Optimal parameters for CUSUM-FIR control charts for monitoring process mean

In some applications of quality control charts it is very important to quickly detect small or moderate shifts in the characteristic that is being monitored when process control starts. In such cases, CUSUM charts with fast initial response (FIR) perform very well. However, optimal performance of a CUSUM-FIR chart is only achieved when the best set of chart's parameters is found. This paper deals with the optimisation of CUSUM-FIR charts to maximise performance for detecting a given process mean shift. The optimisation is carried out using genetic algorithms, and user-friendly software has been developed to promote the use of optimised CUSUM-FIR charts in industry. An extensive set of numerical results is presented to test the effectiveness of CUSUM-FIR optimised chart in detecting small and moderate shifts in the process mean. The results are compared numerically with other similar control charts using the average run length (ARL). An example is presented to illustrate the application of CUSUM-FIR optimised chart.