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Journal articles on the topic 'Symmetric fractional factorial experiments'

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Author: Grafiati

Published: 8 September 2023

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1

Amoah, Emmanuel, Jakperik Dioggban, and Adjabui Michael Jackson. "Efficient Blocked Fractional Factorial Designs for Stated Choice Experiments of Size Two and Four." International Journal of Mathematics and Mathematical Sciences 2023 (March 7, 2023): 1–13. http://dx.doi.org/10.1155/2023/2515605.

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Stated choice experiments are increasingly becoming popular due to their ability to optimize information gain with limited resources. Many designs have been developed for the selection of various attributes and their levels to form choice sets. One such design is blocked fractional factorial design (BFFD). Stated choice experiments for symmetric attributes of 4 choice sets of sizes 2 and 4 and 8 choice sets of sizes 2 and 4 were developed using BFFDs. Generators for the stated choice set of sizes 2 and 4 with resolution three, four, and five were developed. The alias structures and confounding effects for the designs were derived, as well as their clear effects if any for estimation. The A -efficiency was used to compute the efficiencies of the proposed designs since it has better statistical properties. The computed efficiencies for the proposed designs reveal that 4 choice sets of size 4 designs are more efficient. Finally, a practical application of the proposed method was carried out for four choice sets of size 4 using 2 V 5 − 1 − 2 design with attributes and levels of service quality in public transport.

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2

Pettitt, A. N. "Infinite Estimates with Fractional Factorial Experiments." Statistician 45, no. 2 (1996): 197. http://dx.doi.org/10.2307/2988408.

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3

Brugger, Richard M. "How to Construct Fractional Factorial Experiments." Technometrics 34, no. 4 (November 1992): 492–93. http://dx.doi.org/10.1080/00401706.1992.10484968.

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4

Coleman, Shirley, and Jiju Antony. "TEACHING FRACTIONAL FACTORIAL EXPERIMENTS VIA COURSE DELEGATE DESIGNED EXPERIMENTS." Quality Assurance 7, no. 1 (January 2000): 37–48. http://dx.doi.org/10.1080/105294100277714.

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5

Mee, Robert W. "Tips for Analyzing Nonregular Fractional Factorial Experiments." Journal of Quality Technology 45, no. 4 (October 2013): 330–49. http://dx.doi.org/10.1080/00224065.2013.11917942.

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6

Fearn, Tom. "Design of Experiments 4: Fractional Factorial Designs." NIR news 18, no. 5 (August 2007): 14–15. http://dx.doi.org/10.1255/nirn.1035.

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7

Langsrud, Øyvind, Marit Risberg Ellekjaer, and Tormod Naes. "Identifying significant effects in fractional factorial experiments." Journal of Chemometrics 8, no. 3 (May 1994): 205–19. http://dx.doi.org/10.1002/cem.1180080304.

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8

Langsrud, Øyvind. "Identifying Significant Effects in Fractional Factorial Multiresponse Experiments." Technometrics 43, no. 4 (November 2001): 415–24. http://dx.doi.org/10.1198/00401700152672500.

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9

Turiel, Thomas P. "A FORTRAN Program to Generate Fractional Factorial Experiments." Journal of Quality Technology 20, no. 1 (January 1988): 63–72. http://dx.doi.org/10.1080/00224065.1988.11979084.

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10

Bingham, D. R., and R. R. Sitter. "Design Issues in Fractional Factorial Split-Plot Experiments." Journal of Quality Technology 33, no. 1 (January 2001): 2–15. http://dx.doi.org/10.1080/00224065.2001.11980043.

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11

KUMAR, PRAKASH, KRISHAN LAL, ANIRBAN MUKHERJEE, UPENDRA KUMAR PRADHAN, MRINMOY RAY, and OM PRAKASH. "Advanced row-column designs for animal feed experiments." Indian Journal of Animal Sciences 88, no. 4 (January 5, 2023): 499–503. http://dx.doi.org/10.56093/ijans.v88i4.78895.

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Inappropriate statistical designs may misinterpret results of animal feed experiments. Thus complete statistical designs can make animal feed research more appropriate and cost effective. Usually factorial row-column designs are used when the heterogeneity in the experimental material is in two directions and the experimenter is interested in studying the effect of two or more factors simultaneously. Attempts have been to develop the method of construction of balanced nested row column design under factorial setup. Factorial experiments are used in designs when two or more factors have same levels or different levels. The designs that are balanced symmetric factorials nested in blocks are called block designs with nested row-column balanced symmetric factorial experiments. These designs were constructed by using confounding through equation methods.Construction of confounded asymmetrical factorial experiments in row-column settings and efficiency factor of confounded effects was worked out. The design can be used in animal feed experiment with fewer resources by not compromising the test accuracy.

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12

Han, Beichen, and Yuna Zhao. "Construction of Optimal Split-Plot Designs for Various Design Scenarios." Fractal and Fractional 6, no. 10 (October 19, 2022): 608. http://dx.doi.org/10.3390/fractalfract6100608.

