EXACT ECONOMIC DESIGN OF X-OVER-BAR CHARTS FOR GENERAL TIME IN-CONTROL DISTRIBUTIONS

Economic design of control charts seeks to choose the parameters of co ntrol charts that will minimize the cost. In an economic model, the ti me to the occurence of an assignable cause is usually assumed to follo w an exponential distribution. In addition to this assumption, certain approximations are used in the optimization procedures. This paper ex tends the current economic design for XBAR charts in two directions. F irst, economic design is considered for a general distribution for the time to the occurrence of an assignable cause. The method is speciali zed to several distributions such as Weibull, lognormal, folded-normal , folded-logistic, and gamma. Second, an exact method to obtain the op timal design parameters is developed. Using Duncan's examples, the opt imal designs obtained by exact method are compared for different distr ibutions. These are also compared with the approximate optimal designs given by Duncan. This comparison shows that the optimality of the des ign for XBAR charts is insensitive to the distributional assumption of the time to the occurrence of an assignable cause for small values of the sampling interval.