Handbook of Multivariate Process Capability Indices

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgements
Biography of First Author
Biography of Second Author
1. Introduction
	1.1. Concept of Process Capability Index
	1.2. Process Capability Indices in Six Sigma, Lean Six  and Design for Six Sigma (DFSS)
	1.3. Concept of Multivariate Process Capability Index (MPCI)
	1.4. Some Uses of Process Capability Indices
	1.5. Some Applications of MPCIs
	1.6. Overview of the Chapters
	Bibliography
2. Some Useful Concepts of Univariate and Multivariate Statistics
	2.1. Introduction
	2.2. Univariate Statistics
		2.2.1. Normal Distribution
			2.2.1.1. Properties of Normal Distribution
		2.2.2. Radial Error Distribution
		2.2.3. Folded Normal Distribution
		2.2.4. Uniform Distribution
		2.2.5. Log-Normal Distribution
		2.2.6. Exponential Distribution
	2.3. Estimation of Process Mean and Variance Using Control Chart
		2.3.1. Estimation of Process Mean and Variance Based on X????
R Chart Information
		2.3.2. Estimation of Process Mean and Variance Based on X???? S Chart Information
	2.4. Some Bayesian Concepts
	2.5. Multivariate Statistics
		2.5.1. Multivariate Normal Distribution
		2.5.2. Multivariate Folded Normal Distribution
	2.6. Principal Component Analysis (PCA)
	2.7. Delta Method
	Bibliography
3. Univariate Process Capability Indices
	3.1. Introduction
	3.2. Univariate Process Capability Indices for Symmetric Specication Limits
		3.2.1. Unication of Univariate PCIs for Symmetric Specication Limits
	3.3. Univariate Process Capability Indices for Asymmetric Specication Limits
		3.3.1. Uni cation of Univariate PCIs for Asymmetric Specication Limits
	3.4. Univariate Process Capability Indices for Unilateral (One-Sided) Specication Limits
		3.4.1. Unication of Univariate PCIs for Unilateral Specication Limits
	3.5. Univariate Process Capability Indices for Non-Normal Distributions
	3.6. Univariate Process Capability Indices PNC
	3.7. Univariate Process Capability Assessments Using Bayesian Approach
	3.8. Concluding Remarks
	Bibliography
4. Bivariate Process Capability Indices (BPCIs)
	4.1. Introduction
	4.2. Bivariate Generalization of Univariate PCIs for Bilateral Specication Limits
	4.3. Bivariate Generalization of Univariate PCIs for Unilateral Specication Limits
	4.4. Bivariate PCIs for Circular Specication Region
	4.5. Numerical Examples
		4.5.1. Example 1
		4.5.2. Example 2
	4.6. Concluding Remarks
	Bibliography
5. Multivariate Process Capability Indices for Bilateral Specication Region Based on Principal Component Analysis (PCA)
	5.1. Introduction
	5.2. MPCIs Analogous to Univariate PCIs viz., Cp, Cpk, Cpm, and Cpmk
		5.2.1. Probability-Based MPCI Based on First Few Principal Components
	5.3. PCA-Based MPCIs with Unequal Weighting
	5.4. PCA-Based MPCIs Similar to Taam et al.'s [12] Ratio-Based MPCIs
	5.5. MPCIs Based on First Principal Component Only
	5.6. Some Other PCA-Based MPCIs
	5.7. A Real-Life Example
	5.8. Conclusion
	Bibliography
6. Ratio-Based Multivariate Process Capability Indices for Symmetric Specification Region
	6.1. Introduction
	6.2. MPCIs Dened as Multivariate Analogue of Cp
	6.3. MPCIs Dened as Multivariate Analogue of Cpk
	6.4. MPCIs Dened as Multivariate Analogue of Cpm
	6.5. CG(u; v) ???? A Super-structue of MPCIs
	6.6. A Numerical Example
	6.7. Concluding Remark
	Bibliography
7. Multivariate Process Capability Indices for Asymmetric Specification Region
	7.1. Introduction
	7.2. MPCIs Generalizing C 0p (u; v) for u = 0; 1 and v = 0; 1 ???? A Geometric Approach (Grau [11])
	7.3 Multivariate Analogue of C0p (u; v), for u = 0; 1 and v = 0; 1 ???? An Alternative Approach
		7.3.1. Interrelationships between the Member Indices of CM(u; v) for u = 0; 1 and v = 0; 1
	7.4. Threshold Value of CM(0; 0)
		7.4.1. For Bivariate Case
