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Obenchain

Table 1. Fiłl Yolume Summary Statistics

Variable	Observed Mean	Standard Deviation	Min	Max
fili volume	73.32	8.58	51	98
ąuadratic regret	74.06	142.82	0	576.00
inverted normal	0.15	0.23	0	0.83
absolute value	5.87	6.40	0	24.00
Iogistic regret	0.23	0.18	0	0.62

Inverted normal regret is extremely sensitive to choice of the H half-width parameter. Inverted normal can be "flat-tailed" like Iogistic when H is smali (ER is larger than, say, 0.3.) But inverted normal can also behave very much like quadratic (as in the fill-volume example) when H is relatively large (ER is smali).

Another major distinction exists between the unbounded choices (ąuadratic and absolute value) and the bounded choices (goal-posts, inverted normal and Iogistic). We have already observed that regrets which remain bounded as the deviation of X from T increases tend to be sensitive to one's choice of H scaling along the X characteristic axis (as well as to one's choice of target, T). But the unbounded choices tend to result in a long, relatively heavy, right-hand taił of extremely large regret values. Bounded regrets cannot lead to heavy right-hand tails because no index value greater than the maximum regret divided by ER can result. On the other hand, regrets bounded at 1 with ER > 0.5 might tend to luli their users into a State of complacency. After all, really "bad news” about ąuality will never be signaled by an index that cannot be morę than twice standard, I < 2.

Data Cleaning and Current Yersus Ultimate Canability Our data analysis tactics can and should depend on our finał objective. When the data at hand comprise essentially "all" recent production results from routine process operations, we can attempt to characterize the fuli rangę of satisfaction currently being experienced by our customers/regulators, which represents our current capability. But, when our data come from special studies, designed experiments, or relatively "well behaved" subsets of total production, our objective would then usually be to ąuantify any implied improvement over and above current capability. When we have only un-planned, historical data and yet our aim is to characterize the potential "ultimate" capability of our process, then conventional wisdom suggests we should at least reject outliers (if not also