The economic statistical design of variables control charts with an application to exponentially weighted moving average charts

摘要

The purpose of this research is to investigate the design of variables control charts from the economic and statistical viewpoint. A cost model is developed for the exponentially weighted moving average (EWMA) control charts based on Lorenzen and Vance's unified approach. Average run length (ARL) and average time to signal (ATS) are chosen as statistical constraints for the economic statistical design of EWMA charts. Comparisons between the economic designs of X-bar charts and EWMA charts based on cost and ARL criteria show no significant difference. It appears that an optimally designed EWMA chart is slightly better than an optimal X-bar chart. If a non-optimized X-bar chart is used, the difference will be much in favor of the EWMA chart.;Sensitivity analysis shows that cost of the economic statistical design is more sensitive to the smaller out-of-control ATS bounds but relatively insensitive to the larger bounds. Adding additional constraints to the economic statistical designs does not significantly increase cost over the designs without additional constraints but ensures better protection against shifts other than the expected shift.;In summary, economic statistical designs will probably be the best choice for the design of variables control charts in today's industry because they yield designs that are at least as good as statistical designs in terms of statistical properties but are also generally less costly. A protection over a wider range of shifts is another advantage of the economic statistical design.