An economic model for \font\twelveit=cmti10 scaled 1600$\overline{\kern‐0.85ex\hbox{\twelveit X}}$\nopagenumbers\end and R charts with time‐varying parameters

Abstract

Abstract This paper proposes an economic model for the selection of time‐varying control chart parameters for monitoring on‐line the mean and variance of a normally distributed quality characteristic. The process is subject to two independent assignable causes. One cause changes the process mean and the other changes the process variance. The occurrence times of these assignable causes are described by Weibull distributions having increasing failure rates. The paper combines two existing models: (I) the model of Ohta and Rahim (IIE Transactions 1997; 29:481–486) for a dynamic economic design of $\overline{X}$\nopagenumbers\end control charts, where a single assignable cause occurs according to a Weibull distribution and all design parameters are time varying; (II) the model of Costa and Rahim (QRE International 2000; 16:143–156) for the joint economic design of $\overline{X}$\nopagenumbers\end and R control charts where two assignable causes occur independently according to Weibull distribution, with variable sampling intervals. The advantages of the proposed model over traditional $\overline{X}$\nopagenumbers\end and R control charts with fixed parameters are presented. Copyright © 2002 John Wiley & Sons, Ltd.

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