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On the design of experiments considering the division of the experimental area

100%
Szerszunowicz M.
Mathematical Economics
|
2012
|
issue 8 (15)
123-134
EN
The design of experiments is an important tool to improve production processes that use statistical methods. Designing experiments empowers not only setting properly the parameters of the production process and describing the influence of factors on the results, but also leads to improving the economic results of the analyzed process. The aim of this article is the issue of choosing the appropriate layout of experiments when the experimenter, because of the cost or conditions, has no possibility to implement the completion of the design of experiments. The suggested method takes into account the division of the experimental area and uses measures of spatial autocorrelation to determine the design points to carry out an experiment. The implementation of the mentioned method will be presented for selected factorial designs with particular reference to plans used to estimate the non-linear response surface.
2
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On the search for conditions for production process optimization

100%
Szerszunowicz M.
Mathematical Economics
|
2014
|
issue 10(17)
91-102
EN
The experimental design methodology mainly deals with the estimation of a usually unknown response surface function. An important problem in the field of design of experiments is to determine the number of experimental trials, taking into account certain limitations resulting from the nature of the manufacturing process. The experimental design methodology also includes – as if a separate section – methods of searching for conditions for the optimization of processes and the optimal design of experiments. The aim of this paper is to present a method of searching for conditions for the optimization of manufacturing process results. The proposed method uses non-classical statistical methods and is presented for selected empirical data.
3

On the Use of Permutation Tests in the Significance Testing of Response Surface Function Parameters

100%
Złotoś M.
Argumenta Oeconomica Cracoviensia
|
2020
|
issue 1(22)
21-29
EN
Objective: The methods of experimental design were first used in agricultural experiments performed by R. A. Fisher. The development of experimental design methods took place along with their effective use in production companies. The most frequently used designs of experiments are the factorial designs. One of the stages in the factorial design of experiments is the estimation of the response surface function formula which describes the influence of factors on the response variable values. The aim of this article is to propose a method to indicate the factors which have a significant influence on the response variable. Research Design & Methods: In this case, in the classical approach, the t-test of the significance of particular parameters of the response surface function is used. The t-test requires fulfilment of the assumptions about the distribution and independence of the model errors. If the assumptions are not fulfilled, or the sample size is not sufficient, the use of the t-test is unjustified. An alternative approach to verify the significance of response surface parameters is a permutation test. Permutation tests use simulation methods and do not entail the fulfilment of strict assumptions relating to the distribution of errors and the sample size of experimental data. Findings: The paper deals with the use of a permutation test that allows us to assess the significance of response surface function parameters when the quantity of experimental data is small. These results were obtained using parametric tests and permutation tests. Implications/Recommendations: Based on the performed calculations, it was found that it is possible to use permutation tests to analyse the response surface function, especially when the assumptions about the residuals of the model are not fulfilled or the number of considered experimental trials is small. Contribution: A proper analysis of the response surface function is an important stage in the design of experiments. In the case of a small quantity of experimental data, assessment of the significance of the model and the parameters of the response surface function using parametric tests may lead to incorrect conclusions. Therefore, the use of permutation tests was indicated as an alternative approach in the analysis of the response surface function.
4
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ON THE BOOTSTRAP METHOD OF ESTIMATION OF RESPONSE SURFACE FUNCTION

100%
Szerszunowicz M.
Acta Universitatis Lodziensis. Folia Oeconomica
|
2014
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vol. 3
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issue 302
EN
Nowadays, in many fields of science it is necessary to carry out miscellaneous analyses using classical statistical methods, which usually have correct assumptions. These assumptions in the research realities cannot always be met, which makes it impossible to carry out analyses and leads to incorrect conclusions and recommendations. The study of the production process largely consists in the use of tools of statistical quality control which are based on classical statistical methods. These methods result in some improvements in technological and economic results of the manufacturing process. One of the tools of statistical quality control is the design of experiments, whose important element is the estimation of response surface function. The aim of this paper is to present the bootstrap method of estimation of response surface function and its use for empirical data.
5
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On the Use of Permutation Tests in the Analysis of the Factorial Design of Experiment Results

51%
Złotoś M.
Acta Universitatis Lodziensis. Folia Oeconomica
|
2019
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vol. 4
|
issue 343
123-136
PL
Metody planowania eksperymentów są wykorzystywane w statystycznej kontroli jakości procesu produkcyjnego. Właściwe planowanie eksperymentów przed realizacją procesu produkcyjnego prowadzi do poprawy jego rezultatów technologicznych, co w efekcie powoduje poprawę rezultatów ekonomicznych procesu. W ostatnich latach na znaczeniu zyskały metody repróbkowania, wykorzystujące symulacje komputerowe. Jedną z nich są testy permutacyjne służące do weryfikacji hipotez statystycznych. W porównaniu do testów parametrycznych nie wymagają one spełnienia restrykcyjnych założeń i mogą być stosowane do niewielkiej liczby obserwacji. Przedmiotem artykułu jest wskazanie możliwości wykorzystania testów permutacyjnych w analizie wyników eksperymentu. Rozważania przeprowadzone zostały dla danych dotyczących rezultatów ustalonego procesu produkcyjnego.
EN
An experimental design is one of the tools which are used in statistical quality control. The proper implementation of experimental design results in the improvement of technological outcomes of a manufacturing process, which in turn leads to the enhancement of economic results. Permutation tests, among other things, form a group of resampling methods which are used to verify statistical hypotheses. These tests, unlike parametric ones, do not entail the fulfilment of strict criteria and may be used for a small number of observations. The presented article deals with the use of permutation tests in the design of experiments. The proposed method will be presented with reference to selected empirical data.
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