International Journal of Experimental Design and Process Optimisation (5 papers in press)
F-statistic for model validation over experimental regions using least squares response surfaces
by Scott M. Storm, Raymond R. Hill, Joseph J. Pignatiello, Edward D. White, G. Geoffrey Vining
Abstract: When a simulation operates over an array of input settings, it is critical that its validity across all settings is considered. This paper proposes an F-statistic, based on a ratio of mean square errors, to assess model validity. System data is fit to an Ordinary Least Squares response surface and the mean square errors between both system and model data and the fitted surface are calculated. The hypothesis under test is that system and model data that possess the same distributional properties will produce similar measures of disagreement with regard to the fitted surface. If the F-statistic indicates the mean square errors are statistically different, it is determined that the system and model data do not share distributional properties and the model is assessed as invalid. A notional example demonstrates the methodology and considerations to the method's confidence with respect to the model sample size is discussed.
Keywords: experimental design; F-statistic; linear regression; mean square error; response surface; simulation; stochastic model validation.
No-confounding designs with 24 runs for 7-12 factors
by Brian B. Stone, Douglas C. Montgomery, Rachel T. Silvestrini, Bradley Jones
Abstract: When experimenting with more than six independent variables, researchers under significant resource or time constraints often require alternatives to large Resolution V 2k-p fractional factorial designs. Many researchers also desire to avoid the expense of a foldover experiment required to de-alias completely confounded two-factor interactions (2FIs) when using resolution IV 2k-p designs. No-confounding designs are an excellent solution to this problem, as they have orthogonal main effects (ME) and no 2FI is completely confounded with another ME or 2FI. This paper introduces 24-run no-confounding designs for 7-12 factors. It presents a Monte Carlo simulation methodology used to evaluate algorithmically constructed designs and those in the existing literature. The results report the best-performing designs and metrics related to their types I and II error rate from the variable-selection process during repeated simulations of regression analyses.
Keywords: experimental design; Monte Carlo simulation; no-confounding designs; nonregular designs; orthogonal arrays.
Analysis of aluminium brazing sheet differential scanning calorimetry data
by Michael J. Benoit, Mark A. Whitney, Mary A. Wells, Alexander Penlidis, Stephen F. Corbin, Sooky Winkler
Abstract: Differential scanning calorimetry (DSC) measurements have provided insight into metallurgical reactions which can occur during joining of Al brazing sheet. Researchers have claimed that DSC is sensitive enough to differentiate between brazing sheets with different initial conditions; however, no rigorous proof of this claim has been given. The sensitivity of DSC measurements, as measured by changes in melting peak area, to experimental factors such as DSC sample preparation, sample orientation during testing and starting sheet temper has been investigated. A 23 factorial design was used, and the results were analysed using analysis of variance. The results showed that only the sheet punching direction during sample preparation had a statistically significant influence on the DSC measurements. Microstructure analysis revealed that punching on the core layer of the sheet led to extra clad alloy on the side of the sample, which melted during heating and contributed to a greater measured melting peak area.
Keywords: clad aluminium brazing sheet; design of experiments; differential scanning calorimetry; error analysis; experimental setup.
Mathematical modelling and numerical optimisation of machining parameters for the CNC end milling process using response surface methodology
by Boppana V. Chowdary, Mitra Kisraj, Kuldeep Ojha, Fahraz Ali
Abstract: This study applies response surface methodology (RSM) to optimise the machining parameters for minimum surface roughness in the end milling process for 5083 aluminium workpiece using high-speed steel cutting tools. The combination of parameters investigated and varied in this research work was spindle speed, feed rate, depth of cut and diameter of tool. The central composite design method was used to reduce the number of experimental runs, whereas modelling and analysis with RSM were performed to obtain the objective function for surface roughness. Furthermore, optimisation of the objective function for surface roughness was performed. The results indicated that the determined optimal combination of machining parameters improved the performance of the machining process.
Keywords: CCD; CNC; machining; milling; optimisation; RSM.
F-squares based optimal designs for reduced cubic canonical models in four components
by Bushra Husain, Sanghmitra Sharma
Abstract: Aggarwal et al. (2008) presented optimal orthogonal designs in two blocks based on F-squares for Darroch and Waller's quadratic mixture model in four components, while for Becker's and K-model, they presented their results in 2013. In this paper, we have constructed D-, A- and E-optimal designs in two blocks based on F-squares for new models called reduced cubic canonical model Forms I and II in four components when two component proportions are at the same level. Several criteria associated with the information matrix and eigenvalues for the designs are examined to infer characteristics in optimality. Conditions required for orthogonality are given for the reduced cubic canonical model Forms I and II.
Keywords: A-optimality; D-optimality; E-optimality; F-squares; mixture experiments; orthogonality; process variables; reduced cubic canonical model.