Robustness parameter

Sometimes there exists doubt about normal and log-normal distribution and the actual character of the distribution is unknown. Then so-called distribution-free (robust) parameters can be applied. The mostly used of them is the (common) median1... 

Another way is the robust parameter estimation on the basis of median statistics (see Sect. 4.1.2 Danzer [1989] Danzer and Currie [1998]). For this, all possible slopes between all the calibration points bij = (yj — yi)/(xj — X ) for j > i are calculated. After arranging the b j according to increasing values, the average slope can be estimated as the median by... 

CE is not yet as widespread as analytical techniques such as HPLC and GC. Especially as a more recent technique, it needs to demonstrate sufficient robustness to be considered as a conventional routine analytical technique. Robustness (see Chapter 9) of a method should always be tested before starting to calibrate. If the method is later found to be not robust, parameters have to be changed. Then the calibration and consequently its validation have to be repeated. 

For the calculation of the median the data have to be sorted by their value. The median is the central value of this series. If the number of data is even, the median is the arithmetic mean of the central values. The median is a so-called robust parameter, because extreme values or outliers do not affect it. 

Lastly, it is desirable that parameters are able to discriminate between positive and negative conditions in a variety of experimental conditions. In other words they should be robust and reproducible. For this purpose, the Pearson correlation coefficient between all experimental repeats using control wells is calculated. Robust parameters have high Pearson correlation coefficients (above 0.7) in pairwise comparisons of experimental repeats. For this analysis we have developed another R template in KNIME to calculate the Pearson correlation coefficient between experimental runs. 

This chapter addresses the planning, design and optimization of a network of petrochemical processes under uncertainty and robust considerations. Similar to the previous chapter, robustness is analyzed based on both model robustness and solution robustness. Parameter uncertainty includes process yield, raw material and product prices, and lower product market demand. The expected value of perfect information (EVPI) and the value of the stochastic solution (VSS) are also investigated to illustrate numerically the value of including the randomness of the different model parameters. 

A.E. Freeny and V.N. Nair, Robust parameter design with uncontrolled noise variables, Statistica Sinica, 2 (1992). 

R.H. Myers, A.L. Khuri and G.G. Vining, Response surface alternatives to the Taguchi robust parameter design approach, American Statistician, 46 (1992) 131-139. 

Robust parameter estimates are then obtained following Equation 6.11 to Equation 6.13 as... 

Berube, J. and Nair, V. N. (1998). Exploiting the inherent structure in robust parameter design experiments. Statistica Sinica, 8, 43-66. 

Model-robust orthogonal designs Model-robust parameter designs Addelman A Sun h ... 

Robust parameter designs are used to identify the factor levels that reduce the variability of a process or product (Taguchi, 1987). In such experiments, the dispersion effects, which can be identified by examination of control-by-noise interactions (see Chapter 2), are particularly important and hence the models of primary interest are those that contain at least one control-by-noise interaction. This motivated Bingham and Li (2002) to introduce a model ordering in which models are ranked by their order of importance as follows. 

Addelman, S. (1962). Symmetrical and asymmetrical fractional factorial plans. Technometrics, 4, 47-58. Allen, T. T. and Bemshteyn, M. (2003). Supersaturated designs that maximize the probability of identifying active factors. Technometrics, 45, 92-97. Bingham, D. and Li, W. (2002). A class of optimal robust parameter designs. Journal of Quality Technology, 34, 244—259. Biswas, A. and Chaudhuri, P. (2002). An efficient design for model discrimination and ... 

PPK designs with sampling times selected at random from time windows around times determined by individual D-optimality—similar to the informative block randomized design (8)—provide robust parameter estimates. A direct comparison of the efficiency of sampling designs determined using individual and population D-optimality is presented below. 

Theory. The variance criterion (i.e., maximizing the variance in the data) of classical PCA is very sensitive to outlying samples. As a consequence, the real structure of the data cannot always be revealed. To overcome this problem, rPCA (9-13) was introduced, which aims to obtain PCs that are less influenced by outliers. Additionally, robust methods should be able to detect the outlying observations. These goals are achieved by applying a more robust parameter (than variance) as projection index. 

The first step of Croux and Ruiz-Gazen making PCA more robust is centering the data with a robust criterion, the LI-median, that is, the point which minimizes the sum of Euclidean distances to all points of the data. In a next step, directions in the data space, which are not influenced by outliers, are determined by maximizing a robust parameter, the estimator. To calculate this estimator, first all objects are projected onto normalized vectors passing through each point and the LI-median center. Then for each projection, the Qn, that is, the first quartile of all pairwise differences, is calculated as follows ... 

Sorensen PB, Mogensen BB, Carlsen L, Thomsen M (2000) The influence of partial order ranking from input parameter uncertainty. Definition of a robustness parameter. Chemosphere 41 595-601... 

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