On the advantages of economically designed variable sample sizes and sampling intervals T2 control chart: double warning lines scheme

Faraz and Parsian (Stat Pap 47:569-593, 2006) have shown that the double warning lines (DWL) scheme detects process shifts more quickly than the other variable ratio sampling schemes such as variable sample sizes (VSS), variable sampling intervals (VSI) and variable sample sizes and sampling intervals (VSSVSI). In this paper, the DWL T-2 control chart for monitoring the process mean vector is economically designed. The cost model proposed by Costa and Rahim (J Appl Stat 28:875-885, 2001) is used here and is minimized through a genetic algorithm (GA) approach. Then the effects of the model parameters on the chart parameters and resulting operating loss is studied and finally a comparison between all possible variable ratio sampling (VRS) schemes are made to choose the best option economically.