Quality of a product is often measured through various quality characteristics generally correlated. Multivariate control charts are a response to the need for quality control in such situations. If quality characteristics are qualitative, it sometimes happens that the product quality is defined by linguistic variableswhere quality levels are represented by some specific words-and product units are classified into several linguistic forms categories, depending on the degree of fulfillment of expectations, creating a situation of fuzzy classifications. This paper first reviews the concepts found in the literature on the development of fuzzy multivariate control charts. We propose a method to control these fuzzy quality evaluations, with correlated multiple attributes quality characteristics, through the use of a Hotelling T 2 control chart

PurposeThis research proposes a multivariate control chart, whose parameters are optimized using genetic algorithms (GA) in order to accelerate the detection of a change in the vector of means.Design/methodology/approachThis chart is based on a variation of the Hotelling T2 chart using a sampling scheme called generalized multiple dependent state sampling. For the analysis of performances of this chart, the out-of-control average run length (ARL) values were used for different scenarios. In this comparison, it was considered the classic Hotelling T2 chart and the T2 chart using the scheme called multiple dependent state sampling.FindingsIt was observed that the new chart with its optimized parameters is more efficient to detect an out-of-control process. Additionally, a sensitivity analysis was performed, and it was concluded that the best yields are obtained when the change to be considered in the optimization is small. An application in the resolution of a real problem is given.Originality/valueIn this research, a multivariate control chart is proposed based on the Hotelling T2 statistic but adding a sampling scheme. This makes this control chart more efficient than the classic T2 chart because the new chart not only uses the current information of the T2 statistic but also conditions the decision to consider a process as “in- control” on the statistic's previous information. The practitioner can obtain the optimal parameters of this new chart through a friendly program developed by the authors.

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The aim of this paper is to improve the response of the Multivariate Multinomial Fuzzy T2 control chart to detect small shifts by the implementation of a MEWMA control chart. In this research a multivariate control chart based on the MEWMA chart is proposed to improve the sensitivity to detect small shifts in the vector of means of the T2 chart with fuzzy approach presented in the literature, to deal with p correlated multinomial multivariate variables. The parameters for the chart are obtained from historical data and the control limits by simulation. The performance of the new chart proposed is compared with the performance of the T2 control chart through the Average Run Length (ARL) value. The performance of this new chart can be obtained through a program developed by the authors.