On Capability Indices for Multivariate Autocorrelated Processes

• Autor(a) principal: Mingoti, Sueli Aparecida
• Data de Publicação: 2011
• Outros Autores: De Oliveira, Fernando Luiz Pereira
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Brazilian Journal of Operations & Production Management (Online)
• Texto Completo: https://bjopm.org.br/bjopm/article/view/V8N1A9
• topic: Autocorrelated processes; Bootstrap; Multivariate capability indices; Multivariate time series

In this paper the effects of the autocorrelation on some multivariate capability indices commonlyused for independent processes are discussed and a correction is proposed. Some results are shownfor VARMA(1,1) and VAR(1) time series processes under the multivariate normality assumptionand the proportion of non-conforming units is calculated for some bivariate VAR(1) models. Anextension of Veevers capability index for non-centered processes is also a subject addressed inthis paper. An example of application in blast charcoal furnace pig iron process is presented andbootstrap is used to build confidence intervals for its true capability value as well as to evaluatethe performance of the capability estimators. Similar as to what is already known for univariateprocesses the results showed that autocorrelation has a large impact in the multivariate capabilitiesindices. This paper also shows that some care should be taken when using Niverthi and Dey’scapabilities indices since they are very sensitive to any deviations from the process means tothe specification means up to a point that a capable process might be considered non-capable.