The economic design of variable sampling interval (X)over-bar control charts when there is a fuzzy shift amount in the process

Control charts with variable sampling interval (VSI) in which the next sample is taken sooner than usual if there is an indication that the process is off-target have been shown quicker than the traditional. control charts in detecting a small shift in process mean. Previous studies addressed the economic design of VSI control charts considering the magnitude of process shift can be precisely known. However, imprecision in process shift normally occurs in real working cases and results in a barrier to the implementation of economic designs. In this work, a design procedure was developed for the economic design of the variable sampling interval (VSI) chart when the magnitude of process shift can not be precisely known but can be represented as a fuzzy number. Considering those magnitudes ranged in the a cut-set of this fuzzy number, the procedure determines the optimum design for the VSI chart according to the minimax criterion. In doing so, a hybrid approach of fuzzy simulation and genetic algorithm. is employed. An industrial example is provided to illustrate this procedure. Sensitivity analysis is then carried out to investigate the effect of model parameters on the optimum solution of the economic design. Significance: Imprecision in process shift normally results in a barrier to the implementation of economic designs. A design procedure is developed in this study for the economic design of the VSI chart with imprecision in process shift.