A two control limits double sampling control chart by optimizing producer and customer risks

Standard shewhart process control chart has been widely used,but it is not sensitive in detecting small shift. a number of alternatives have been proposed to improve the capability of control chart. the double sampling (ds) control chart is aimed at improving the capability to detect any small shift out-of control condition by observing the second sample without interruption. the capabilities of ds control chart were measured as the expected sample size (as a measure of inspection cost) or the control chart power (as a measure for customer risk). optimization of these criteria is used to determine the control limits. in this paper,we optimize both producer and customer risks under a certain expected number of sample sizes as the constraint. comparing the result to the previous procedure that only optimize customer risk,the proposed optimization procedure gives the same first control limit but smaller second control limits with higher value of control chart power.