Sigma-plus parameters

Reactions where the reaction centre becomes positively charged and may attract electrons from a substituent via a resonance pathway will give poor correlations with 

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Fig. 11. Plot of pK for aromatic acids (ArC02H2 ArCOjH + H ) versus sigma-plus. Data from K. Yates (1960) J. Am. Chem. Soc. 82, 4059. Open and filled circles represent Hammett sigma values, open circles sigma-plus parameters.

I) the hydrophobic term, 1-octanol/water partition coefficient, log KQyy, and two discrete variables, (2) the ability to accept hydrogen, Ha, and (3) the ability to donate hydrogen, Hd. Several electronic parameters were selected (4) the Hammett sigma constant for the para position (see Jaffe 1953), and its special cases, (5) (normalized), (6) (minus), and (7) (plus) (see Hansch and Leo 1979) (8) the polar or field parameter, F (Swain and Lupton 1968) and (9) the resonance parameters, R (Swain and Lupton 1968), (10) R°,... 

The first out-of-control condition is when the process generates part parameters outside of some predetermined distance from the center of the output distribution. These limits are sometimes referred to as the upper process limits (UPL) and the lower process limits (LPL). Some authors refer to these limits as the upper and lower natural process limits. The selection of these limits is arbitrary. The current custom is to select plus and minus three sigma limits. If the distribution of the process output is a normal distribution, then 99.74% of the process will typically be between the upper and lower three sigma process limits. In some cases, such as for extremely stable processes, it is more practical to use 3.5 or 4.0 sigma limits instead of 3.0 sigma limits. This minimizes the number of false out-of-control signals. 

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