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Introduction To Quality The qualityTools Package Contents Of The R-Course R esum e Teaching Statistics In Quality Science Using The R-Package qualityTools Thomas Roth, Joachim Herrmann The Department of Quality Science - Technical

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SLIDE 1

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e

Teaching Statistics In Quality Science Using The 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

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e

Outline

1

Introduction To Quality Quality And Quality Management Process-Model For Continual Improvement Statistics In Problem Solving

2

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

3

Contents Of The R-Course Contents And Teaching Methodology Improvement Project A Students Example

ProjectCharter Process Capability Design Of Experiments

4

R´ esum´ e Opinions Regarding The Contents Opinions Regarding R Summary

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

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SLIDE 3

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Quality And Quality Management Process-Model For Continual Improvement Statistics 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

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SLIDE 4

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Quality And Quality Management Process-Model For Continual Improvement Statistics In Problem Solving

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

C u s t

  • m

e r s C u s t

  • 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

  • n

Management responsibility Resource management

Input Output Product

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

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SLIDE 5

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Quality And Quality Management Process-Model For Continual Improvement Statistics In Problem Solving

The Role Of Statistics In The Field Of Quality

Process Capability Pareto Chart Desirabilities Hypothesis Test Quality Control Charts Correlation Multi Vari Chart Probability Plot

Problem 1: engineers dislike statistics

  • r engineers fail to see applications

Solution: exchange statistics with data analysis and problem solving Problem 2: statistics comprise to much calculations Solution: Use R with all its favorable aspects Use R to keep the focus on methods rather than calculation Use R as a software that is available on all platforms Use R to visualize important key concepts by simulation

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

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SLIDE 6

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e 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 of generic methods (show, print, plot, summary, as.data.frame, nrow, . . .) S4 OOP Accessor and Replacement functions as well as Validity functions i.e. check the validity 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

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SLIDE 7

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Scope Of The qualityTools Package (S4) Overview Of Methods Within The qualityTools Package

