Economic design of variable sampling intervals X charts with B%L switching rule

The control chart with variable sampling intervals (VSIs) scheme has been shown to give substantially faster detection of most process shifts than the conventional control charts. In 2002, Bai and Lee (2002) improved the operation of VSI X chart by applying a switching rule, which is denoted by B%L switching rule, to reduce the number of switches and consequently to enhance the convenience of control-chart operation, in which the long sampling interval is used if l2 (≥ 2) consecutive sample means fall in the safe region. In the present paper, we develop the economic design of VSI X chart with B%L switching rule to determine the appropriate values of the six test and switching parameters of the chart (i.e., the sample size, the long and short sampling intervals, the warning-limit and control-limit coefficients, and the switching parameter) such that the expected total cost related to control-chart operation is minimised. An illustrative example is provided and genetic algorithm is employed to search for the solution of economic design. Sensitivity analyses are conducted to study the effects of the switching parameter (l2) and the cost and model parameters on the solution of economic design, and then some important conclusions are drawn from the analyses.