Monitoring capability study and genetic economic design of X-bar control chart

Abstract

Employing automatic gauges is one of the fundamental steps in advanced manufacturing system not only for assuring product quality, but also monitoring process stability. Statistical process control (SPC), therefore, is developed to detect the occurrence of assignable causes so that unnecessary quality costs can be avoided. However, it is necessary to provide a practical way to evaluate the monitoring capability of an automatic gauge for its application. That is, the monitoring capability study should be conducted before applying any automatic gauge on SPC application. The economic SPC chart then can be properly designed. Rather than conventionally considering the relationship between both manufacturing cappability and control limits, gauge capability is further and concurrently considered to analyze the monitoring error of an automatic gauge in this paper. After interpreting the effect of manufacturing capability, gauge capability, and control limits to construct the monitoring error model, furthermore, the engineer can then distinctly evaluate monitoring capability by the expected cost incurred in the SPC process. Also, genetic algorithm is successfully applied to determine the economic design of X-bar control chart with the realistic monitoring error model embedded.