Recent studies have shown that a double sampling (DS) scheme yields improvements in detection times of process shifts over variable ratio sampling (VRS) methods that have been extensively studied in the literature. Additionally, a DS scheme is more practical than some of the VRS methods since the sampling interval is fixed. In this paper, we investigate the effect of double sampling on cost, a criterion as important as detection rate. We study economic statistical design of the DS T 2 chart (ESD DS T 2) so that designs are found that are economically optimal but yet meet desired statistical properties such as having low probabilities of false searches and high probabilities of rapid detection of process shifts. Through an illustrative example, we show that relatively large benefits can be achieved in a comparison with the classical T 2 chart and the statistical DS T 2 charts with our ESD DS T 2 approach. Furthermore, the economic performance of the ESD DS T 2 charts is favorably compared to the MEWMA and other VRS T 2 control charts in the literature.
- Hotelling's T control chart
- double sampling (DS)
- economic statistical design (ESD)
- genetic algorithm (GA)