Visual Representation Of The qualityTools Package

N = 14 k = 2 p = 0 .centerPoints Cube: 3 Axial: 3 N = 8 k = 2 p = 0 .centerPoints Cube: 0 Axial: 0 N = 20 k = 3 p = 0 .centerPoints Cube: 2 Axial: 2 N = 18 k = 3 p = 0 .centerPoints Cube: 2 Axial: 2 N = 14 k = 3 p = 0 .centerPoints Cube: 0 Axial: 0 N = 34 k = 4 p = 0 .centerPoints Cube: 2 Axial: 2 N = 30 k = 4 p = 0 .centerPoints Cube: 2 Axial: 2 N = 28 k = 4 p = 0 .centerPoints Cube: 2 Axial: 2 N = 24 k = 4 p = 0 .centerPoints Cube: 0 Axial: 0 N = 62 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 54 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 50 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 48 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 42 k = 5 p = 0 .centerPoints Cube: 0 Axial: 0 N = 53 k = 5 p = 1 .centerPoints Cube: 6 Axial: 1 N = 41 k = 5 p = 1 .centerPoints Cube: 6 Axial: 1 N = 35 k = 5 p = 1 .centerPoints Cube: 6 Axial: 1 N = 28 k = 5 p = 1 .centerPoints Cube: 0 Axial: 0 N = 98 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 90 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 86 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 84 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 83 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 76 k = 6 p = 0 .centerPoints Cube: 0 Axial: 0 N = 80 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 64 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 56 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 52 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 46 k = 6 p = 1 .centerPoints Cube: 0 Axial: 0 N = 169 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 169 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 161 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 157 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 155 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 154 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 142 k = 7 p = 0 .centerPoints Cube: 0 Axial: 0 N = 92 k = 7 p = 1 .centerPoints Cube: 1 Axial: 4 2 3 4 5 5 6 6 7 7 number of factors k 1 2 3 5 9 17 number of blocks C = AB 2III (3−1) D = ABC 2IV (4−1) E = AC D = AB 2III (5−2) F = BC E = AC D = AB 2III (6−3) G = ABC F = BC E = AC D = AB 2III (7−4) E = ABCD 2V (5−1) F = BCD E = ABC 2IV (6−2) G = ACD F = BCD E = ABC 2IV (7−3) H = ABD G = ABC F = ACD E = BCD 2IV (8−4) J = ABCD H = ABD G = ACD F = BCD E = ABC 2III (9−5) K = AB J = ABCD H = ABD G = ACD F = BCD E = ABC 2III (10−6) L = AC K = AB J = ABCD H = ABD G = ACD F = BCD E = ABC 2III (11−7) F = ABCDE 2VI (6−1) G = ABDE F = ABCD 2IV (7−2) H = BCDE G = ABD F = ABC 2IV (8−3) J = ABCE H = ABDE G = ACDE F = BCDE 2IV (9−4) K = BCDE J = ACDE H = ABDE G = ABCE F = ABCD 2IV (10−5) L = ADEF K = AEF J = ACD H = CDE G = BCD F = ABC 2IV (11−6) G = ABCDEF 2VII (7−1) H = ABEF G = ABCD 2V (8−2) J = CDEF H = ACEF G = ABCD 2IV (9−3) K = ABCE J = ABDE H = ACDF G = BCDF 2IV (10−4) L = ADEF K = BDEF J = ABF H = ABCD G = CDE 2IV (11−5) H = ABCDEFG 2VIII (8−1) J = BCEFG H = ACDFG 2VI (9−2) K = ACDF J = BCDE H = ABCG 2V (10−3) L = ABCDEFG K = ACDF J = BCDE H = ABCG 2V (11−4) number of runs N number of variables k 3 4 5 6 7 8 9 10 11 4 8 16 32 64 128 0.8 1.0 Half-Normal plot for effects of fdo A:B:C A:B p > 0.1 p < 0.05 Lenth Plot of effects 0.6 0.686 A B C D Standardized main effects and interactions 40 50 41.461 A B C winglength bodylength cut Standardized main effects and interactions 40 50 41.461 A B C winglength bodylength cut 0.0 0.5 1.0 0.0 0.2 0.4 0.6 Effects Theoretical Quantiles B A B:C A:C C A B C D A:B A:C B:C y 0.0 0.2 0.4 0.113 ME 0.271 SME 0.017 0.007 0.023 A B C A:B B:C A:B:C A:C flights
  • 20
  • 10
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 flights 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 y Respone Surface for y > -2 > -1.5 > -1
  • 200
  • 100
100 200 300 400 0.000 0.002 0.004 0.006 0.008 LSL USL TARGET 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 50 150 250 200 400 600 0.000 0.002 0.004 0.006 0.008 0.010 LSL USL TARGET 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 = 95.453 100 200 300 50 150 250
  • 500
500 1000 1500 2000 2500 3000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 LSL USL TARGET 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 = 1.281 200 400 600 50 150 250 flights
  • +
  • +
  • +
5.5 6.0 6.5 1

A

1 5.0 5.5 6.0 6.5 7

A

B
  • 1
1 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
1 B
  • 1
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 C coded 0 0 0 136 -0 816

Components of Variation component totalRR repeatability reproducibility PartToPart 0.0 0.4 0.8 VarCompContrib StudyVarContrib Measurement by Part Part Measurement 2 4 6 8 10 0.3465 0.3475 Measurement by Operator Interaction Operator:Part s = 84.913 n = 25 USL = 349.041 LSL = -160.438 s = 84.913 n = 25 USL = 605.205 LSL = 0.149 s = 84.913 n = 25 USL = 2463.585 LSL = 1.134 6 8 10 12 14 16 18 0.0 0.2 0.4 0.6 y Desirability scale = 2

coded 0.0 0.136 -0.816 real 1.2 51.361 1.892 y1 y2 y3 y4 Responses 130.660 1299.669 456.937 67.980 Desirabilities 0.213 0.999 0.569 0.936

