On Some Construction of the Design of Experiments for Two Response Variables

Authors

DOI:

https://doi.org/10.15678/krem.18759

Keywords:

design of experiments, response surface function, response variable, wood pellet production process

Abstract

Objective: The aim of the article is to propose an alternative approach to constructing a design of experiments that allows for identifying settings of factor levels so that the response variables achieve desired values. The presented method will be used to determine the parameters of the wood pellet production process, which is characterised by two response variables.

Research Design & Methods: This paper presents a proposal for the construction of an experimental design that allows for the inclusion of two outcome variables characterising the production process under study. The method employs an appropriate synthetic variable and considers the desired ranges of variation of the outcome variables. Furthermore, permutation tests were utilised in the analysis of the experimental results.

Findings: A method of constructing an experimental plan was proposed, which allowed unambiguous recommendations to be made for the wood pellet production process under study. The settings of the individual factors for which the quality of the pellets produced and the efficiency of the production line take on values within the specified range were indicated.

Implications / Recommendations: The presented method of constructing the experimental plan, based on the analysis of an appropriately constructed synthetic variable, allowed the wood pellet production process to be designed accordingly.

Contribution: An alternative method of constructing an experimental design has been proposed that allows for the analysis of the influence of factors on the two outcome variables that characterise the production process under study.

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References

Aczel, A. D. (2000). Statystyka w zarządzaniu. Wydawnictwo Naukowe PWN.

Antony, J. (2023). Design of Experiments for Engineers and Scientists. Elsevier.

Antony, J., Coleman, S., Montgomery, D. C., Anderson, M. J., & Silvestrini, R. T. (2011). Design of Experiments for Non-manufacturing Processes: Benefits, Challenges and Some Examples. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 225(11), 2078–2084. https://doi.org/10.1177/0954405410395857 DOI: https://doi.org/10.1177/0954405411395857

Boateng, I. D. (2023). Application of Graphical Optimization, Desirability, and Multiple Response Functions in the Extraction of Food Bioactive Compounds. Food Engineering Reviews, 15(2), 309–328. https://doi.org/10.1007/s12393-023-09339-1 DOI: https://doi.org/10.1007/s12393-023-09339-1

Dean, A., Voss, D., & Draguljić, D. (2017). Design and Analysis of Experiments. Springer. https://doi.org/10.1007/978-3-319-52250-0 DOI: https://doi.org/10.1007/978-3-319-52250-0

Derringer, G., & Suich, R. (1980). Simultaneous Optimization of Several Response Variables. Journal of Quality Technology, 12(4), 214–219. https://doi.org/10.1080/00224065.1980.11980968 DOI: https://doi.org/10.1080/00224065.1980.11980968

Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.

Fisher, R. A. (1935). The Design of Experiments. Oliver and Boyd.

GUS. (2023). Energia ze źródeł odnawialnych w 2022 roku.

Kocsis, Z., & Csanády, E. (2019). Theory and Practice of Wood Pellet Production. Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-030-26179-5 DOI: https://doi.org/10.1007/978-3-030-26179-5

Kończak, G. (2007). Metody statystyczne w sterowaniu jakością produkcji. Wydawnictwo Akademii Ekonomicznej w Katowicach.

Kończak, G. (2016). Testy permutacyjne. Teoria i zastosowania. Wydawnictwo Uniwersytetu Ekonomicznego w Katowicach.

Lawson, J. (2015). Design and Analysis of Experiments with R. CRC Press. DOI: https://doi.org/10.1201/b17883

Montgomery, D. C. (2009). Introduction to Statistical Quality Control. John Wiley & Sons.

Montgomery, D. C. (2020). Design and Analysis of Experiments. John Wiley & Sons.

Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons.

Rigdon, S. E., Pan, R., Montgomery, D. C., & Freeman, L. (2022). Design of Experiments for Reliability Achievement. John Wiley & Sons.

Ryan, T. P. (2007). Modern Experimental Design. John Wiley & Sons. https://doi.org/10.1002/0470074353 DOI: https://doi.org/10.1002/0470074353

Szerszunowicz, M. (2011). Planowanie eksperymentów z uwzględnieniem czynników losowych. In: Materiały VI Krakowskiej Konferencji Młodych Uczonych (pp. 1057–1065). Grupa Naukowa Pro Futuro. Fundacja dla AGH.

Wawrzynek, J. (1993). Statystyczne planowanie eksperymentów w zagadnieniach regresji w warunkach małej próby. Wydawnictwo Akademii Ekonomicznej we Wrocławiu.

Wawrzynek, J. (2009). Planowanie eksperymentów zorientowane na doskonalenie jakości produktu. Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu.

Złotoś, M. (2020). On the Use of Permutation Tests in the Significance Testing of Response Surface Function Parameters. Argumenta Oeconomica Cracoviensia, 1(22), 21–29. https://doi.org/10.15678/AOC.2020.2202 DOI: https://doi.org/10.15678/AOC.2020.2202

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Published

24-06-2026

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How to Cite

Złotoś, M. (2026). On Some Construction of the Design of Experiments for Two Response Variables. Krakow Review of Economics and Management Zeszyty Naukowe Uniwersytetu Ekonomicznego W Krakowie, 2(1012), 81-95. https://doi.org/10.15678/krem.18759