Weighted signal-to-noise ratio robust design for a new double sampling [formula omitted] chart

Abstract

Recently, to monitor the mean shifts of a process by using attribute inspection, a new np chart, called npx chart, was proposed to synthesize the advantages of attribute and variable charts. Attracted by the easy-implementation property and good performance of this chart, in this paper, we propose a double-sampling (DS) npx chart to improve the efficiency of the single-sampling npx chart. We build up a process cost model to compare the performance of DS npx chart and the traditional npx chart. To minimize the process cost with uncertainty, we introduce a robust design method based on the “weighted signal-to-noise ratio (WSNR)”. Specifically, we take into account the weighted expectation on multiple scenarios and regard signal-to-noise ratio as a response to variance. Compared to the traditional designs, the WSNR robust design not only preserves the statistical strengths and economic efficiency, but also shows the advantages of flexibility and adaptability. Then, numerical experiments are conducted to measure the performance of our model. The results demonstrate that the DS npx chart is superior to the npx chart in controlling the ARL1 and the process cost. By analyzing the process cost, we find that the larger the scenario range is, the better the WSNR robust design performs. In addition, the performance of the proposed robust design presents clear advantages to the existing robust measures (e.g., absolute robustness, robust deviation, and relative robustness), for which the WSNR will be a promising approach for the practitioners.