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12.6 Skewness Control Error General data LPM Name: skew_CE_norm Category: Basic Statistic Description The skewness is the third central moment divided by the cube of the standard deviation. Skewness is a measure of the asymmetry of the data around the sample mean. If skewness is negative, the data are spread out more to the left of the mean than to the right. If skewness is positive, the data are spread out more to the right. The skewness of the normal distribution (or any perfectly symmetric distribution) is zero. s E ( x ) 3 3 Purpose Assess the symmetry of the control error. Interpretation The skewness is an important indicator of control problems, especially for nonlinear phenomena. Unit & range Dimensionless, [-max, +max]. Nominal Non-skew data has a skewness of zero. Significant if outside [-1, +1]. Pre-requisite None Background Basic statistic theory. Reference Any textbook on basic statistics. Good Situation Bad Situation Index = 0.27 Index = 1.88 Document Title cpmPlus Loop Performance Manager User Manual ABB. All rights reserved Doc no 3BJTCC497LDC750 Rev Pages 3.3 F Page 227 of 299
