An Economic Design of $${\rm \bar X}$$ -Charts with Warning Limits to Control Non-Normal Process Means

Abstract

In this paper, we develop an expected cost model for a production process under the surveillance of an x-chart with warning limits for controlling the non-normal process mean. The economic design of control charts involves the optimal determination of the design parameters that minimize the expected total cost of monitoring the quality of the process output. The design parameters of a general control chart with warning limits are the sample size, the sampling interval, the action limit coefficient, the warning limit coefficient, and the critical run length. To develop the expected loss-cost function, expressions for the average run lengths, when the process is in control, and when the process is out of control are derived. A direct search technique is employed to obtain the optimal values of the design parameters. The effects of non-normality parameters on the loss-cost function and on the design parameters are discussed using a numerical example.