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When performing fractional factorial experiments in a completely random order is impractical, fractional factorial split-plot designs are suitable options as an alternative. It is well recognized that the more there are lower order effects of interest at lower order confounding, the better the designs. From this viewpoint, this paper considers the construction of optimal regular two-level fractional factorial split-plot designs. The optimality criteria for two different design scenarios are proposed. Under the newly proposed optimality criteria, the theoretical construction methods of optimal regular two-level fractional factorial split-plot designs are then proposed. In addition, we also explore the theoretical construction methods of some optimal regular two-level fractional factorial split-plot designs under the widely adopted general minimum lower order confounding criterion.

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13

McLeod, Robert G., and John F. Brewster. "The Design of Blocked Fractional Factorial Split-Plot Experiments." Technometrics 46, no. 2 (May 2004): 135–46. http://dx.doi.org/10.1198/004017004000000176.

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14

Bingham, Derek, and Randy R. Sitter. "Fractional Factorial Split-Plot Designs for Robust Parameter Experiments." Technometrics 45, no. 1 (February 2003): 80–89. http://dx.doi.org/10.1198/004017002188618725.

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15

Cheng, Ching-Shui, and Rahul Mukerjee. "On regular-fractional factorial experiments in row–column designs." Journal of Statistical Planning and Inference 114, no. 1-2 (June 2003): 3–20. http://dx.doi.org/10.1016/s0378-3758(02)00459-7.

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16

Capehart, Shay R., Ahmet Keha, Murat Kulahci, and Douglas C. Montgomery. "Designing fractional factorial split-plot experiments using integer programming." International Journal of Experimental Design and Process Optimisation 2, no. 1 (2011): 34. http://dx.doi.org/10.1504/ijedpo.2011.038050.

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17

Wan, Hong, and Bruce E. Ankenman. "Two-Stage Controlled Fractional Factorial Screening for Simulation Experiments." Journal of Quality Technology 39, no. 2 (April 2007): 126–39. http://dx.doi.org/10.1080/00224065.2007.11917680.

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18

Zhao, Yuna. "Split-Plot Designs with Few Whole Plot Factors Containing Clear Effects." Fractal and Fractional 6, no. 8 (August 20, 2022): 453. http://dx.doi.org/10.3390/fractalfract6080453.

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Fractional factorial split-plot designs are widely used when it is impractical to perform fractional factorial experiments in a completely random order. When there are too many subplots per whole plot, or too few whole plots, fractional factorial split-plot designs with replicated settings of the whole plot factors are preferred. However, such an important study is undeveloped in the literature. This paper considers fractional factorial split-plot designs with replicated settings of the WP factors from the viewpoint of clear effects. We investigate the sufficient and necessary conditions for this class of designs to have clear effects. An algorithm is proposed to generate the desirable designs which have the most clear effects of interest. The fractional factorial split-plot design with replicated settings of the WP factors is analysed and the results are discussed.

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19

Peachey, T. C., N. T. Diamond, D. A. Abramson, W. Sudholt, A. Michailova, and S. Amirriazi. "Fractional Factorial Design for Parameter Sweep Experiments Using Nimrod/E." Scientific Programming 16, no. 2-3 (2008): 217–30. http://dx.doi.org/10.1155/2008/943696.

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The techniques of formal experimental design and analysis are powerful tools for scientists and engineers. However, these techniques are currently underused for experiments conducted with computer models. This has motivated the incorporation of experimental design functionality into the Nimrod tool chain. Nimrod has been extensively used for exploration of the response of models to their input parameters; the addition of experimental design tools will combine the efficiency of carefully designed experiments with the power of distributed execution. This paper describes the incorporation of one type of design, the fractional factorial design, and associated analysis tools, into the Nimrod framework. The result provides a convenient environment that automates the design of an experiment, the execution of the jobs on a computational grid and the return of results, and which assists in the interpretation of those results. Several case studies are included which demonstrate various aspects of this approach.

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20

Wang, P. C., and D. F. Lin. "Dispersion effects in signal-response data from fractional factorial experiments." Computational Statistics & Data Analysis 38, no. 1 (November 2001): 95–111. http://dx.doi.org/10.1016/s0167-9473(01)00045-7.

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21

McLeod, Robert G., and John F. Brewster. "Blocked Fractional Factorial Split-Plot Experiments for Robust Parameter Design." Journal of Quality Technology 38, no. 3 (July 2006): 267–79. http://dx.doi.org/10.1080/00224065.2006.11918614.

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22

Chen, Yen-Sheng, and Ting-Yu Ku. "Efficiency Improvements of Antenna Optimization Using Orthogonal Fractional Experiments." International Journal of Antennas and Propagation 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/708163.

