CONTROL CHART TO PROCESSES WITH CROSS-AUTOCORRELATION Requeijo,

Abstract: Today's society is characterized by consumers becoming more educated and demanding for products and services they use. Wherever, organizations are structured to respond the explicit or implicit needs of consumers, which lead to increased competitiveness of organizations. This competitiveness is reflected in the ongoing quest to provide high quality products and excellence process development. The monitoring of productive processes is essential to respond adequately to these objectives and therefore the implementation of statistical techniques suited to different situations is crucial, as is the case of statistical control charts introduced in the 1920s by Walter Shewhart. The Statistical Process Control (SPC), initially applied to a single variable, proved inadequate in studying simultaneously several quality characteristics of the same product. T 2 Charts, introduced in 1985 by Alt, are the appropriate statistical techniques to the simultaneous control of the averages of several product characteristics, advantages over the univariate study, once on the other hand it prevents the production of a large number of documents and leads to more accurate analysis by considering the correlation among variables. As for the univariate study, the multivariate control is based on the assumptions of Normality and data independence of all characteristic. When the assumption of independence of at least one characteristic is violated, the construction of T 2 charts directly on the data is an inadequate solution, being necessary to isolate the autocorrelation for each variable and construct T 2 charts based on residuals/forecast errors. Another relevant question, that has not deserved much attention by the scientific community, is related with possibility of cross-autorrelation existence among variables, i.e., the autocorrelation occurring in a variable is not exclusive of the influence of that variable but its effect may be transmitted for part or all variables. This paper presents a methodology for implementation of multivariate statistical control, considering the cross-autocorrelation, both for Phase I (preliminary or retrospective) and Phase II (monitoring) statistical control. In Phase I, it seems that the process is in-control and estimates the process parameters, the mean vector and covariance matrix. In addition, the multivariate process capability using specific indicators will be study. One suggestion is the use of capability indices CpM, PV, and LI. Verified the stability and capability of the process, Phase II begins consisting of monitoring the process in real time based on estimates performed in Phase I. When there is significant autocorrelation at least in one of the variables, it is necessary to model the process in order to contemplate cross-autocorrelation effect acting in the variables. Variables are estimated by a VAR(p) model, considering only the significant parameters. An example application for Phase I of multivariate statistical process control is presented, as well as multivariate process capability.