ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

Phase I Distribution-Free Analysis of Multivariate Data: Current Approaches and New Proposals

13 September 2016, 12:10 – 12:40

Abstract

Submitted by
Giovanna Capizzi
Authors
Giovanna Capizzi (Department of Statistical Sciences, University of Padua)
Abstract
Phase I distribution-free methods have received an increasing attention in the recent statistical process monitoring literature. A general discussion and some contributions in the univariate framework can be found in Capizzi (2015), Jones-Farmer et al (2009), Jones-Farmer, Champ (2010), Graham et al (2010) and Capizzi, Masarotto (2013). Two distribution-free Phase I Shewhart control charts, based on the Mahalanobis depth ranks and the spatial signs, have been recently suggested for the analysis of subgrouped data from a multidimensional elliptical distribution. The need for using distribution-free methods in Phase I applications will be illustrated. After briefly reviewing the existing nonparametric Phase I procedures for multivariate observations, two alternative Shewhart schemes, based on multivariate signed and spatial ranks, respectively will be introduced and discussed. Following the proposed approach, the assumption of an elliptical underlying distribution, often difficult to be checked before establishing process stability, can be avoided, also when the sample size is not large. Further, a multivariate generalization of the Recursive Segmentation and Permutation procedure, suggested in Capizzi, Masarotto (2013), is introduced. This new Phase I control chart (i) can handle individual and sugbgrouped multivariate data; (ii) does not require that the in-control distribution belongs to the elliptical family and it can be used for the simultaneous monitoring of discrete count and continuous variables; (iii) is designed to effciently detect isolated or single-step shifts but also more complex out-of-control patterns commonly encountered in practical applications. The results of a simulation study will be presented to compare the different surveillance schemes in a variety of out-of-control scenarios.
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