Economic Statistical Design of Multivariate 􀢀􀫛 Control Chart with Variable Sample Sizes

Today, quality improvement and cost reduction are key factors for achieving business success, growth and position. One of the primary tools for quality improvement and cost reduction in online activities of statistical process control is control charts. As the need for monitoring several correlated quality characteristics is extensively growing, the use of multivariate control charts becomes more popular. Among these, the ???? control chart is the most popular due to many advantages. In this paper, the variable sampling scheme is studied to increase the power of the fixed sampling rate (??????) ???? control chart to show small shifts. In this study, one of the parameters of ???? control chart, e.g., the sample size, vary between three values, depending on the most recent ???? value. The design of ???? control chart with three variable sample sizes (3??????) from the statistical and economic perspective has been investigated, when the shift in the process mean does not occur at the beginning but at some random time in the future. Therefore, the Markov Chain approach used to develop the cost function. Then, the genetic algorithm (GA) is applied to search for the optimal values of the parameters of the 3?????? control chart. Finally, numerical comparisons among ?????? and 3?????? schemes are made and discussed.