Multi Vari Plot for temp[, 1] and temp[, 2] temp[, 3] temp[, 1] 1 2 3 20 22 24 1.8 2.0 2.2 2.4 Q-Q Plot for "log-normal" distribution Quantiles for x 1.8 2.0 2.2 2.4 Q-Q Plot for "exponential" distribution Quantiles for x Probability Plot for "log-normal" distribution Probability 0.41 0.5 0.59 0.68 0.77 0.86 0.95 Probability Plot for "weibull" distribution Probability 0.23 0.32 0.41 0.5 0.59 0.68 0.77 0.86 0.95 Operator Measurement A B C 0.3465 0.3475 1 1 1 1 1 1 1 1 1 1 0.3464 0.3468 0.3472 Part mean of Measurement 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 A B C D E F G H I J 1 2 3 Operator A B C

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

temp[, 2] 16 18 1 2 3 1 2 3 1 2 3 1.4 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 Quantiles for x 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 Quantiles for x C B E G A H D I F Pareto Chart for defects Frequency C B E G A H D I F 20 40 60 80 0.25 0.5 0.75 1 Cumulative Percentage 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 Probability 0.32 0.41 0.5 0.59 0.68 0.77 0.86 0.95
  • 2
  • 1
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 0.211 Part to Part 2.12e-08 0.1667 1.45e-04 0.000873 0.408 totalVar 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 0.05 0.14 0.23
  • 2
  • 1
1 2 x

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

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SLIDE 8

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Scope Of The qualityTools Package (S4) Overview Of Methods Within The qualityTools Package

Visual Representation Of The qualityTools Package

( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − )

  • 200
  • 100

100 200 300 400 0.000 0.002 0.004 0.006 0.008

LSL USL TARGET

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 50 150 250

200 400 600 0.000 0.002 0.004 0.006 0.008 0.010

LSL USL TARGET

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

100 200 300 50 150 250

  • 500

500 1000 1500 2000 2500 3000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

LSL USL TARGET

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

200 400 600 50 150 250

A

coded

  • 816

Components of Variation

component totalRR repeatability reproducibility PartToPart 0.0 0.4 0.8 VarCompContrib StudyVarContrib

Measurement by Part

Part Measurement 2 4 6 8 10 0.3465 0.3475 s = 84.913 n = 25 USL = 349.041 LSL = -160.438 s = 84.913 n = 25 USL = 605.205 LSL = 0.149 s = 84.913 n = 25 USL = 2463.585 LSL = 1.134

y

coded

  • 816

P t 211 t

  • 211

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

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SLIDE 9

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Scope Of The qualityTools Package (S4) Overview Of Methods Within The qualityTools Package

Visual Representation Of The qualityTools Package

( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − )

coded

  • 816

Measurement by Operator Interaction Operator:Part

y

coded

  • 816

Operator Measurement A B C 0.3465 0.3475 1 1 1 1 1 1 1 1 1 1 0.3464 0.3468 0.3472 Part mean of Measurement 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 A B C D E F G H I J 1 2 3 Operator A B C

Gage R&R VarComp VarCompContrib Stdev StudyVar StudyVarContrib totalRR 1.06e-07 0.8333 3.25e-04 0.001952 0.913 repeatability 6.50e-09 0.0512 8.06e-05 0.000484 0.226 reproducibility 9.93e-08 0.7822 3.15e-04 0.001891 0.884 Operator 9.37e-08 0.7375 3.06e-04 0.001836 0.859 O t P t 5 67 09 0 0446 7 53 05 0 000452 0 211 Operator:Part 5.67e-09 0.0446 7.53e-05 0.000452 0.211 Part to Part 2.12e-08 0.1667 1.45e-04 0.000873 0.408 totalVar 1.27e-07 1.0000 3.56e-04 0.002138 1.000

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

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SLIDE 10

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Scope Of The qualityTools Package (S4) Overview Of Methods Within The qualityTools Package

