Combining process and product information for quality improvement

Abstract

This paper considers a two-step monitoring scheme that is used to jointly monitor process and product characteristics for manufacturing quality improvement. The two-step monitoring scheme uses an X¯ chart to continuously monitor the mean of the process characteristics. When the process sample mean falls outside of control limits, a warning signal triggers an np chart to check product quality. If the number of nonconforming products exceeds a pre-determined threshold, corrective actions are initiated to restore the manufacturing process back to normal. Otherwise, the process will continue with X¯ chart monitoring individually. We derive an economic model for the two-step monitoring scheme, which considers general cases where sampling costs for both process and product quality characteristics are involved. It is shown that the two-step monitoring scheme includes the traditional process and product control charts as special cases. We compare the two-step monitoring scheme with the individual process and product control charts, respectively, in terms of economic efficiency. Analytical conditions are derived under which the two-step monitoring scheme is preferred against the individual charts in practice. Numerical examples are provided to demonstrate the effectiveness and sensitivity of the comparison.