Abstract

Control charts are widely used in manufacturing and non-manufacturing processes to monitor process average and to reduce variations in quality characteristic. The variations could be either due to common causes, which are inherent nature of the process and unavoidable, or assignable causes which can be diagnosed for rectification. The state of the process, i.e., whether or not the process is statistically in control, is traditionally judged using control limits and unnatural patterns exhibited on control charts. These unnatural patterns, in addition to help in determining the process state, also provide hints on possible assignable cause(s) whenever the process goes out of control. However, there are certain ambiguities associated with this traditional method, such as judging the process state when a point falls exactly on or very near to control limits and vagueness in interpreting unnatural patterns when multiple patterns co-exist on the control chart and relating them to assignable cause. Fuzzy logic has been proved to be an excellent tool for handling such ambiguities and vagueness by quantifying the uncertainty mathematically. A fuzzy inference engine is developed for X歔 chart, based on a chart pattern-cause relationship network. The domain of assignable causes is categorized based on the nature of the shift they can produce, and accordingly related to chart patterns. Each link in the network is represented by a fuzzy inference system which determines the intensity of each cause in the interval [0-1] based on degree of presence of each pattern. All the evidence supporting each cause from the unnatural patterns are aggregated using fuzzy connective operators (max, algebraic sum) and causes are prioritized accordingly so that when process goes out of control, the investigation can be done for the cause having highest priority. The developed fuzzy inference engine is tested with different combinations of unnatural patterns and the results are compared with manual interpretation of control charts and with results from a control chart software tool (MINITAB)