Economic design of $\bar X$ & S control charts based on Taguchi’s loss function and its optimization

Abstract

Much research effort has been devoted to economic design of $\bar X$ & S control charts, however, there are some problems in usual methods. On the one hand, it is difficult to estimate the relationship between costs and other model parameters, so the economic design method is often not effective in producing charts that can quickly detect small shifts before substantial losses occur; on the other hand, in many cases, only one type of process shift or only one pair of process shifts are taken into consideration, which may not correctly reflect the actual process conditions. To improve the behavior of economic design of control chart, a cost & loss model with Taguchi’s loss function for the economic design of $\bar X$ & S control charts is embellished, which is regarded as an optimization problem with multiple statistical constraints. The optimization design is also carried out based on a number of combinations of process shifts collected from the field operation of the conventional control charts, thus more hidden information about the shift combinations is mined and employed to the optimization design of control charts. At the same time, an improved particle swarm optimization (IPSO) is developed to solve such an optimization problem in design of $\bar X$ & S control charts, IPSO is first tested for several benchmark problems from the literature and evaluated with standard performance metrics. Experimental results show that the proposed algorithm has significant advantages on obtaining the optimal design parameters of the charts. The proposed method can substantially reduce the total cost (or loss) of the control charts, and it will be a promising tool for economic design of control charts.