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E-raamat: Handbook of Multivariate Process Capability Indices [Taylor & Francis e-raamat]

(Indian Statistical Institute, WB, India), (Assistant Professor, Lady Brabourne College, University of Calcutta, India)
  • Formaat: 352 pages, 17 Tables, black and white; 39 Illustrations, black and white
  • Ilmumisaeg: 28-Dec-2020
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9780429298349
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Handbook of Multivariate Process Capability IndicesSuurem pilt
  • Formaat: 352 pages, 17 Tables, black and white; 39 Illustrations, black and white
  • Ilmumisaeg: 28-Dec-2020
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9780429298349
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429298349
Providing a single-valued assessment of the performance of a process is often one of the greatest challenges for a quality professional. Process Capability Indices (PCIs) precisely do this job. For processes having a single measurable quality characteristic, there is an ample number of PCIs, dened in literature. The situation worsens for multivariate processes, i.e., where there is more than one correlated quality characteristic. Since in most situations quality professionals face multiple quality characteristics to be controlled through a process, Multivariate Process Capability Indices (MPCIs) become the order of the day. However, there is no book which addresses and explains dierent MPCIs and their properties. The literature of Multivariate Process Capability Indices (MPCIs) is not well organized, in the sense that a thorough and systematic discussion on the various MPCIs is hardly available in the literature.

Handbook of Multivariate Process Capability Indices provides an extensive study of the MPCIs dened for various types of specication regions. This book is intended to help quality professionals to understand which MPCI should be used and in what situation. For researchers in this eld, the book provides a thorough discussion about each of the MPCIs developed to date, along with their statistical and analytical properties. Also, real life examples are provided for almost all the MPCIs discussed in the book. This helps both the researchers and the quality professionals alike to have a better understanding of the MPCIs, which otherwise become dicult to understand, since there is more than one quality characteristic to be controlled at a time.

Features:











A complete guide for quality professionals on the usage of dierent MPCIs.





A step by step discussion on multivariate process capability analysis, starting from a brief discussion on univariate indices.





A single source for all kinds of MPCIs developed so far.





Comprehensive analysis of the MPCIs, including analysis of real-life data.





References provided at the end of each chapter encompass the entire literature available on the respective topic.





Interpretation of the MPCIs and development of threshold values of many MPCIs are also included.

