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Simpson & Keats
Figures 2 and 3 present the same type of information in a clustered bar format, which enables the designer to view the ARL structures of the chart altematives. FigurÄ™ 2 shows several designs with improved ARL1 and ARL2. For only a 1.2% cost increase, the in-control ARL can be increased 50% (41.8 to 61.5) and ARL2 can also be reduced slightly. FigurÄ™ 3 is plotted using a logarithmic scalÄ™ because the design altematives can be Ä…uite large. For example, the ARL1 can be increased from the optimal cost ARL1 of 393.9 to nearly 8700 while obtaining a slightly smaller ARL2. This design costs about 6.1% morÄ™ than the optimal design, but may be worthwhile in some situations.
Montgomery Example The results of the grid search show a flatter cost surface than the LV example. Using the same grid search method (and grid sizes) of determining optimal designs for yarious values of n and H, the initial cost parameters from this example resulted in morÄ™ design altematives with the same percent increase in cost. Thus, it is possible that morÄ™ significant improvements in the statistical properties of the control chart design can be madÄ™ for the same fractional increase in cost. In the case of the 0.25 shift (FigurÄ™ 4), the ARL1 can be doubled (16.7 to 33.9) with only a smali increase in ARL2 (6.0-7.8) while cost increases just 0.9%.
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