ECONOMICALLY OPTIMAL DETERMINATION OF THE PARAMETERS OF x¯ -CHARTS WITH WARNING LIMITS WHEN QUALITY CHARACTERISTICS ARE NON-NORMALLY DISTRIBUTED

Abstract

In this paper, an expected cost model for a production process under the surveillance of an it-chart with warning limits for controlling the non-normal process mean, is developed It is assumed that the process is subject to the occurrence of a single assignable cause. The design parameters of an 3c-chart with warning limits are the sample size, the sampling interval, the action limit coefficient, the warning limit coefficient, and the critical run length. The economic design of control charts involves the optimal determination of the design parameters that minimize the expected total loss cost of monitoring the quality of the process output. To develop the expected loss-cost function, the required 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. Numerical examples are provided, and the effects of the non-normality parameters on the loss-cost function and on the design parameters are discussed. Conclusions are drawn about the relative efficiencies of the economic design of it-charts with and without warning limits. A simplified form of the algorithm is also devised which could be useful for practical application at the workshop level.