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, deﬁned 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 diﬀerent 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 deﬁned for various types of speciﬁcation regions. This book is intended to help quality professionals to understand which MPCI should be used and in what situation. For researchers in this ﬁeld, 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 diﬃcult to understand, since there is more than one quality characteristic to be controlled at a time.
- A complete guide for quality professionals on the usage of diﬀerent 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 ﬁeld of Industrial Statistics, as well as practitioners requiring thorough guidance regarding selection of an appropriate MPCI suitable for the problem at hand.
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