Handbook of Multivariate Process Capability Indices

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, de?ned 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 di?erent 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 de?ned for various types of speci?cation 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 di?cult 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 di?erent 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.

1 Introduction

2 Some Useful Concepts of Univariate and Multivariate Statistics

3 Univariate Process Capability Indices

4 Bi-variate Process Capability Indices (BPCIs)

5 Multivariate Process Capability Indices for Bilateral Specification Region Based on Principal Component Analysis (PCA)

6 Ratio Based Multivariate Process Capability Indices for Symmetric Specification Region

7 Multivariate Process Capability Indices for Asymetric Specification Region

8 Multivariate Process Capability Indices for Unilateral Specification Region

9 Multivariate Process Capability Indices Based on Proportion of Non-conformance

10 Multivariate Process Capability Indices for Quality Characteristics Having Non-Normal Statistical Distributions

11 Multivariate Process Capability Indices Based on Bayesian Approach

12 Multivariate Process Capability Indices for Auto-correlated Data

13 Multivariate Process Capability Vectors

14 MPCIs Defined by Other Miscellaneous Approaches

15 Applications of MPCIs

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.