FUZZY RULES FOR FUZZY X AND R CONTROL CHARTS

Abstract

Statistical process control (SPC), an internationally recognized technique for improving product quality and productivity, has been widely employed in various industries. SPC relies on the use of control charts to monitor a manufacturing process for identifying causes of process variation and signaling the necessity of corrective action for the process. Fuzzy data exist ubiquitously in the modern manufacturing process, and in this paper, two alternative approaches to control charts are developed for monitoring sample averages and range. These approaches are based on fuzzy mode and fuzzy rules methods, when the measures are expressed by non-symmetric triangular numbers. In contrast to the existing control charts, the proposed approach does not require the use of the defuzzication and this prevents the loss of information included in samples. A numeric example illustrates the performance of the method and interprets the results. Statistical process control (SPC) is a large class of methods aiming at evaluating, monitoring and possibly reducing variability in industrial production processes and it plays an important role to assure the process is in statistical control. The two of the SPC functions are control charts and process capability analyses (PCA). Even though the rst control chart was proposed by Shewhart (19), today they are still subject to new application areas that deserve further attention. Control charts are used to monitor whether or not the process is in statistical control. These charts are based on data representing one or several quality-related characteristics of the product or service. If these characteristics are measurable on a numerical scale, then variable control charts are used. If the quality-related characteristics cannot be easily represented in a numerical form, then attribute control charts are useful. Shewhart control charts consist of a center line, the estimated process nominal level, and two control lines, the upper control limit and the lower control limit (usu- ally set at away from the center line with a distance of three-sigma), indicating the boundaries of the normal variability that are used to verify whether the ma- jority of the observations (approximately 99.73%) are lying within control limits. A process is in statistical control, if the control chart displays known patterns of variation and if the control chart points deviate from these known patterns, the process is considered to be out of control. Precise data are not always available. So, the theory of sets can adequately model processes where observed data are uncertain. Therefore, some researchers