		7.4.2. For Multivariate Case
		7.4.3. Plug-in Estimators of the Member Indices of CM(u; v) for u = 0; 1 and v = 0; 1 and Their Estimation Procedures
	7.5. A Real-Life Example
	7.6. Concluding Remark
	Bibliography
8. Multivariate Process Capability Indices for Unilateral Specification Region
	8.1. Introduction
	8.2. MPCI for Unilateral Specication Region Based on Proportion of Nonconformance
	8.3. MPCI for Unilateral Specication Region Based on Principal
Component Analysis
	8.4. A Numerical Example
	8.5. Concluding Remarks
	Bibliography
9. Multivariate Process Capability Indices Based on Proportion of Nonconformance
	9.1. Introduction
	9.2. MPCIs Based on Location-Scale Family of Distributions
	9.3. Other MPCIs Based on Proportion of Conformance
	Bibliography
10. Multivariate Process Capability Indices for Quality Characteristics Having Nonnormal Statistical Distributions
	10.1. Introduction
	10.2. MPCIs for Nonnormal Data Using Principal Component Analysis
	10.3. MPCIs for Multivariate Nonnormal Data Using Distance Approach
	10.4. MPCIs Using Multivariate g and h Distribution
	10.5. MPCIs for Multivariate Nonnormal Processes Using Skewness Reduction Approach
	10.6. Nonparametric MPCIs for Nonnormal Processes
	10.7. Numerical Example
	10.8. Concluding Remark
	Bibliography
11. Multivariate Process Capability Indices Based on Bayesian Approach
	11.1. Introduction
	11.2. Cb(D) : A Bayesian MPCI Analogous to Cpk
	11.3. Vector Valued Multivariate Analogues of Cp and Cpk from Bayesian Perspective
	11.4. A Numerical Example
	11.5. Concluding Remark
	Bibliography
12. Multivariate Process Capability Indices for Autocorrelated Data
	12.1. Introduction
	12.2. MPCIs Analogous to Cp for Autocorrelated Processes
	12.3. MPCIs Analogous to Cpm for Autocorrelated Processes
	12.4. MPCIs for Autocorrelated Processes Having Unilateral Specification Region
	12.5. Data Analysis
	12.6. Concluding Remarks
	Bibliography
13. Multivariate Process Capability Vectors
	13.1. Introduction
	13.2. Multivariate Process Capability Vectors for Bilateral Specication
Region ???? A Modication of Traditional MPCIs
	13.3. Multivariate Process Capability Vector Based on One-Sided Models
	13.4. Multivariate Process Incapability Vector
	13.5. An MPCV for Both the Unilateral and Bilateral Specication Regions
	13.6. A Numerical Example
	13.7. Concluding Remark
	Bibliography
14. MPCIs Defined by Other Miscellaneous Approaches
	14.1. Introduction
	14.2. Priority-Based Multivariate Process Capability Indices (MPCIs)
	14.3. MPCIs Based on Concepts of Linear Algebra
	14.4. Viability Index
	14.5. MPCIs Defined on Process-Oriented Basis
	14.6. Multivariate Process Performance Analysis with Special Emphasis on Accuracy and Precision
	14.7. Multivariate Process Capability Analysis Using Fuzzy Logic
		14.7.1. A Fuzzy Logic-Based MPCI
		14.7.2. Fuzzy Multivariate Process Capability Vector
	14.8. MPCIs for Processes Having Linear and Nonlinear
		14.8.1. MPCIs for Simple Linear Profile
		14.8.2. MPCIs for Multivariate Nonlinear Profiles
	14.9. Concluding Remark
	Bibliography
15. Applications of MPCIs
	15.1. Introduction
	15.2. Supplier Selection Based on Multivariate Process Capability Analysis
		15.2.1. Supplier Selection Problem for Processes Having Symmetric Bilateral Specication Region
		15.2.2. Supplier Selection Problem for Processes Having Unilateral
Specication Region
		15.2.3. Supplier Selection Problem for Processes Having Asymmetric
Specication Region
	15.3. Assessing Process Capability of Multivariate Processes Aeffcted by Gauge Measurement Error
		15.3.1. Impact of Gauge Measurement Error on MCp
		15.3.2. MPCIs Based on Principal Component Analysis for Processes Affected by Measurement Error
	15.4. Multiresponse Optimization Using MPCIs
	15.5. Concluding Remark
	Bibliography
Conclusion
Index