Visual Representation Of The qualityTools Package

( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) y

Multi Vari Plot for temp[, 1] and temp[, 2] temp[, 3] temp[, 1] 1 2 3 20 22 24 1.8 2.0 2.2 2.4 Q-Q Plot for "log-normal" distribution Quantiles for x 1.8 2.0 2.2 2.4 Q-Q Plot for "exponential" distribution Quantiles for x temp[, 2] 16 18 1 2 3 1 2 3 1 2 3 1.4 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 Quantiles for x 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 Quantiles for x C B E G A H D I F Pareto Chart for defects Frequency C B E G A H D I F 20 40 60 80 0.25 0.5 0.75 1 Cumulative Percentage 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

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

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SLIDE 11

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Scope Of The qualityTools Package (S4) Overview Of Methods Within The qualityTools Package

Visual Representation Of The qualityTools Package

( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) y

Probability Plot for "log-normal" distribution Probability 0.41 0.5 0.59 0.68 0.77 0.86 0.95 Probability Plot for "weibull" distribution Probability 0.23 0.32 0.41 0.5 0.59 0.68 0.77 0.86 0.95

Operator

Gage R&R VarComp totalRR 1.06e-07 repeatability 6.50e-09 reproducibility 9.93e-08 Operator 9.37e-08 O t P t 5 67 09

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 Probability 0.32 0.41 0.5 0.59 0.68 0.77 0.86 0.95

  • 2
  • 1

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 Part to Part 2.12e-08 totalVar 1.27e-07

x 1.6 1.8 2.0 2.2 2.4 0.05 0.14 0.23

  • 2
  • 1

1 2 x

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

slide-12
SLIDE 12

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Scope Of The qualityTools Package (S4) Overview Of Methods Within The qualityTools Package

Visual Representation Of The qualityTools Package

N = 14 k = 2 p = 0 .centerPoints Cube: 3 Axial: 3 N = 8 k = 2 p = 0 .centerPoints Cube: 0 Axial: 0 N = 20 k = 3 p = 0 .centerPoints Cube: 2 Axial: 2 N = 18 k = 3 p = 0 .centerPoints Cube: 2 Axial: 2 N = 14 k = 3 p = 0 .centerPoints Cube: 0 Axial: 0 N = 34 k = 4 p = 0 .centerPoints Cube: 2 Axial: 2 N = 30 k = 4 p = 0 .centerPoints Cube: 2 Axial: 2 N = 28 k = 4 p = 0 .centerPoints Cube: 2 Axial: 2 N = 24 k = 4 p = 0 .centerPoints Cube: 0 Axial: 0 N = 62 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 54 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 50 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 48 k = 5 p = 0 .centerPoints Cube: 2 Axial: 4 N = 42 k = 5 p = 0 .centerPoints Cube: 0 Axial: 0 N = 53 k = 5 p = 1 .centerPoints Cube: 6 Axial: 1 N = 41 k = 5 p = 1 .centerPoints Cube: 6 Axial: 1 N = 35 k = 5 p = 1 .centerPoints Cube: 6 Axial: 1 N = 28 k = 5 p = 1 .centerPoints Cube: 0 Axial: 0 N = 98 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 90 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 86 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 84 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 83 k = 6 p = 0 .centerPoints Cube: 1 Axial: 6 N = 76 k = 6 p = 0 .centerPoints Cube: 0 Axial: 0 N = 80 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 64 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 56 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 52 k = 6 p = 1 .centerPoints Cube: 4 Axial: 2 N = 46 k = 6 p = 1 .centerPoints Cube: 0 Axial: 0 N = 169 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 169 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 161 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 157 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 155 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 154 k = 7 p = 0 .centerPoints Cube: 1 Axial: 11 N = 142 k = 7 p = 0 .centerPoints Cube: 0 Axial: 0 N = 92 k = 7 p = 1 .centerPoints Cube: 1 Axial: 4 2 3 4 5 5 6 6 7 7 number of factors k 1 2 3 5 9 17 number of blocks

C = AB

2III (3−1)

D = ABC

2IV (4−1)

E = AC D = AB

2III (5−2)

F = BC E = AC D = AB

2III (6−3)

G = ABC F = BC E = AC D = AB

2III (7−4)

E = ABCD

2V (5−1)

F = BCD E = ABC

2IV (6−2)