This reference book is aimed at the post graduate students in Industrial Statistics. It will also serve researchers working in the eld of Industrial Statistics, as well as practitioners requiring thorough guidance regarding selection of an appropriate MPCI suitable for the problem at hand.
Preface xiii
Acknowledgements xv
Biography of First Author xvii
Biography of Second Author xviii
1 Introduction
1(18)
1.1 Concept of Process Capability Index
2(3)
1.2 Process Capability Indices in Six Sigma, Lean Six Sigma, and Design for Six Sigma (DFSS)
5(2)
1.3 Concept of Multivariate Process Capability Index (MPCI)
7(1)
1.4 Some Uses of Process Capability Indices
8(2)
1.5 Some Applications of MPCIs
10(2)
1.6 Overview of the
Chapters
12(7)
Bibliography
15(4)
2 Some Useful Concepts of Univariate and Multivariate Statistics
19(27)
2.1 Introduction
19(1)
2.2 Univariate Statistics
20(10)
2.2.1 Normal Distribution
20(1)
2.2.1.1 Properties of Normal Distribution
21(2)
2.2.2 Radial Error Distribution
23(1)
2.2.3 Folded Normal Distribution
24(2)
2.2.4 Uniform Distribution
26(1)
2.2.5 Log-Normal Distribution
27(1)
2.2.6 Exponential Distribution
28(2)
2.3 Estimation of Process Mean and Variance Using Control Chart Information
30(3)
2.3.1 Estimation of Process Mean and Variance Based on X-R Chart Information
31(1)
2.3.2 Estimation of Process Mean and Variance Based on X -- S Chart Information
32(1)
2.4 Some Bayesian Concepts
33(1)
2.5 Multivariate Statistics
34(4)
2.5.1 Multivariate Normal Distribution
35(1)
2.5.2 Multivariate Folded Normal Distribution
36(2)
2.6 Principal Component Analysis (PCA)
38(1)
2.7 Delta Method
39(7)
Bibliography
41(5)
3 Univariate Process Capability Indices
46(32)
3.1 Introduction
46(1)
3.2 Univariate Process Capability Indices for Symmetric Specification Limits
47(4)
3.2.1 Unification of Univariate PCIs for Symmetric Specification Limits
50(1)
3.3 Univariate Process Capability Indices for Asymmetric Specification Limits
51(5)
3.3.1 Unification of Univariate PCIs for Asymmetric Specification Limits
53(3)
3.4 Univariate Process Capability Indices for Unilateral (Onesided) Specification Limits
56(7)
3.4.1 Unification of Univariate PCIs for Unilateral Specification Limits
58(5)
3.5 Univariate Process Capability Indices for Non-Normal Distributions
63(4)
3.6 Univariate Process Capability Indices PNC
67(1)
3.7 Univariate Process Capability Assessments Using Bayesian Approach
68(1)
3.8 Concluding Remarks
68(10)
Bibliography
70(8)
4 Bivariate Process Capability Indices (BPCIs)
78(34)
4.1 Introduction
78(1)
4.2 Bivariate Generalization of Univariate PCIs for Bilateral Specification Limits
79(8)
4.3 Bivariate Generalization of Univariate PCIs for Unilateral Specification Limits
87(1)
4.4 Bivariate PCIs for Circular Specification Region
88(17)
4.5 Numerical Examples
105(2)
4.5.1 Example 1
105(1)
4.5.2 Example 2
106(1)
4.6 Concluding Remarks
107(5)
Bibliography
108(4)
5 Multivariate Process Capability Indices for Bilateral Specification Region Based on Principal Component Analysis (PCA)
112(18)
5.1 Introduction
112(1)
5.2 MPCIs Analogous to Univariate PCIs viz., Cp, Cpk, Cpm, and Cpmk
113(4)
5.2.1 Probability-Based MPCI Based on First Few Principal Components
115(2)
5.3 PCA-Based MPCIs with Unequal Weighting
117(1)
5.4 PCA-Based MPCIs Similar to Taam et al.'s [ 12] Ratio-Based MPCIs
118(2)
5.5 MPCIs Based on First Principal Component Only
120(3)
5.6 Some Other PCA-Based MPCIs
123(1)
5.7 A Real-Life Example
123(2)
5.8 Conclusion
125(5)
Bibliography
127(3)
6 Ratio-Based Multivariate Process Capability Indices for Symmetric Specification Region
130(38)
6.1 Introduction
130(1)
6.2 MPCIs Defined as Multivariate Analogue of Cp
131(11)
6.3 MPCIs Defined as Multivariate Analogue of Cpk
142(5)
6.4 MPCIs Defined as Multivariate Analogue of Cpm
147(10)
6.5 CG(u,v) - A Super-structue of MPCIs
157(3)
6.6 A Numerical Example
160(3)
6.7 Concluding Remark
163(5)
Bibliography
164(4)
7 Multivariate Process Capability Indices for Asymmetric Specification Region
168(22)
7.1 Introduction
168(1)
7.2 MPCIs Generalizing Cp(v,v) for v - 0,1 and v -- 0,1 - A Geometric Approach (Grau [ 11])
169(5)
7.3 Multivariate Analogue of C'p (v, v), for v = 0,1 and v = 0,1 - An Alternative Approach
174(3)
7.3.1 Interrelationships between the Member Indices of Cm(v,v) for v = 0,1 and v = 0,1
175(2)
7.4 Threshold Value of CM(0,0)
177(7)
7.4.1 For Bivariate Case
177(4)
7.4.2 For Multivariate Case
181(1)
7.4.3 Plug-in Estimators of the Member Indices of Cmv,v) for v = 0,1 and V = 0,1 and Their Estimation Procedures
182(2)
7.5 A Real-Life Example
184(2)
7.6 Concluding Remark
186(4)
Bibliography
188(2)
8 Multivariate Process Capability Indices for Unilateral Specification Region
190(12)
8.1 Introduction
190(1)
8.2 MPCI for Unilateral Specification Region Based on Proportion of Nonconformance
191(4)
8.3 MPCI for Unilateral Specification Region Based on Principal Component Analysis
195(1)
8.4 A Numerical Example
196(3)
8.5 Concluding Remarks
199(3)
Bibliography
200(2)
9 Multivariate Process Capability Indices Based on Proportion of Nonconformance
202(12)
9.1 Introduction
202(1)
9.2 MPCIs Based on Location-Scale Family of Distributions
