Economic design of variable sampling intervals X¯ charts with A&L switching rule using genetic algorithms

The major function of control chart is to detect the occurrence of assignable causes so that the necessary corrective action can be taken before a large quantity of nonconforming product is manufactured. The control chart for averages (or the X¯ chart) dominates the use of any other control chart technique if quality is measured on a continuous scale. The control chart with variable sampling intervals (VSI) scheme has been shown to give substantially faster detection of most process shifts than the conventional control charts. In 1991, Amin and Letsinger [Amin, R. W., & Letsinger, W. C. (1991). Improved switching rules in-control procedures using variable sampling intervals. Communications in Statistics – Simulation and Computation, 20  , 205–230] improved the operation of VSI X¯ chart by applying a switching rule, which is denoted by A&L switching rule, to reduce the number of switches and consequently to enhance the convenience of the chart. In the present paper, we develop the economic design of VSI X¯ chart with A&L switching rule to determine the values of the seven test and switching parameters of the chart (i.e., the sample size, the long and short sampling intervals, the warning- and control-limit coefficients, and two switching parameters) such that the expected total cost is minimized. An illustrative example is provided and the genetic algorithm is employed to search for the solution of the economic design. A sensitivity analysis is carried out to study the effects of cost and model parameters on the solution of the economic design.