A demerit control chart with linguistic weights

A classical demerit control chart is used to monitor counts of several different categories of defects simultaneously in a complex product. The traditional recommendation is to plot the demerit statistic, a weighted sum of the number of defects of each category, on a control chart. Such approach assumed that the severe degree of the same category is equally treated and a crisp weight is assigned subjectively. Furthermore, the assignment of an actual and crisp weight to each category is somewhat difficult for process and quality engineers. A linguistic variable to represent the importance and severity is more suitable. Thus, on the basis of the fuzzy set theory, the fuzzy demerit control chart which uses linguistic weights to represent the severe degree of each category is proposed. The procedure of constructing the proposed chart is described in five steps. In addition, a fuzzy ranking method using α-cuts is adopted to generate the crisp statistic and control limits in coordination with the custom of classical control charts. A guideline is suggested for deciding the values of α and the width of control limits. By a numerical example, the results show that such approach can provide more realistic modeling to monitor the number of demerits per inspection unit and identify the process variation.