G = ACD F = BCD E = ABC

2IV (7−3)

H = ABD G = ABC F = ACD E = BCD

2IV (8−4)

J = ABCD H = ABD G = ACD F = BCD E = ABC

2III (9−5)

K = AB J = ABCD H = ABD G = ACD F = BCD E = ABC

2III (10−6)

L = AC K = AB J = ABCD H = ABD G = ACD F = BCD E = ABC

2III (11−7)

F = ABCDE

2VI (6−1)

G = ABDE F = ABCD

2IV (7−2)

H = BCDE G = ABD F = ABC

2IV (8−3)

J = ABCE H = ABDE G = ACDE F = BCDE

2IV (9−4)

K = BCDE J = ACDE H = ABDE G = ABCE F = ABCD

2IV (10−5)

L = ADEF K = AEF J = ACD H = CDE G = BCD F = ABC

2IV (11−6)

G = ABCDEF

2VII (7−1)

H = ABEF G = ABCD

2V (8−2)

J = CDEF H = ACEF G = ABCD

2IV (9−3)

K = ABCE J = ABDE H = ACDF G = BCDF

2IV (10−4)

L = ADEF K = BDEF J = ABF H = ABCD G = CDE

2IV (11−5)

H = ABCDEFG

2VIII (8−1)

J = BCEFG H = ACDFG

2VI (9−2)

K = ACDF J = BCDE H = ABCG

2V (10−3)

L = ABCDEFG K = ACDF J = BCDE H = ABCG

2V (11−4) number of runs N number of variables k 3 4 5 6 7 8 9 10 11 4 8 16 32 64 128 0.8 1.0 Half-Normal plot for effects of fdo A:B:C A:B p > 0.1 p < 0.05 Lenth Plot of effects 0.6 0.686 A B C D Standardized main effects and interactions 40 50 41.461 A B C winglength bodylength cut Standardized main effects and interactions 40 50 41.461 A B C winglength bodylength cut 0.0 0.5 1.0 0.0 0.2 0.4 0.6 Effects Theoretical Quantiles B A B:C A:C C A B C D A:B A:C B:C y 0.0 0.2 0.4 0.113 ME 0.271 SME 0.017 0.007 0.023 A B C A:B B:C A:B:C A:C flights

  • 20
  • 10

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 flights 10 20 30 40

  • 16.503

4.656

  • 2.719
  • 1.438

0.653 0.077 2.228 Main Effect Plot for fdo Filled Contour for y Respone Surface for y

7

A

coded

  • 816

y

coded

  • 816

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

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SLIDE 13

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Scope Of The qualityTools Package (S4) Overview Of Methods Within The qualityTools Package

Visual Representation Of The qualityTools Package

( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − ) ( − )

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 y Respone Surface for y

> -2 > -1.5 > -1

flights

  • +
  • +
  • +

5.5 6.0 6.5

1

A

1 5.0 5.5 6.0 6.5 7

A

B

  • 1

1 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

1 B

  • 1

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 C coded 0 0 0 136 -0 816

6 8 10 12 14 16 18 0.0 0.2 0.4 0.6 y Desirability scale = 2

coded 0.0 0.136 -0.816 real 1.2 51.361 1.892 y1 y2 y3 y4 Responses 130.660 1299.669 456.937 67.980 Desirabilities 0.213 0.999 0.569 0.936

.2 2.4 Q-Q Plot for "log-normal" distribution .2 2.4

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

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SLIDE 14

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Contents And Teaching Methodology Improvement Project A Students Example

Contents And Teaching Methodology Of The R-Course

Process Capability Pareto Chart Desirabilities Hypothesis Test Quality Control Charts Correlation Multi 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

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SLIDE 15

Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Contents And Teaching Methodology Improvement Project A Students Example

The (Revised) Helicopter Improvement Project

Problem Statement Insufficient and unstable helicopter flight times. Come up with a better design. Start by working out a Project Charter (take into account costs) and standardizing the release process of the helicopter. Project Charter Define the problem, scope, objective and participants of the project Process Capability Reduce the variation of flight times by standardizing the release-process of the helicopter Design of Experiments Devise and run a sequential factorial

