Joint economic design of variable sampling intervals ((X)over-bar) and R charts using genetic algorithms

Control charting is a graphical expression and operation of statistical hypothesis testing. In this article, we develop the joint economic design of the variable sampling intervals (VSI) (X) over bar and R charts to determine the values of the seven test parameters of the charts (i.e., the sample size, the long sampling interval, the short sampling interval, the warning limits of the (X) over bar chart, the control limits of the (X) over bar chart, the warning limit of the R chart, and the control limit of the R chart) such that the expected total cost associated with the test procedure is minimized. The genetic algorithm (GA) is employed to search for the optimal values of the seven test parameters of the VSI (X) over bar and R charts, and an example is provided to illustrate the solution procedure. A sensitivity analysis then is carried out to investigate the effects of cost and model parameters on the solution of the joint economic design.