Optimization design of control charts based on Taguchi's loss function and random process shifts

An algorithm was developed for the optimization design of control charts based on the probability distribution of the random process shifts (e.g. mean shift). The design objective was to minimize the overall mean of Taguchi's loss function per out-of-control case (denoted as ML) by adjusting the sample size, sampling interval and control limits of the chart in an optimal manner. The optimal chart was therefore named as the ML chart. A three-phase operational scenario for statistical process control (SPC) was also proposed to design and operate the ML chart. The probability distribution of the mean shifts can be modelled by a Rayleigh distribution based on the sample data of the mean shifts acquired in the three-phase scenario. Unlike in the economic control chart designs, the design of the ML chart only requires a limited number of specifications that can be easily determined. The results of the comparison studies show that the ML chart is significantly superior to the Shewhart control chart in view of overall performance. Although the ML chart was discussed in detail only for the chart, the general idea can be applied to many other charts such as CUSUM and EWMA.