Optimization Design Of A Cusum Control Chart Based On Taguchi's Loss Function

The optimization of control charts for statistical process control(SPC)has been geared towards two directions,namely statistical design and economic design. However,statistical design does not directly measure the cost resulting in the out-of-control cases.On the other hand,economic design aims at minimizing the total cost associated with the implementation of SPC in a process.Much research has pointed out the pitfalls of economic design,such as poor statistical properties and difficulty in estimating a large number of costs and other model parameters.This paper proposes an algorithm for the optimal design of a EWMA control chart detecting process shifts in the mean value.The algorithm optimizes the sample size,sampling interval,control limit and reference parameter of the EWMA chart through minimizing the overall mean value(ML)of a Taguchi's loss function over the probability distribution of the random process mean shift.Comparative studies reveal that the proposed ML-EWMA chart is considerably superior to the Shewhart ML-(?)chart and the conventional EWMA chart in terms of the overall loss of ML.Furthermore,a new feature related to the exponential of the sample mean shift is elaborated.