCube: 0Axial: 0
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 161k = 7p = 0.centerPointsCube: 1Axial: 11
N = 157k = 7p = 0.centerPointsCube: 1Axial: 11
N = 155k = 7p = 0.centerPointsCube: 1Axial: 11
N = 154k = 7p = 0.centerPointsCube: 1Axial: 11
N = 142k = 7p = 0.centerPointsCube: 0Axial: 0
N = 92k = 7p = 1.centerPointsCube: 1Axial: 4
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
Standardized main effects and interactions
40
50
41.461
ABC
winglengthbodylengthcut
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" distribution
Pro
babi
lity
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 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
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package
Visual Representation Of The qualityTools Package
N = 14k = 2p = 0.centerPointsCube: 3Axial: 3
N = 8k = 2p = 0.centerPointsCube: 0Axial: 0
N = 20k = 3p = 0.centerPointsCube: 2Axial: 2
N = 18k = 3p = 0.centerPointsCube: 2Axial: 2
N = 14k = 3p = 0.centerPointsCube: 0Axial: 0
N = 34k = 4p = 0.centerPointsCube: 2Axial: 2
N = 30k = 4p = 0.centerPointsCube: 2Axial: 2
N = 28k = 4p = 0.centerPointsCube: 2Axial: 2
N = 24k = 4p = 0.centerPointsCube: 0Axial: 0
N = 62k = 5p = 0.centerPointsCube: 2Axial: 4
N = 54k = 5p = 0.centerPointsCube: 2Axial: 4
N = 50k = 5p = 0.centerPointsCube: 2Axial: 4
N = 48k = 5p = 0.centerPointsCube: 2Axial: 4
N = 42k = 5p = 0.centerPointsCube: 0Axial: 0
N = 53k = 5p = 1.centerPointsCube: 6Axial: 1
N = 41k = 5p = 1.centerPointsCube: 6Axial: 1
N = 35k = 5p = 1.centerPointsCube: 6Axial: 1
N = 28k = 5p = 1.centerPointsCube: 0Axial: 0
N = 98k = 6p = 0.centerPointsCube: 1Axial: 6
N = 90k = 6p = 0.centerPointsCube: 1Axial: 6
N = 86k = 6p = 0.centerPointsCube: 1Axial: 6
N = 84k = 6p = 0.centerPointsCube: 1Axial: 6
N = 83k = 6p = 0.centerPointsCube: 1Axial: 6
N = 76k = 6p = 0.centerPointsCube: 0Axial: 0
N = 80k = 6p = 1.centerPointsCube: 4Axial: 2
N = 64k = 6p = 1.centerPointsCube: 4Axial: 2
N = 56k = 6p = 1.centerPointsCube: 4Axial: 2
N = 52k = 6p = 1.centerPointsCube: 4Axial: 2
N = 46k = 6p = 1.centerPointsCube: 0Axial: 0
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 161k = 7p = 0.centerPointsCube: 1Axial: 11
N = 157k = 7p = 0.centerPointsCube: 1Axial: 11
N = 155k = 7p = 0.centerPointsCube: 1Axial: 11
N = 154k = 7p = 0.centerPointsCube: 1Axial: 11
N = 142k = 7p = 0.centerPointsCube: 0Axial: 0
N = 92k = 7p = 1.centerPointsCube: 1Axial: 4
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
Standardized main effects and interactions
40
50
41.461
ABC
winglengthbodylengthcut
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" distribution
Pro
babi
lity
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package
Visual Representation Of The qualityTools Package
N = 14k = 2p = 0.centerPointsCube: 3Axial: 3
N = 8k = 2p = 0.centerPointsCube: 0Axial: 0
N = 20k = 3p = 0.centerPointsCube: 2Axial: 2
N = 18k = 3p = 0.centerPointsCube: 2Axial: 2
N = 14k = 3p = 0.centerPointsCube: 0Axial: 0
N = 34k = 4p = 0.centerPointsCube: 2Axial: 2
N = 30k = 4p = 0.centerPointsCube: 2Axial: 2
N = 28k = 4p = 0.centerPointsCube: 2Axial: 2
N = 24k = 4p = 0.centerPointsCube: 0Axial: 0
N = 62k = 5p = 0.centerPointsCube: 2Axial: 4
N = 54k = 5p = 0.centerPointsCube: 2Axial: 4
N = 50k = 5p = 0.centerPointsCube: 2Axial: 4
N = 48k = 5p = 0.centerPointsCube: 2Axial: 4
N = 42k = 5p = 0.centerPointsCube: 0Axial: 0
N = 53k = 5p = 1.centerPointsCube: 6Axial: 1
N = 41k = 5p = 1.centerPointsCube: 6Axial: 1
N = 35k = 5p = 1.centerPointsCube: 6Axial: 1
N = 28k = 5p = 1.centerPointsCube: 0Axial: 0
N = 98k = 6p = 0.centerPointsCube: 1Axial: 6
N = 90k = 6p = 0.centerPointsCube: 1Axial: 6
N = 86k = 6p = 0.centerPointsCube: 1Axial: 6
N = 84k = 6p = 0.centerPointsCube: 1Axial: 6
N = 83k = 6p = 0.centerPointsCube: 1Axial: 6
N = 76k = 6p = 0.centerPointsCube: 0Axial: 0
N = 80k = 6p = 1.centerPointsCube: 4Axial: 2
