Weighted signal-to-noise ratio robust design for a new double sampling npx chart. (January 2020) - Zhou, Wenhui; Wang, Zixuan; Xie, Wei
Highlights: The WSNR robust design has the smallest mean and variance than traditional design. The WSNR robust design can minimize the worst case and control data fluctuations. The new design outperforms than other robust designs as the uncertainty increases. The DS npx chart is better than the npx chart in controlling the process cost. Abstract: Recently, to monitor the mean shifts of a process by using attribute inspection, a new np chart, called np x 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) np x chart to improve the efficiency of the single-sampling np x chart. We build up a process cost model to compare the performance of DS np x chart and the traditional np x 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 np x chart is superior to the np x chart in controlling the ARL 1 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.