Economic design of EWMA control charts using regions of maximum and minimum ARL

Nowadays, it is common to find industries that utilize processes that either have a value of the process capability index C _pk larger than two or are very difficult to adjust. In these cases, the detection of very small shifts may not be of interest due to the possible extra variability introduced into the process by the detection process. It would be more interesting in these situations to decide what shift size is important for detection, and to design a chart capable of quickly detecting this shift whilst having a low probability of false alarms for the shifts that we do not wish to detect. The Exponentially Weighted Moving Average (EWMA) control chart, although originally developed to successfully detect small shifts, can be designed to cope with these requirements. This paper presents a method for the economic-statistical design of EWMA charts for control processes, in which the detection of small shifts is not necessary, and which is, at the same time, effective in detecting important shifts. A genetic algorithm is used to optimize the design. A sensitivity analysis of the optimal solution is performed to determine the influence of certain factors on the economic model.

Acknowledgements

We would like to acknowledge the helpful comments of the anonymous reviewers. The authors acknowledge the financial support of the Ministry of Education and Science of Spain, Research Project Reference DPI2002-03537 and European FEDER funding. In addition, the authors would like to thank the Foreign Language Co-ordination Office at the Polytechnic University of Valencia for their help in translating this paper.

Notes

*Denotes a statistically significant difference.