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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. Figurę 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. Figurę 3 is plotted using a logarithmic scalę because the design altematives can be ąuite 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% morę 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 morę design altematives with the same percent increase in cost. Thus, it is possible that morę significant improvements in the statistical properties of the control chart design can be madę for the same fractional increase in cost. In the case of the 0.25 shift (Figurę 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%.