(SpringerBriefs in Statistics 14)
Edgar Santos-Fernandez  (auth.)-
Multivariate Statistical Quality Control Using R
-Springer New York (2013)
SSN 2191-544X ISSN 2191-5458 (electronic)
ISBN 978-1-4614-5452-6 ISBN 978-1-4614-5453-3 (eBook)
DOI 10.1007/978-1-4614-5453-3
Springer New York Heidelberg Dordrecht London
Library of Congress Control Number: 2012947029
# Springer Science+Business Media New York 2012
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Contents
1 A Small Introduction ..................................................... 1
1.1 A Small Introduction ................................................ 1
1.1.1 A Brief on R................................................ 1
1.1.2 R Installation and Managing ............................... 2
1.1.3 General Principles of Data Manipulation .................. 3
1.1.4 Datasets Used.............................................. 3
1.1.5 The R Help ................................................. 4
1.1.6 Graphics in R............................................... 5
1.1.7 Probability Distributions ................................... 6
1.1.8 Descriptive Statistics ....................................... 7
1.1.9 Statistical Inference (Hypothesis Testing) ................. 10
1.1.10 A Short Introduction to Statistical Process
Control (SPC). Univariate Control Charts ................. 10
1.1.11 Univariate Process Capability Indices
(Cp, Cpk and Cpm) ........................................ 12
2 Multivariate Control Charts ............................................ 17
2.1 The Multivariate Normal Distribution ............................. 17
2.2 Data Structure ...................................................... 19
2.3 The mult.chart Function ............................................ 21
2.4 Contour Plot and w 2 Control Chart ................................ 22
2.5 Hotelling T 2 Control Chart (Phase I) .............................. 27
2.6 Interpretation, Decomposition, and Phase II ....................... 31
2.6.1 T 2 for Individuals .......................................... 35
2.7 Generalized Variance Control Chart ............................... 43
2.8 Multivariate Exponentially Weighted Moving
Average Control Chart ............................................. 46
2.9 Multivariate Cumulative Sum Control Chart...................... 49
2.10 Control Chart Based on Principal Component
Analysis (PCA) ..................................................... 54
2.11 Exercises ........................................................... 59
ix
3 Multivariate Process Capability Indices (MPCI) ...................... 63
3.1 The mpci Function ................................................... 64
3.2 Multivariate Process Capability Vector ............................. 65
3.3 Multivariate Capability Index ....................................... 69
3.4 Revision of the Multivariate Capability Index ...................... 71
3.5 Multivariate Process Capability in a Presence
of Rational Subgroup—A Three-Dimensional Case ................ 74
3.6 Multivariate Capability Indices Based on
Principal Component Analysis ...................................... 75
3.7 Methodology to Select the Number
of Principal Components ............................................ 80
3.8 Exercises ............................................................. 82
4 Tools of Support to MSQC .............................................. 87
4.1 Tools of Support to MSQC .......................................... 87
4.1.1 Graphical Methods .......................................... 87
4.1.2 Marginal Normality Test .................................... 89
4.1.3 Assessing Multivariate Normality ........................... 95
4.1.4 Solutions to Departures from Normality .................... 100
4.1.5 The Autocorrelation Problem ............................... 103
4.1.6 Exercises ..................................................... 105
5 Study Cases ............................................................... 107
5.1 Study Case #1. Pitching controlling ................................. 107
5.2 Study Case #2. Target Archery ...................................... 114
References ..................................................................... 121
Index ........................................................................... 125