Two-stage control charts for high yield processes

In this paper, a two-stage control chart for monitoring the defective rate of high-yield processes is proposed and studied. The Cumulative Count of Conforming control chart is generalized by using the number of items inspected until two defective items are observed. As this will increase the time to alarm, a two-stage approach combining both schemes is proposed. The occurrence of a defective within n1 items inspected in the first stage indicates that the process is out of control. If no defective occurs within n1 items inspected, the occurrence of two defectives within the next n2 - n1 in the second stage also indicates that the process is out of control. The probability of making a false alarm at the first and second stages are equal to α1 and α2, respectively. This procedure improves the sensitivity of the control chart in detecting shifting of the process defective rate p when p is at the parts-per-million order of magnitude.