Modeling attribute control charts by interval type-2 fuzzy sets

Fuzzy attribute control charts, where data are classified into conforming/nonconforming product units, are used to monitor fuzzy fractions of nonconforming units for variable sample sizes and the fuzzy number of nonconforming units for constant sample sizes. Data defined as quality characteristics can be imprecise due to the subjective decisions of the quality control operator. Type-2 fuzzy set theory deals with ambiguity associated with the uncertainty of membership functions by incorporating footprints and modeling high-level uncertainty. In this paper, the structure of an interval type-2 fuzzy p-control chart and interval type-2 fuzzy np-control chart with constant sample size are developed and applied to real data. The main advantage in using interval type-2 fuzzy sets in control charts is the flexibility allowed in determining control limits for process monitoring by incorporating fuzzy set theory. Therefore, fuzzy control charts with interval type-2 fuzzy numbers afford the decision maker the opportunity to see and detect process defects.