  • design. 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

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Contents And Teaching Methodology Improvement Project A Students Example

ProjectCharter - Kick off the improvement project

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

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Contents And Teaching Methodology Improvement Project A 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 =0.2317 alternative hypothesis: true distribution is not equal to normal

5.6 5.8 6.0 6.2 2 4 6 8

LSL USL TARGET

Process Capability using normal distribution for flights

x = 5.941 s = 0.062 n = 20 Nominal Value = 5.941 USL = 6.241 LSL = 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

  • ● ●●
  • ● ●
  • 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

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Contents And Teaching Methodology Improvement Project A 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 high 90 100 60 name winglength bodylength cut unit mm mm mm type numeric numeric numeric

  • StandOrd

RunOrder Block A B C flights 7 7 1 1 -1 1 1 4.882 1 1 2 1 -1 -1 -1 5.155 8 8 3 1 1 1 1 6.372 ... 17 17 17 1 5.948 18 18 18 1 5.826

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

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Contents And Teaching Methodology Improvement Project A Students Example

Design Of Experiments - Visualization

> effectPlot(fdo) > interactionPlot (fdo) > paretoPlot(fdo) > wirePlot(flights , A, B, data=fdo)

Standardized main effects and interactions 40 50 41.461 A B C winglength bodylength cut

A: winglength B: bodylength C: cut

Main Effect Plot for fdo ghts 20 30 40 ghts 6.0 6.5 fli 10 4.656

  • 2.719
  • 1.438

0.653 0.077

  • 2.228

2.228 fli 5.5 A B C A:B B:C A:B:C A:C

  • 20
  • 10
  • 16.503
  • +
  • +
  • +

Interaction plot for fdo

Respone Surface for flights

A
  • 1
1
  • 1
1

A

A
  • 1
1 6.0 6.5 7.0
  • 1
1

A

Interaction plot for fdo 6.5 7.0 > +4.5 > +5 > +5.5 > +6 > +6.5 > +7 > +7.5

A

5.0 5.5

A

B
  • 1
1 6.5 7.0

f l i g h t s 5.0 5.5 6.0

5.0 5.5 6.0

B

A 0.0 0.5 1.0 B

  • 0.5

0.0 0.5 1.0

C

A

  • 1.0
  • 0.5
  • 1.0

flights ~ A + B + A:B

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

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Contents And Teaching Methodology Improvement Project A Students Example

Steepest Ascent - Improving The Design

Flight Time improved by 44%

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

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Opinions Regarding The Contents Opinions Regarding R Summary

Student Survey Results (I)

1 2 3 4 5 6

Practical relevance

Frequency 10 20 30 40 50 6 43 28 10 4 25 41 20 5 1 Satisfaction Importance

very satisfied very dissatisfied very important very unimportant

1 2 3 4 5 6

Improvement project

Frequency 10 20 30 40 50 18 30 27 7 6 2 25 29 23 11 3 Satisfaction Importance

very satisfied very dissatisfied very important very unimportant Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Opinions Regarding The Contents Opinions Regarding R Summary

Student Survey Results (II)

1 2 3 4 5 6

Usage of software R

Frequency 10 20 30 40 50 8 34 29 12 7 2 17 32 30 10 2 1 Satisfaction Importance

very satisfied very dissatisfied very important very unimportant

1 2 3 4 5 6

Introduction to R

Frequency 10 20 30 40 50 10 37 28 13 1 3 36 35 15 5 1 1 Satisfaction Importance

very satisfied very dissatisfied very important very unimportant Thomas Roth, Joachim Herrmann Teaching Statistics In Quality Science Using The R-Package qualityTools

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Introduction To Quality The qualityTools Package Contents Of The R-Course R´ esum´ e Opinions Regarding The Contents Opinions Regarding R Summary

Summary

Summary R has become an integral part in the education of engineers R is used for an introduction to statistics and their application in quality sciences So far about 700 (undergraduate) students successfully conducted an improvement project using R Use R We Use R, do you?

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