This study aims at developing models in analyzing the results of proficiency testing (PT) schemes for a limited number of participants. The models can determine the best estimators of location and dispersion using unsatisfactory results as a criterion by combining: (a) robust and classical estimators; (b) kernel density plots; (c) Z-factors; (d) Monte Carlo simulations; (e) distributions derived from the addition of one or two contaminating distributions and one main Gaussian. The standards ISO 13258:2015, ISO 5725:2:1994, and EN ISO/IEC 17043:2010 are the basis of the analysis. The study describes an algorithm solving the optimization problem for (a) Gaussian, bimodal or trimodal distributions; (b) participating labs from 10 to 30; (c) fraction of the contaminating population up to 0.10; (d) variation coefficient of the main distribution equal to 2; (e) equal standard deviations of all the distributions, and provide figures with the optimal estimators. We also developed a generalized algorithm using kernel density plots and the previous algorithm, which is not subject to restrictions (b)–(e) and implemented in the results of a PT for the 28-day strength of cement with 12–13 participants. Optimal estimators’ figures and the generalized algorithm are helpful for a PT expert in choosing robust estimators.
-Based on a dynamical model of the grinding process in closed circuit mills, efficient efforts have been made to optimize PID controllers of cement milling. The process simulation is combined with an autoregressive model of the errors between the actual process values and the computed ones. Long term industrial data have been used to determine the model parameters. The data include grinding of various cement types. The M -Constrained Integral Gain Optimization (MIGO) loop shaping method is utilized to determine PID sets satisfying a certain robustness constraint. The maximum sensitivity is considered as such a criterion. Both dynamical parameters and PID sets constitute the inputs of a detailed simulator which involves all the main process characteristics. The simulation is applied over all the PID sets aiming to find the parameter region that provides the minimum integral of absolute error, which functions as a performance criterion. For each cement type a PID set is selected and put in operation in a closed circuit cement mill. The performance of the regulation is evaluated after a sufficient time period, concluding that the developed design combining criteria of both robustness and performance leads to PID controllers of high efficiency.
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