FEWMA and Fuzzy Regression Model Control Chart one a-cut With Application

Abstract

In many real-world applications, the data to be used in a control charting method are not crisp since they are approximated due to environmental uncertainties, In these situations, fuzzy numbers and linguistic variables are used to grab such uncertainties. That is why the use of a fuzzy control chart, in which fuzzy data are used, is justified. As an exponentially weighted moving average (EWMA) scheme is usually used to detect small shifts, in this paper a fuzzy EWMA (F-EWMA) control chart is proposed to detect small shifts in the process mean when fuzzy data are available. As well as The fuzzy regression control chart which is a functional technique to evaluate the process in which the average has a trend and the data represents a linguistic or approximate value.

In this paper, the application of fuzzy logic in statistical quality control have been done by plotting fuzzy EWMA chart and Fuzzy linear regression model control chart depending on a suggested algorithm prepared for this purpose, as well as the theoretical structure of the “a-level fuzzy midrange for a-cut fuzzy -regression control chart” is proposed for triangular  membership functions and applying that to the chemical analysis data of a water component, Total Dissolved Solid ( TDS) in water from the KANY Factory to  detect small shifts in the process means, the data contains three groups (TDS-a, TDS-b, TDS-c), for 24 days each day containing 5 hour data, as shown in Table (1)

The comparison showed that the fuzzy linear regression model Control chart is a good technique and more suitable, accuracy, sensitivity than the traditional linear regression model Control chart.