Economic Design of a Joint X- and R -Control Chart

Abstract

Abstract An economic model is developed which determines the design of joint X- and R-control charts to minimize costs. The design parameters are sample size, width of X -control chart limits, width of R-control chart limits, and sampling interval in hours. Duncan's approach to the economic design of control charts is used. The control states permitted are the mean and variance in control, mean only out of control, variance only out of control, and both mean and variance out of control. The model developed considers the situation in which a second process parameter can go out of control after the first process parameter has gone out of control. Central composite experimental designs and a pattern search technique are used to optimize the model. Experience with the model indicates that the cost of a traditional design of an X- and R-control chart can be considerably higher than the cost of the optimum design. An example is presented.