ENBIS-8 in Athens

21 – 25 September 2008 Abstract submission: 14 March – 11 August 2008

A Two-Sided Multivariate c Control Chart

22 September 2008, 15:40 – 16:00


Submitted by
Paolo Cozzucoli
Paolo Cozzucoli
Department of Economics and Statistics, University of Calabria - Via P. Bucci, Cubo 0C , 87036 Rende (CS) , Italy
In modern industrial environment operators are frequently interested in evaluating the quality of complex products. Supposing that the quality of the product depends on several quality characteristics, then it is correct to use multivariate quality control methodology. If the quality characteristics are defined on nominal or ordinal scale then the corresponding process to monitor is known as multivariate attribute process. In this paper, we assume that the operator is interested in monitoring a Multivariate Poisson Process, that is the main purpose is to monitor simultaneously the number of non conformities belonging to each of the k ordered, distinct and not mutually exclusive defect categories; specifically, defects of different types may be classified according to the degree of effect that they have on the performance of the product. Usually the process is said to be capable if the total number of defect, identified on the selected inspection unit, is very small and remains low, or declines, over time. In this case, because we have chosen to classify the defects into k ordered and not mutually exclusive classes of defects, the overall number of non conformities identified on the inspection unit depends on the k categories, which are not necessary independent, and we are interested in evaluating over time the number of defects in each category as well as the overall (across the k categories) number of nonconforming items. Also, we may use this approach to evaluate the overall demerit in the system. To achieve this goal, in this paper we propose i) a normalized index that can be used to evaluate the overall quality of the process in terms of the weighted sum of non conformities identified in each class of defects and ii) a two sided Shewhart-type multivariate control chart with asymptotic probabilistic limits useful to monitor the overall number of nonconformities for each inspection unit. In addition, we suggest a solution to the identification problem when an out control signal occurs. The same sample statistic is used to define the normalized index and the multivariate c control chart.
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