The Non-Parametric Approach to the Quantification of the Uncertainty in the Design of Experiments Modelling

Abstract

Abstract. The classic design of experiments (DoE) typically uses the least-square method for a model identification and requires associated assumption about the normality of a noise factor. It is very convenience because it leads to a relative simple computations and well-known asymptotic statistics based on the normality assumption. However, if that assumption is not satisfied it may fail and obtained results may differ radically from the verification tests. The rationale for the caution may be the comparison of interval plots (based on the normality hypothesis) and box-plots (based on raw data). The useful approach is the bootstrap-based methodology which replaces the requirement of the normality assumption with weaker requirement of the independent and identical distribution (i.i.d.) of the random term. The industrial applications of this approach are still rare because the industry is very conservative and

Application of the Image Analysis Methods for the Study of Al2O3 Surafce Coatings

“…Obtained results may be interested for other researchers focused on coatings and surface layer modifications (Skoneczny and Bara, 2007;Bara et al, 2009;Kmita and Bara, 2012;Skoneczny et al, 2018;Bara et al, 2019), even in the combustion technology (Opydo et al, 2016). They may be also inspiring for related areas of materials science (Lipinski, 2015;Lipinski 2018;Szczotok et al, 2018), heavy-duty machines design and experimental design methodology (Pietraszek and Goroshko, 2014;Pietraszek et al, 2016), especially with the uncertainty quantification (Pietraszek et al, 2017) and fuzzy logic decision scheme Krawczyk and Sobczyk, 2018). The obtained data should be disseminated in scientific databases e.g.…”

The Smoothed Bootstrap Fine-Tuning

“…a statistical analysis without additional assumption about distribution, may be useful in other areas like e.g. industrial management (Maszke et al, 2018), materials science (Pietraszek and Gadek-Moszczak, 2013;Novy, 2016, Ulewicz et al, 2016;Dudek et al, 2017;Pietraszek et al, 2017;Jambor et al, 2018;Radek et al, 2018), especially supported by an image analysis (Gadek-Moszczak, 2017;Gadek-Moszczak and Matusiewicz, 2017), even in biomaterials (Gadek-Moszczak et al, 2015), hydraulic machines design (Pobedza and Sobczyk, 2013a;Pobedza and Sobczyk, 2013b;Guzowski and Sobczyk, 2014;Walczak and Sobczyk, 2014) and corrosion protection (Klimecka-Tatar, 2016). It may be also very useful in power industry (Dwornicka, 2014), chemical industry (Ulewicz and Radzyminska-Lenarcik, 2014;Gnatowski et al, 2018) or pharmaceutical and biotechnology industry (Skrzypczak- Pietraszek, 2016;Skrzypczak-Pietraszek et al, 2018b), where phytochemistry investigation (Skrzypczak- Pietraszek and Pietraszek, 2009;Skrzypczak-Pietraszek et al, 2017) are conducted with a huge random noise from individual differences in plant reactions.…”

Simulations of Safety Vales for Fluid Power Systems

“…Presented methods may be useful in many areas of the simulation-based engineering and science, e.g. temperature fields (Styrylska and Pietraszek, 1992) or the statistical estimation of an uncertainty (Pietraszek and Gadek-Moszczak, 2014;Goroshko and Royzman, 2015;Kozien and Kozien, 2017a), especially with non-parametric (Pietraszek et al, 2017a;Pietraszek et al, 2017b) or even fuzzy (Pietraszek and Skrzypczak-Pietraszek, 2014;Pietraszek et al, 2016) approach. Such simulations require systematic approach usually based on the design of experiments methodology (Montgomery, 2008) which is applied widely from biotechnology (Skrzypczak-Pietraszek et al, 2018a;Skrzypczak-Pietraszek et al, 2018b) and phytochemistry (Skrzypczak- Pietraszek and Pietraszek, 2009;Skrzypczak-Pietraszek et al, 2017) through materials science (Scendo et al, 2014;Klimecka-Tatar et al, 2015), the machining (Dwornicka et al, 2017;Radek et al, 2018a;Radek et al, 2018b), the technical stereology (Gadek-Moszczak, 2017;Gadek-Moszczak and Matusiewicz, 2017) up to a large scale research facilities (Baussan et al, 2014;Singh et al, 2016;Singh et al, 2017), a commercialization of scientific research (Kozien and Kozien, 2017b) and a factory lean management (Ulewicz et al, 2013;Ulewicz, 2016;Maszke et al, 2018).…”