## 1 Introduction
Such studies may also be under stringent restrictions that consider, as a pivotal parameter, the time to respond to a process improvement call, as well as the actual (required) duration to complete a full schedule of experiments. To overcome such hindrances, there are several design of experiments (DOE) procedures--in the realm of statistical engineering--that may assist process engineers and scientists [25; 26; 27; 28; 29; 30]. DOE tools and techniques may aid in expediting customized quality improvement projects by optimizing research efforts and reducing the lead time required to arrive at consistent solutions. Moreover, DOE methodologies are part of the systematized Lean Six Sigma toolbox that is utilized to couple lean-and-green engineering with statistical engineering to assist achieving innovative and sustainable results [31; 32; 33; 34]. A quick and economical way to program structured DOE trials is to implement fractional factorial designs (FFDs) [25; 26]. Non-linear orthogonal arrays (OAs) are FFDs that have been applied in resolving essential research issues in filtration and recycling in order to improve the quality performance of a wastewater operation [35; 36]. In published research, FFDs are implemented in experimental schemes, which are appropriate for both replicated and unreplicated trials; the choice usually depends on the degree of difficulty to gather enough tailor-made measurements. Replicated FFD datasets are easier to treat by using classical methods such as regression analysis and analysis of variance (ANOVA) [25; 26; 37]. Unreplicated factorial experiments, while indispensable in environmental analysis and water management, pose more problems in the analysis phase [38; 39; 40]. Researchers, in the search for FFDs, also seek to maximize the number of effects studied. This leads to the saturation of the selected FFD scheme. Consequently, the quantification of a residual error cannot be attained, which makes the overall effort rather subjective. To overcome this problem, there are a great number of multifactorial techniques that have been developed to interpret unreplicated experiments in different ways [41]. This paper will concentrate on a very compact FFD design suitable for simultaneously detecting potential curvilinear effects. It is the Taguchi-type L\({}_{9}\)(3\({}^{4}\)) OA, which can program minimal experiments for up to four controlling factors [26]; it can be conveniently extended to resolve realistic output conditions that simultaneously involve several characteristics [26]. This sampling approach has been suggested due to the influence of the Taguchi method in the screening and optimization of chemometrical systems [42]. Although the Taguchi method is primarily used for optimally adjusting multiple controls, aiming to improve the performance of a single-characteristic response, methods have been devised to handle multi-characteristic cases, too [43; 44; 45]. The rationale behind this work is the use of the two-culture approach in aquimetric modeling, i.e., statistical inference and algorithmic information [46]. The statistical analysis part is novel because the proposed method uses a well-known specialized technique, which is devoted to treating unreplicated datasets, so as to evaluate the repeatability of the predictions in replicated trials, using elements from evidence theory [47]. The selected multi-parameter screener is the classical Lenth method [48], with critical values for the four-factor three-level L\({}_{9}\)(3\({}^{4}\)) OA adjusted by [PERSON] and [PERSON] [49]. The examined algorithmic solver, operating on the fully replicated L\({}_{9}\)(3\({}^{4}\)) OA dataset, is the support vector machine learning approach, which is an alternative artificial intelligence technique to neural networks [50]. Water innovation projects aspire to use the predictive capabilities of artificial intelligence to accomplish improved efficiencies in intricate wastewater operations [51; 52; 53].