Shewhart Control Chart Based on Fuzzy Data with Ranked Set Sampling

Quality control charts with fuzzy data have been successfully used in many real-world applications in recent years. These methods have been extended to estimate the fuzzy population mean based on simple random sampling techniques. In this study, a different strategy is used to develop Shewhart control charts with fuzzy means based on fuzzy data. For this purpose, the conventional rank set sampling is first extended to a well-established fuzzy random variable. Then, based on the concept of fuzzy mean and exact variance, the lower, mean, and upper fuzzy control charts are introduced.Additionally, an estimation procedure is presented that can be used to evaluate the proposed fuzzy control limits in cases where the fuzzy mean and exact variance of the population are unknown. An inclusion degree for monitoring process variability is also introduced and discussed. A real case study from photolithography is presented to demonstrate the efficiency of the proposed method for monitoring control charts with fuzzy data based on fuzzy rank set sampling.

کلیدواژه ها:

Fuzzy random variable ، fuzzy control chart ، fuzzy ranked set sampling ، degree of inclusion ، fuzzy control region ، fuzzy mean ، exact variance