Fuzzy X¯ and R control charts: Fuzzy dominance approach

The statistical process control (SPC), an internationally recognized technique for improving products quality and productivity, has been widely employed throughout various industries. The SPC relies on the use of control charts to monitor a manufacturing process for identifying special causes in the process variation and signaling the necessity of a certain corrective action for the process. Since fuzzy data ubiquitously exist in the modern manufacturing process, for monitoring its sample average and variance, we propose the fuzzy X¯ and R control charts, whose fuzzy control limits are obtained on the basis of the results of the resolution identity, a well-known theory in the fuzzy set field. By using the fuzzy dominance approach, which compares the fuzzy averages and variances to their respective fuzzy control limits, we are capable of determining whether the manufacturing process is needed to be adjusted or not. Finally, a practical manufacturing process illustrates the proposed methodologies to show the potential application in monitoring its average and variability while its fuzzy sample data are taken into consideration.

► The fuzzy control limits are constructed from the resolution identity.
► A fuzzy dominance is used to compare the fuzzy control limits.
► Membership degrees can be obtained by solving the optimization problems.