N = 64k = 6p = 1.centerPointsCube: 4Axial: 2
N = 56k = 6p = 1.centerPointsCube: 4Axial: 2
N = 52k = 6p = 1.centerPointsCube: 4Axial: 2
N = 46k = 6p = 1.centerPointsCube: 0Axial: 0
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 161k = 7p = 0.centerPointsCube: 1Axial: 11
N = 157k = 7p = 0.centerPointsCube: 1Axial: 11
N = 155k = 7p = 0.centerPointsCube: 1Axial: 11
N = 154k = 7p = 0.centerPointsCube: 1Axial: 11
N = 142k = 7p = 0.centerPointsCube: 0Axial: 0
N = 92k = 7p = 1.centerPointsCube: 1Axial: 4
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
Standardized main effects and interactions
40
50
41.461
ABC
winglengthbodylengthcut
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" distribution
Pro
babi
lity
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Scope Of The qualityTools Package (S4)Overview Of Methods Within The qualityTools Package
Visual Representation Of The qualityTools Package
N = 14k = 2p = 0.centerPointsCube: 3Axial: 3
N = 8k = 2p = 0.centerPointsCube: 0Axial: 0
N = 20k = 3p = 0.centerPointsCube: 2Axial: 2
N = 18k = 3p = 0.centerPointsCube: 2Axial: 2
N = 14k = 3p = 0.centerPointsCube: 0Axial: 0
N = 34k = 4p = 0.centerPointsCube: 2Axial: 2
N = 30k = 4p = 0.centerPointsCube: 2Axial: 2
N = 28k = 4p = 0.centerPointsCube: 2Axial: 2
N = 24k = 4p = 0.centerPointsCube: 0Axial: 0
N = 62k = 5p = 0.centerPointsCube: 2Axial: 4
N = 54k = 5p = 0.centerPointsCube: 2Axial: 4
N = 50k = 5p = 0.centerPointsCube: 2Axial: 4
N = 48k = 5p = 0.centerPointsCube: 2Axial: 4
N = 42k = 5p = 0.centerPointsCube: 0Axial: 0
N = 53k = 5p = 1.centerPointsCube: 6Axial: 1
N = 41k = 5p = 1.centerPointsCube: 6Axial: 1
N = 35k = 5p = 1.centerPointsCube: 6Axial: 1
N = 28k = 5p = 1.centerPointsCube: 0Axial: 0
N = 98k = 6p = 0.centerPointsCube: 1Axial: 6
N = 90k = 6p = 0.centerPointsCube: 1Axial: 6
N = 86k = 6p = 0.centerPointsCube: 1Axial: 6
N = 84k = 6p = 0.centerPointsCube: 1Axial: 6
N = 83k = 6p = 0.centerPointsCube: 1Axial: 6
N = 76k = 6p = 0.centerPointsCube: 0Axial: 0
N = 80k = 6p = 1.centerPointsCube: 4Axial: 2
N = 64k = 6p = 1.centerPointsCube: 4Axial: 2
N = 56k = 6p = 1.centerPointsCube: 4Axial: 2
N = 52k = 6p = 1.centerPointsCube: 4Axial: 2
N = 46k = 6p = 1.centerPointsCube: 0Axial: 0
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 169k = 7p = 0.centerPointsCube: 1Axial: 11
N = 161k = 7p = 0.centerPointsCube: 1Axial: 11
N = 157k = 7p = 0.centerPointsCube: 1Axial: 11
N = 155k = 7p = 0.centerPointsCube: 1Axial: 11
N = 154k = 7p = 0.centerPointsCube: 1Axial: 11
N = 142k = 7p = 0.centerPointsCube: 0Axial: 0
N = 92k = 7p = 1.centerPointsCube: 1Axial: 4
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
Standardized main effects and interactions
40
50
41.461
ABC
winglengthbodylengthcut
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" distribution
Pro
babi
lity
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Contents And Teaching MethodologyImprovement ProjectA Students Example
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
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Contents And Teaching MethodologyImprovement ProjectA Students Example
ProjectCharter - Kick off the improvement project
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Contents And Teaching MethodologyImprovement ProjectA Students Example
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
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Quantiles from distribution distribution
5.85 5.95 6.05
5.85
5.95
6.05
Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools
Abwurf.wmvMedia File (video/x-ms-wmv)
Introduction To QualityThe qualityTools Package
Contents Of The R-CourseRésumé
Contents And Teaching MethodologyImprovement ProjectA Students Example
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
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