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The past decade has seen rapid advances in the development of new methods for the design and analysis of split-plot experiments. Unfortunately, the value of these designs for industrial experimentation has not been fully appreciated. In this paper, we review recent developments and provide guidelines for the use of split-plot designs in industrial applications.

This study proposes the inclusion of noise variables in an experimental design to develop a predictive model of surface roughness in the face milling process of duplex stainless steel. A central composite design arrangement was conducted, incorporating controlled variables (cutting speed, feed rate, milling width, and depth of cut) and noise variables (tool flank wear, fluid flow, and protrusion length). Each experimental configuration was employed in duplex stainless steel milling, with the collection of roughness data under each condition. The collected data were used to train eight configurations of artificial neural networks, which were then applied to predict roughness. The results indicate that the 7-20-14-1 network configuration exhibited the lowest root mean square error, which is a measure of the difference between predicted and observed values of (0.063), followed by 7-64-32-1 (0.064) and 7-14-12-1 (0.068), respectively. Additionally, these configurations also demonstrated the lowest mean absolute error values, which calculate the average of the absolute differences between predicted and observed values of (0.046, 0.053, and 0.055, respectively), and the coefficient of determination, which is a statistical measure indicating the proportion of data variability explained by the statistical model of (0.914, 0.908, and 0.901, respectively). Therefore, the inclusion of noise variables alongside controllable process factors resulted in a more accurate and robust predictive model of surface roughness for duplex stainless steel face milling.

Helical milling is an alternative to conventional drilling which, applied to the molds and dies industry, greatly impacts its competitiveness once it guarantees high levels of surface and geometrical quality. Excellent surface quality and the ability to drill holes with just one tool are some of the advantages of this process. Concerning the machining of hardened materials, its low machinability is another aspect that compromises the competitiveness of the mold segment. Faced with the challenges of hard machining, the present research aims the robust multi-objective optimization of AISI H13 hardened steel at high speeds to achieve competitive levels of surface quality and increase the productivity of the helical milling process. Experimental planning, robust parameter design with a focus on the crossed array, response surface methodology, and enhanced normalized normal constraint method were employed in the conduction of experiments, analysis, modeling, and optimization of the responses of interest. The responses evaluated were the mean roughness R a , the total circularity Ron t , and the material removal rate MRR . The control variables used were the axial feed per tooth f za , the tangential feed per tooth f zt , and the cutting speed v c . For the robust parameter design, the tool overhang length l to and borehole depth l b were considered as noise variables. The possibility of increasing the productivity of helical milling in a hardened material, maintaining the quality of the holes, was concluded. It was verified to the total circularity robustness about the two noise variables, and the average of the confirmation runs is equal to the mean model.

Airfoils play significant roles in aerodynamic engineering as they are important devices in designing aircraft and engines. For airfoils, geometric design variables often deviate from nominal values that deteriorate airfoil quality. Thus, the design optimization of airfoils under the noises of design variables is important. However, the existing literature does not consider functional responses that can more adequately describe airfoil performances than univariate and multivariate responses. To fill in this gap and further improve airfoil quality, we develop a surrogate-based robust parameter design methodology for the design optimization of airfoils with functional responses. A new optimization criterion that involves both location and dispersion effects associated with the functional feature of quality losses, noises of design variables, and emulator uncertainty is proposed. A Gaussian process (GP) model with functional responses is employed as a surrogate/emulator. An efficient method for computing the proposed criterion is developed. The proposed methodology is applied to a typical airfoil design optimization problem to demonstrate that better and more robust solutions are obtained with the proposed criterion for airfoils, and the computing time is significantly reduced with the proposed estimation method.

Fisher's pioneering work in design of experiments has inspired further work with broader applications, especially in industrial experimentation. This article discusses three topics in physical experiments: principles of effect hierarchy, sparsity, and heredity for factorial designs, a new method called conditional main effect (CME) for de-aliasing aliased effects, and robust parameter design. I also review the recent emergence of virtual experiments on a computer. Some major challenges in computer experiments, which must go beyond Fisherian principles, are outlined.

In this experimental study, picosecond laser treatment was performed on a nickel-based superalloy Nimonic 263, aiming to investigate the surface effects induced by irradiation in different atmospheric conditions and, concerning changes in surface composition, regarding the possibility for improvement of its functionality. Besides the varying laser parameters, such as a number of pulses and pulse energy, environmental conditions are also varied. All surface modifications were carried out in standard laboratory conditions and a nitrogen- and argon-rich atmosphere. The resulting topography effects depend on the specific laser treatment and could be categorized as increased roughness, crater formation, and formation of the laser-induced periodic surface structures (LIPSS). Changes in the chemical surface composition are distinguished as the potential formation of the protective oxides/nitrides on the sample surface. Numerous characterization techniques analyse the resulting effects on the topography and surface parameters. The multi-response parametric optimization of the picosecond laser process was performed using an advanced statistical method based on Taguchi’s robust parameter design. Finally, the optimal parameter conditions for Nimonic 263 modification are suggested.

