Number Of Optimization Criteria Research Articles

Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

In life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. Lately, an adaptive progressive type-II hybrid censoring scheme is suggested to enhance the efficiency of the statistical inference. By utilizing this scheme, this paper seeks to investigate classical and Bayesian estimations of the Dagum distribution. The maximum likelihood and Bayesian estimation methods are considered to estimate the distribution parameters and some reliability indices. The Bayesian estimation is developed under the assumption of independent gamma priors and by employing symmetric and asymmetric loss functions. Due to the tough form of the joint posterior distribution, the Markov chain Monte Carlo technique is implemented to gather samples from the full conditional distributions and in turn obtain the Bayes estimates. The approximate confidence intervals and the highest posterior density credible intervals are also obtained. The effectiveness of the various suggested methods is compared through a simulated study. The optimal progressive censoring plans are also shown, and number of optimality criteria are explored. To demonstrate the applicability of the suggested point and interval estimators, two real data sets are also examined. The outcomes of the simulation study and data analysis demonstrated that the proposed scheme is adaptable and very helpful in ending the experiment when the experimenter’s primary concern is the number of failures.

АНАЛІЗ МЕТОДІВ ОПТИМАЛЬНОГО ПЛАНУВАННЯ БАГАТОФАКТОРНОГО ЕКСПЕРИМЕНТУ ЗА ВАРТІСНИМИ ТА ЧАСОВИМИ ПОКАЗНИКАМИ

The object of research is the analysis of the state of development of methods of optimal planning of multifactorial experiment on cost and time indicators. The subject of the research is the methods of optimization of multifactor experiment plans in terms of cost and time indicators. The objective: the development of practical recommendations for the application of existing optimization methods of multifactorial experiment plans in terms of cost and time criteria based on their comparative analysis. The tasks are the comparing of optimization methods of multifactorial experiment plans by characteristics: the allowable number of factors for effective optimization, type of plan, accuracy of the method, the number of optimization criteria, speed; development of practical recommendations for the use of these methods; the determine of directions for further development of the research topic. Methods: method of comparative analysis, optimization methods based on the study of nature, combinatorial optimization methods, graph optimization methods, approximate optimization methods. The results of study. The 20 methods of multifactorial experiment plans in terms of cost and time criteria are analyzed. The 6 practical recommendations for their application in the range of factors number 2 < k ≤ 16 are given. Conclusions. The scientific novelty of the obtained results is the improved comparative analysis of existing methods of multifactorial experiment plans based on 5 characteristics in terms of the experimenter's choice, namely: the allowable number of factors for effective optimization, type of plan, method accuracy, number of optimization criteria; speed-code. In the future, it is planned to study the classification of methods of multifactorial experiment plans, the development and improvement of two-criteria optimization methods for cost and time characteristics, the speed analysis of approximate optimization methods for k > 7 and their improvement.

Многокритериальное моделирование процессов и конструкции камеры смешения пароструйного эжектора конденсационной турбины

The paper presents recommendations on designing an efficient mixing chamber and regulating air and steam flows in the elements of a steam-jet apparatus based on the results of multi-criteria modeling of gas-dynamic pro-cesses. The paper also reveals the possibilities to provide a greater reduction in losses, air suction into the turbine and equipment repair costs compared to the cases when individual criteria for increasing the steam turbine equipment efficiency are used. The selected calculation methods, i.e. innovative (multi-criteria) and standard (standard), have been analyzed comparatively. As a result of the methods evaluation, the authors se-lected the following indicators: increased energy efficiency of the turbine due to the prevention of air suction in the turbine seals; increased efficiency of condensing turbines; reduced repair and maintenance costs for the turbine and ejector due to the ejector mixing chamber cross-sectional area optimization. Based on the comparison, the best results were shown with the multi-criteria modeling according to the indicated parameters, the coefficients of the flow rate, working steam consumption, size reduction and increase in service life from 20 to 40 years. The innovative method requires a larger number of optimality criteria and the regulation of process pa-rameters and design geometry based on direct and feedback multi-criteria models. Using multi-criteria modeling, the authors determined the necessary composition of optimization parameters, i.e. the flow area of the designed mixing chamber, steam flow rate and thermodynamic flow parameters, as well as suction pressure.

Structural analysis of technological processes with multivariate machining operations

This article addresses the issue of structure optimization for machining technological processes. A technological process typically offers multivariate operations. A choice of one option is an optimization problem. A mathematical solution of it is complicated since a number of optimization criteria can be present. However, a multivariate technological process can be presented as a directed graph. First, all paths of the graph are found and their length that correspond to values of certain optimization criteria are determined. Then the optimal path is selected (that is, the optimal technological process) by finding generalized optimization criteria and comparing them.

Techniki eksperymentalne w optymalizacji procesu wtryskiwania tworzyw termoplastycznych - skurcz wtorny wyprasek

Experimental presentation of the problem of injection molding of thermoplastics (low density PE) optimization, using injection molding machines of one pressure degree and constant injection rate. The two-level fractional factorial design and the method of steepest descent, being together a sequence procedure of experimental investigations, were used. The solution takes into consideration five investigated parameters (mold temperature, temperature of a polymer, injection time, time of moldings cooling, pressure Table 1) and one result parameter - after-shrinkage of moldings (s). Particular steps of optimization investigations were described, viz. survey measurements (Figs. 1 and 2), looking for extremum neighborhood (Tables 2-5) and determination of a model approximating s value at extremum neighborhood (Table 6, Fig. 4). Coordinates of the point of factorial space for minimal s value were determined (Table 7). It has been found that low temperature of injection mold, long time of moldings cooling and high value of pressure show the biggest effects on shrinkage decrease. The method described let make the optimization independent on injection molding machine construction as well as on character and number of optimization criteria.

Pure states, polarized waves, and principal components in the spectra of multiple, geophysical time-series

This paper outlines the connection between pure states, polarized waves, and principal components in the spectral representation of multichannel or multivariate geophysical time series. If a wave is a pure state or a polarized wave (e.g. a teleseismic P-wave), the multidimensional spectral representation can be reduced to a one-dimensional spectral representation. The objective of this paper is to develop estimators of the spectral representations of these pure states, which are based on a number of optimality criteria. If nothing is known about the noise in the data, then an estimator similar to the principal components of real multivariate analysis is most useful. If some knowledge of the spectral density matrix of the noise is available, then a number of other optimality criteria can be used. Minimization of the prediction error in the spectral representation of the pure states leads to estimators similar to those used to estimate factor-scores in factor-analytic methods. These estimators of the spectral representations of polarized waves should be extremely useful to the geophysical experimenter because they allow a more objective evaluation of the parameters of the wave, and because they allow the multichannel data to be filtered to extract polarized waves, without specific knowledge of the type of polarization (e.g. elliptical or linear, and orientation of polarization ellipse). Some practical examples using spectral representations of ULF (1–20 mHz) magnetic fields are given in order to illustrate the usefulness of these methods in interpreting multichannel data.