CONTROL CHARTS FOR STATIONARY VECTOR ARMA PROCESSES

J. Yadavalli, S.J. Claasen, N. Singh

Abstract


ENGLISH ABSTRACT: In practice, there are many quality control situations where a product under consideration may have two or more interrelated quality characteristics and observations of each characteristic are serially correlated. One of the objectives of management is to investigate whether or not all these characteristics of the product simultaneously satisfy the required specifications. To the author's best knowledge, no concrete attempts have been made so far to construct the control charts for such situations, particularly when the data arise from vector autoregressive-moving average (VARMA) processes. It is this problem that has been addressed in this paper. A few methods are suggested for constructing the control charts. When assumptions about independence and normality break down, a bootstrap method, perhaps for the first time, is suggested to attack the problem. Some illustrative examples are discussed.

AFRIKAANSE OPSOMMING: In die praktyk is daar vele kwaliteitbeheersituasies waar 'n betrokke produk een of twee onderling verbonde kenmerke kan hen waarnemings van elke kenmerk serie gekorreleer is. Een van die doelwitte van bestuur is om te ondersoek of hierdie kenmerke van die produk gelyktydig aan die vereiste spesifikasies voldoen al dan nie. Na die outeur se beste wete, is daar tot dusver geen daadwerklike pogings aangewend om die beheergrafieke vir sodanige situasies op te stel nie, veral waar die data ontstaan uit vektor outoregressief bewegende gemiddelde (VARMA) prosesse. Hierdie probleem geniet in hierdie artikel aandag. 'n Aantal metodes vir die opstel van die beheergrafieke word voorgestel. Wanneer aannames oor selfstandigheid en normaliteit faal, word 'n skoenlusmetode voorgestel om die probleem die hoof te bied. 'n Aantal voorbeelde ter toeligting word bespreek.


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DOI: https://doi.org/10.7166/14-1-296

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