A Simplified Scheme for the Economic Design of X̄-Charts

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Abstract
This paper proposes a very simple semi-economic scheme for the design of a control plan using an X̄-chart, that can be applied at the work-shop level. Once the quality control engineer has selected a consumer's risk point on the OC-curve for his desired degree of protection against inferior quality, he can quickly determine by a table provided three control parameters: the sample size, the control limits coefficient, and the sampling interval. Three features may be mentioned: (1.) Although these parameters only minimize the average loss-cost subject to a constraint, the restricted minimum is in general very close to the exact minimum. (2.) The present method has wide practical applications-three models being studied here. (3.) If an exact optimum is sought, the present solution provides a good initial point for a direct search.

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