On Capability Indices for Multivariate Autocorrelated Processes

  • Sueli Aparecida Mingoti UFMG
  • Fernando Luiz Pereira De Oliveira UFOP
Keywords: Autocorrelated processes, Bootstrap, Multivariate capability indices, Multivariate time series


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

Author Biographies

Sueli Aparecida Mingoti, UFMG
Sueli Aparecida Mingoti is an Associate Professor at the Statistics Departament of Federal University of Minas Gerais (UFMG),Brazil. She received her Ph.D degree in Statistics from the Iowa State University located at Ames, United States of America, in 1989. Her research interests includes applied probability and inference, multivariate and industrial statistics.
Fernando Luiz Pereira De Oliveira, UFOP
Fernando Luiz Pereira de Oliveira  received his D.Sc. from the Department of Statistics at Federal University of Minas Gerais, in 2011. Since then he has been serving on the Department of Mathematics at Federal University of Ouro Preto (UFOP), Minas Gerais, Brazil. His major interests are process capability, statistical quality control and clusters detection.
How to Cite
Mingoti, S. A., & De Oliveira, F. L. (2011). On Capability Indices for Multivariate Autocorrelated Processes. Brazilian Journal of Operations & Production Management, 8(1), 133-152. Retrieved from https://bjopm.emnuvens.com.br/bjopm/article/view/V8N1A9