Optimization design of control charts based on minimax decision criterion and fuzzy process shifts

This paper presents a novel procedure for optimally designing the control chart with vagueness in process shift. This procedure treats the process shift as a fuzzy number with a given membership function, and takes a range of values from the fuzzy cut set for possible shifts to implement the chart design. Taking multiple shifts into account, the design parameters of control charts are optimally determined according to the minimax decision criterion: (1) approximating the maximum cost each potential design may suffer by means of simulation techniques; and (2) using genetic algorithm as a search tool to find the optimum design that minimizes the maximum cost. An industrial example is provided to illustrate this procedure and how to set its operative condition. Sensitivity analysis is then carried out to investigate the effect of model parameters on the optimum design.