Performance Comparisons for the Synthetic Control Chart for Detecting Increases in Fraction Nonconforming

Abstract

The performance of the recently proposed synthetic control chart for detecting increases in fraction nonconforming is re-evaluated and comparisons with a wider range of alternative charts are presented. It is shown that the previously reported strong performance of the synthetic chart was due to the implicit inclusion of a ‘head-start’ feature when computing the reported values of average time to signal (ATS). The comparisons considered here, using both initial-state and steady-state evaluations of ATS, show that, without the head-start feature, the performance of the synthetic chart is not much better than that of the np chart and also that there are better alternatives, in particular, the use of a CUSUM of the run lengths of conforming items (termed the run-length CUSUM). Consideration may also be given to the use of the RL2 chart, which is based on the moving sum of two successive conforming run lengths. While the superior performance of the run-length CUSUM is clearly demonstrated, the RL2 chart also performs quite well, except for specified circumstances, when it should not be used.