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Performance of Multivariate Process Capability Indices Under Normal and Non‐Normal Distributions
Author(s) -
Dianda Daniela F.,
Quaglino Marta B.,
Pagura José A.
Publication year - 2016
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1939
Subject(s) - process capability , principal component analysis , process capability index , process (computing) , multivariate statistics , context (archaeology) , quality (philosophy) , computer science , multivariate normal distribution , range (aeronautics) , sensitivity (control systems) , measure (data warehouse) , data mining , reliability engineering , statistics , econometrics , mathematics , work in process , machine learning , engineering , artificial intelligence , operations management , paleontology , philosophy , epistemology , electronic engineering , biology , operating system , aerospace engineering
In the context of process capability analysis, the results of most processes are dominated by two or even more quality characteristics, so that the assessment of process capability requires that all of them are considered simultaneously. In recent years, many researchers have developed different alternatives of multivariate capability indices using different approaches of construction. In this paper, four of them are compared through the study of their ability to correctly distinguish capable processes from incapable processes under a diversity of simulated scenarios, defining suitable minimum desirable values that allow to decide whether the process meets or does not meet specifications. In this sense, properties analyzed can be seen as sensitivity and specificity, assuming that a measure is sensitive if it can detect the lack of capability when it actually exists and specific if it correctly identifies capable processes. Two indices based on ratios of regions and two based on the principal component analysis have been selected for the study. The scenarios take into account several joint distributions for the quality variables, normal and non‐normal, several numbers of variables, and different levels of correlation between them, covering a wide range of possible situations. The results showed that one of the indices has better properties across most scenarios, leading to right conclusions about the state of capability of processes and making it a recommendable option for its use in real‐world practice. Copyright © 2015 John Wiley & Sons, Ltd.