J. Surtihadi et M. Raghavachari, EXACT ECONOMIC DESIGN OF X-OVER-BAR CHARTS FOR GENERAL TIME IN-CONTROL DISTRIBUTIONS, International Journal of Production Research, 32(10), 1994, pp. 2287-2302
Citations number
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Categorie Soggetti
Engineering,"Operatione Research & Management Science
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.