Fuzzy MaxGWMA chart for identifying abnormal variations of on-line manufacturing processes with imprecise information

The exponentially-weighted-moving-average (EWMA) control chart was developed to detect small shifts in mean and variability of a key quality characteristic in a manufacturing process. To improve its performance, several modified statistical schemes on manipulation of random samples of real data (precise numbers) collected from the quality characteristic have been proposed. Among them, the recently recommended control chart named the maximum generally weighted moving average (MaxGWMA) is found superior in recognition of its outstanding diagnostic abilities at warning abnormal-manufacturing variations swiftly. In this paper, based on the well-known fuzzy set theory, we develop a Fuzzy-MaxGWMA (F-MaxGWMA) chart, an extension of the MaxGWMA chart, to well accommodate the fuzzy environment where both the randomness and fuzziness of imprecise sample data (fuzzy numbers) are taken into consideration. Moreover, for identifying assignable variations of the on-line manufacturing process with fuzzy data, an index-of-optimism criterion is implemented to instantaneously monitoring as well as classifying the process conditions into multi-intermittent states between in control and out of control. It can overcome the constraints of binary classifications of the process condition used by the MaxGWMA chart when fuzzy data inevitably appear in practical manufacturing processes. Finally, a realistic example to control the coating thickness of an industrial cutting-tool manufacturing process is illustrated to demonstrate the adaptability and effectiveness of this newly extended approach.