Balancing competing objectives to select an optimal design of experiments involves flexibly combining measures to select a winner. The Pareto front approach for simultaneously considering multiple responses is adapted to design of experiments. The Pareto approach identifies a suite of potential best designs based on different emphases of the objectives. We propose a new algorithm, the Pareto Aggregating Point Exchange (PAPE) algorithm, to more efficiently explore candidate designs by populating the Pareto frontier with all possible contending designs identified during the search. The connection between the Pareto and the Derringer-Suich (1980) desirability function approaches is established and graphical methods are given which enable the user to easily explore design robustness to different weightings of the competing objectives as well as trade-offs between criteria among competing designs. The method is illustrated with two examples: a screening design setting in which it is of interest to simultaneously consider D-efficiency and protect against model misspecification, and a robust parameter design example where simultaneous consideration of D s -mean, D s -variance, and design size is of interest. This article has supplementary material online.

The aim of the paper is to develop a method for increasing the signal-to-noise ratio of eddy current measurement of geometric anomalies in static planar objects without actually eliminating the inherent effects of noise factors. This is achieved by means of Taguchi's robust parameter design of rectangular frame surface probes, which allows determining the optimal configuration of their constructions. On a specific example, a robust configuration construction of the eddy current probe design is found, i.e., its technical variant that ensures a reduction of the output signal variance near its average value, i.e., resistance to noise disturbances, due only to the appropriate determination of the values of the controllable design and operating parameters of the probe without eliminating uncontrollable interference inherent in the test objects. For the robust design of a number of eddy current meters with different functionalities, a universal magnetodynamic model of the probe was used, which, together with the application of orthogonal arrays, allows the creation and implementation of Taguchi-design of experiments. The software that implements this model has been verified, including by comparing it with the results of calculations on test’s examples performed using the finite element method. The accuracy achieved in this case allows us to assert the adequacy of the created computer program. The data obtained as part of the Taguchi-design of experiment were used to evaluate design options using the “larger is better“ quality loss function and the signal-to-noise ratios calculated on its basis, which made it possible to select the optimal combination of design and operating parameters of the eddy current probe. The reliability of the found optimal configuration of the eddy current probe design was proved by confirmatory calculations. The research results were also experimentally verified on a prototype. References 21, figures 6, tables 9.

To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of accurately estimating the control-by-noise interactions. Moreover, the existing space-filling designs focus on uniformly distributing the points in the design space, which are not suitable for noise factors because they usually follow nonuniform distributions such as normal distribution. This would suggest placing more points in the regions with high probability mass. However, noise factors also tend to have a smooth relationship with the response and therefore, placing more points toward the tails of the distribution is also useful for accurately estimating the relationship. These two opposing effects make the experimental design methodology a challenging problem. We propose optimal and computationally efficient solutions to this problem and demonstrate their advantages using simulated examples and a real industry example involving a manufacturing packing line. Supplementary materials for the article are available online.

Purpose: When designing an input-output system susceptible to noise, engineers assume a functional relation between the input and the output. The Taguchi method, which uses a dynamic, robust parameter design (RPD) to evaluate the robustness of the input-output relation against noise, is employed. This study aims to address extending the scope of use of a dynamic RPD. Methodology/Approach: A target system in a typical dynamic RPD can be interpreted as one in which the relation between the input and the output is a linear model, and the output error follows a normal distribution. However, an actual system often does not conform to this premise. Therefore, we propose a new analysis approach that can realize a more flexible system design by applying a response surface methodology (RSM) based on a generalized linear model (GLM) to dynamic RPD. Findings: The results demonstrate that 1) a robust solution can be obtained using the proposed method even for a typical dynamic RPD system or an actual system, and 2) the target function can be evaluated using an adjustment parameter. Research Limitation/implication: Further analysis is required to determine which factor(s) in the estimated process model largely contribute(s) to changes in the adjustment parameter. Originality/Value of paper: The applicability of typical dynamic RPD is limited. Hence, this study’s analytical process provides engineers with greater design flexibility and deeper insights into dynamic systems across various contexts. Category: Research paper Keywords: robust parameter design; dynamic system; generalized linear model; response surface methodology; Taguchi method