THE ECONOMIC DESIGN OF DOUBLE SAMPLING X CONTROL CHARTS WITH 2 CONTROL LIMITS - YULIANI (NIM: 23407018), ANI
Croasdale (1974) introduced Double Sampling (DS) X control chart for the first time. Subsequently, the development of DS X control chart was conducted by Daudin (1992), Irianto and Shinozaki (1998), Irianto (2005), Sutrisno (2006) and Miyazumi (2007). Related researches to DS X control chart are focused on consumer's risk (B) to maximize power of control chart. Producer's risk (a) is ignored by assuming a certain value. In economic design of control charts, a risk and B risk must be considered. The aim of this research is to develop an economic design of DS X control chart with 2 control limits. The model which is developed is minimizing costs caused by a risk and B risk with the total sample expectation as the constraint. Numerical calculation result shows that when consumer's risk is bigger than producer's risk, control limits are in the second observation, L2, they are sensitive to a large shift in process. L2 control limits become more narrow as consumer's risk increases. When consumer's risk is smaller than producer's risk, L2 control limits become wider as producer's risk increases. The bigger the total sample expectation is, the smaller the cost and the bigger the power. The use of bigger total sample expectation will lead a risk and B risk to be well corrected. The bigger the power is, the smaller the cost of a risk and B risk become as process shift increases. In small process shift, the power increases while the cost decreases, both in a slow manner. Reversely in a large process shift, the power experiences a dramatic rise dan the cost experiences a sharp fall.