An alternative approach to fuzzy control charts: Direct fuzzy approach

The major contribution of fuzzy set theory lies in its capability of representing vague data. Fuzzy logic offers a systematic base to deal with situations, which are ambiguous or not well defined. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. In this paper, some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of α-cut to provide the ability of determining the tightness of the inspection: the higher the value of α the tighter inspection. A new alternative approach "Direct Fuzzy Approach (DFA)" is also developed in this paper. In contrast to the existing fuzzy control charts, the proposed approach is quite different in the sense it does not require the use of the defuzziffication. This prevents the loss of information included by the samples. It directly compares the linguistic data in fuzzy space without making any transformation. We use some numeric examples to illustrate the performance of the method and interpret its results.