203(2)
9.3 Other MPCIs Based on Proportion of Conformance or Nonconformance
205(9)
Bibliography
211(3)
10 Multivariate Process Capability Indices for Quality Characteristics Having Nonnormal Statistical Distributions
214(22)
10.1 Introduction
214(1)
10.2 MPCIs for Nonnormal Data Using Principal Component Analysis
215(2)
10.3 MPCIs for Multivariate Nonnormal Data Using Distance Approach
217(4)
10.4 MPCIs Using Multivariate g and h Distribution
221(1)
10.5 MPCIs for Multivariate Nonnormal Processes Using Skewness Reduction Approach
222(4)
10.6 Nonparametric MPCIs for Nonnormal Processes
226(4)
10.7 Numerical Example
230(1)
10.8 Concluding Remark
231(5)
Bibliography
233(3)
11 Multivariate Process Capability Indices Based on Bayesian Approach
236(12)
11.1 Introduction
236(2)
11.2 Cb(D): A Bayesian MPCI Analogous to Cpk
238(2)
11.3 Vector Valued Multivariate Analogues of Cp and Cpk from Bayesian Perspective
240(3)
11.4 A Numerical Example
243(2)
11.5 Concluding Remark
245(3)
Bibliography
246(2)
12 Multivariate Process Capability Indices for Auto correlated Data
248(8)
12.1 Introduction
248(1)
12.2 MPCIs Analogous to Cp for Autocorrelated Processes
249(2)
12.3 MPCIs Analogous to Cpm for Autocorrelated Processes
251(1)
12.4 MPCIs for Autocorrelated Processes Having Unilateral Specification Region
251(1)
12.5 Data Analysis
252(1)
12.6 Concluding Remarks
253(3)
Bibliography
254(2)
13 Multivariate Process Capability Vectors
256(24)
13.1 Introduction
256(1)
13.2 Multivariate Process Capability Vectors for Bilateral Specification Region - A Modification of Traditional MPCIs
257(6)
13.3 Multivariate Process Capability Vector Based on One-Sided Models
263(5)
13.4 Multivariate Process Incapability Vector
268(3)
13.5 An MPCV for Both the Unilateral and Bilateral Specification Regions
271(3)
13.6 A Numerical Example
274(3)
13.7 Concluding Remark
277(3)
Bibliography
278(2)
14 MPCIs Denned by Other Miscellaneous Approaches
280(34)
14.1 Introduction
280(1)
14.2 Priority-Based Multivariate Process Capability Indices (MPCIs)
280(6)
14.3 MPCIs Based on Concepts of Linear Algebra
286(2)
14.4 Viability Index
288(5)
14.5 MPCIs Defined on Process-Oriented Basis
293(2)
14.6 Multivariate Process Performance Analysis with Special Emphasis on Accuracy and Precision
295(3)
14.7 Multivariate Process Capability Analysis Using Fuzzy Logic
298(6)
14.7.1 A Fuzzy Logic-Based MPCI
300(2)
14.7.2 Fuzzy Multivariate Process Capability Vector
302(2)
14.8 MPCIs for Processes Having Linear and Nonlinear Profiles
304(6)
14.8.1 MPCIs for Simple Linear Profile
304(3)
14.8.2 MPCIs for Multivariate Nonlinear Profiles
307(3)
14.9 Concluding Remark
310(4)
Bibliography
311(3)
15 Applications of MPCIs
314(14)
15.1 Introduction
314(1)
15.2 Supplier Selection Based on Multivariate Process Capability Analysis
314(5)
15.2.1 Supplier Selection Problem for Processes Having Symmetric Bilateral Specification Region
315(1)
15.2.2 Supplier Selection Problem for Processes Having Unilateral Specification Region
316(3)
15.2.3 Supplier Selection Problem for Processes Having Asymmetric Specification Region
319(1)
15.3 Assessing Process Capability of Multivariate Processes Affected by Gauge Measurement Error
319(3)
15.3.1 Impact of Gauge Measurement Error on MCP
320(1)
15.3.2 MPCIs Based on Principal Component Analysis for Processes Affected by Measurement Error
321(1)
15.4 Multiresponse Optimization Using MPCIs
322(2)
15.5 Concluding Remark
324(4)
Bibliography
325(3)
Conclusion 328(2)
Index 330
Dr. Ashis Kumar Chakraborty has completed B.Stat(Hons.) and M.Stat in Statistics from Indian Statistical Institute, Kolkata and Ph.D from Indian Institute of Science, Bangalore, India. He has authored several books and contributed in several other books. His reserach interest is in Reliability, particularly in software reliability, process control, hybrid modelling and similar areas. More than sixty articles are published by him in well known peer-reviewed national and international journals. He has about 35 years of teaching, training and consulting experience. He is a life member of Operations Research Society of India and Indian Association for Productivity, Quality and Reliability. He served in the governing body of both. He is in the editorial Advisory Board of two journals and a regular reviewer of articles for several international journals.

Dr. Moutushi Chatterjee Received her B.Sc. (Honours) degree in Statistics from University of Calcutta, M. Sc. in Statistics from Kalyani University and M. Tech. in Quality, Reliability and Operations Research (QROR) from Indian Statistical Institute, Kolkata, India. She has also done Ph. D. in QROR from Indian Statistical Institute,, Kolkata. At present she is working as an Assistant Professor of Statistics at Lady Brabourne College (affiliated to University of Calcutta). Her publications include 12 research articles in international journals and a Chapter in an edited book. Her primary research interests are multivariate statistics, statistical quality control, reliability analysis and supply chain management.
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