n South African Journal of Industrial Engineering - Economic design of VSI GCCC charts for correlated samples from high-yield processes




Generalised cumulative count of conforming (GCCC) charts have been proposed for monitoring a high-yield process that allows the items to be inspected sample by sample and not according to the production order. Recent study has shown that the GCCC chart with a variable sampling interval (VSI) is superior to the traditional one with a fixed sampling interval (FSI) because of the additional flexibility of sampling interval it offers. However, the VSI chart is still costly when used for the prevention of defective products. This paper presents an economic model for the design problem of the VSI GCCC chart, taking into account the correlation of the production outputs within the same sample. In the economic design, a cost function is developed that includes the cost of sampling and inspection, the cost of false alarms, the cost of detecting and removing the assignable cause, and the cost when the process is out-of-control. An evolutionary search method using the cost function is presented for finding the optimal design parameters of the VSI GCCC chart. Comparisons between VSI and FSI charts for expected cost per unit time are also made for various process and cost parameters.

Veralgemeende Kumulatiewe Telling van Konformasie-grafieke (VKTK) word voorgehou as metode om 'n hoë opbrengs proses, wat toelaat dat items monster-vir-monster eerder as in produksievolgorde geïnspekteer word, te monitor. Onlangse navorsing toon dat die VKTK-grafiek met 'n wisselende monsterneminginterval (WMI) beter is as dié met 'n vasgestelde monsterneminginterval (VMI) vanweë die addisionele aanpasbaarheid wat dit bied ten opsigte van die monsterneminginterval. Die VKTK-grafiek met WMI is egter duur wanneer dit gebruik word vir die voorkoming van defektiewe produkte. Hierdie artikel bied 'n ekonomiese model vir die ontwerpprobleem van die WMI VKTK-grafiek. Die model neem die korrelasie van produksieuitsette met die huidige monster in ag. In die ekonomiese ontwerp word 'n kostefunksie ontwikkel wat die koste van monsterneming en inspeksie, die koste van vals alarms, die koste van identifisering en verwydering van toerekenbare oorsake en die koste wanneer die proses buite beheer is, in ag neem. 'n Evolusionêre soekmetode wat van die kostefunksie gebruik maak om die optimale ontwerp parameters van die WMI VKTK-grafiek te vind, word voorgehou. Vergelykings tussen die WMI- en VMI-grafieke vir verwagte koste per tydseenheid word ook voorgehou vir verskillende proses- en kosteparameters.


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