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

SUMMARYThis 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 X 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 X 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 X and R control charts with fixed parameters are presented.

Designs of &S control charts with optimal manpower deployment

“…Amin and Ethridge (1998) discussed the designs of the X&MR charts (the individual measurement chart and the moving range chart) for different combinations of mean shift and standard deviation shift. Many statistical and economic models for the optimization designs of the X&S or X&R charts have been proposed (Costa, 1999;Ohta, Kumar, & Rahim, 2002;Rahim & Costa, 2000;Saniga, 1989;Wu & Shamsuzzaman, 2006;Wu & Wang, 1997). However, none of these studies investigated the effect of optimal deployment of manpower to an SPC scheme.…”

Integrated control chart system—optimization of sample sizes, sampling intervals and control limits

“…The general algorithms discussed in this article can be modified and then extended to the designs of other types of control charts, such as the joint X and R charts for monitoring process shifts in both mean and variance (Costa 1999, Ohta et al 2002.…”

Monitoring Process Mean and Variability with One Non-central Chi-square Chart

“…It is standard practice to use an X -chart for detecting assignable causes that shift the process mean, and an R-chart for detecting assignable causes that increase the process variability, especially when n, the size of the samples, is small (or even 8). The joint use of X and R charts has been extensively studied for monitoring processes which might be subject to different types of assignable causes, including the assignable cause that shifts the process mean and increases variability (see Jones & Case, 1981;Saniga, 1989;Rahim, 1989;Costa, 1993Costa, , 1998Rahim & Costa, 2000;Ohta et al, 2002). However, both these charts are not effective in detecting small changes in the process parameters.…”