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This paper presents an extremely efficient method for antenna design and optimization. Traditionally, antenna optimization relies on nature-inspired heuristic algorithms, which are time-consuming due to their blind-search nature. In contrast, design of experiments (DOE) uses a completely different framework from heuristic algorithms, reducing the design cycle by formulating the surrogates of a design problem. However, the number of required simulations grows exponentially if a full factorial design is used. In this paper, a much more efficient technique is presented to achieve substantial time savings. By using orthogonal fractional experiments, only a small subset of the full factorial design is required, yet the resultant response surface models are still effective. The capability of orthogonal fractional experiments is demonstrated through three examples, including two tag antennas for radio-frequency identification (RFID) applications and one internal antenna for long-term-evolution (LTE) handheld devices. In these examples, orthogonal fractional experiments greatly improve the efficiency of DOE, thereby facilitating the antenna design with less simulation runs.

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23

Shen, D. Eric, Leandro A. Estrada, Anna M. Österholm, Danielle H. Salazar, Aubrey L. Dyer, and John R. Reynolds. "Understanding the effects of electrochemical parameters on the areal capacitance of electroactive polymers." J. Mater. Chem. A 2, no. 20 (2014): 7509–16. http://dx.doi.org/10.1039/c4ta01375a.

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24

Oles, Philip J. "Fractional Factorial Design Approach for Optimizing Analytical Methods." Journal of AOAC INTERNATIONAL 76, no. 3 (May 1, 1993): 615–20. http://dx.doi.org/10.1093/jaoac/76.3.615.

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Abstract Experimental designs based on procedures of Taguchi are described for optimizing analytical methods. Methods were efficiently developed, with improvements in precision and accuracy, for the determination of cholesterol in foods, magnesium in feed premix, and moisture in mayonnaise. Significant factors and interactions were identified by using 2-level designs, analysis of variance techniques, and commercially available computer software. The designs were prepared by using Taguchi linear diagrams. The methods developed as a result of these experiments have proven to be rugged and reliable.

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25

Frey, Daniel D., and Rajesh Jugulum. "The Mechanisms by Which Adaptive One-factor-at-a-time Experimentation Leads to Improvement." Journal of Mechanical Design 128, no. 5 (August 31, 2005): 1050–60. http://dx.doi.org/10.1115/1.2216733.

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This paper examines mechanisms underlying the phenomenon that, under some conditions, adaptive one-factor-at-a-time experiments outperform fractional factorial experiments in improving the performance of mechanical engineering systems. Five case studies are presented, each based on data from previously published full factorial physical experiments at two levels. Computer simulations of adaptive one-factor-at-a-time and fractional factorial experiments were carried out with varying degrees of pseudo-random error. For each of the five case studies, the average outcomes are plotted for both approaches as a function of the strength of the pseudo-random error. The main effects and interactions of the experimental factors in each system are presented and analyzed to illustrate how the observed simulation results arise. The case studies show that, for certain arrangements of main effects and interactions, adaptive one-factor-at-a-time experiments exploit interactions with high probability despite the fact that these designs lack the resolution to estimate interactions. Generalizing from the case studies, four mechanisms are described and the conditions are stipulated under which these mechanisms act.

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26

Tazliqoh, A. Z., A. H. Wigena, and U. D. Syafitri. "Fractional factorial and D-optimal design for discrete choice experiments (DCE)." IOP Conference Series: Earth and Environmental Science 299 (July 29, 2019): 012067. http://dx.doi.org/10.1088/1755-1315/299/1/012067.

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27

Dingus, Cheryl, Bruce Ankenman, Angela Dean, and Fangfang Sun. "Identification of Dispersion Effects in Replicated Two-Level Fractional Factorial Experiments." Journal of Statistical Theory and Practice 7, no. 4 (October 2, 2013): 687–702. http://dx.doi.org/10.1080/15598608.2013.781851.

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28

Bush, Stephen. "Optimal Designs for Stated Choice Experiments Generated From Fractional Factorial Designs." Journal of Statistical Theory and Practice 8, no. 2 (March 24, 2014): 367–81. http://dx.doi.org/10.1080/15598608.2013.805451.

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29

DANTE, R., J. ESCAMILLA, V. MADRIGAL, T. THEUSS, J. DEDIOSCALDERON, O. SOLORZA, and R. RIVERA. "Fractional factorial design of experiments for PEM fuel cell performances improvement." International Journal of Hydrogen Energy 28, no. 3 (March 2003): 343–48. http://dx.doi.org/10.1016/s0360-3199(02)00069-1.

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30

Babiak, I., E. Brzuska, and J. Perkowski. "Fractional factorial design of screening experiments on cryopreservation of fish sperm." Aquaculture Research 31, no. 3 (March 2000): 273–82. http://dx.doi.org/10.1046/j.1365-2109.2000.00383.x.

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31

Vegliò, F. "The optimization of manganese dioxide bioleaching media by fractional factorial experiments." Process Biochemistry 31, no. 8 (November 1996): 773–85. http://dx.doi.org/10.1016/s0032-9592(96)00024-6.

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32

Woodward, Phil, and Rosalind Walley. "Bayesian Variable Selection for Fractional Factorial Experiments with Multilevel Categorical Factors." Journal of Quality Technology 41, no. 3 (July 2009): 228–40. http://dx.doi.org/10.1080/00224065.2009.11917778.

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33

Bingham, D. R., E. D. Schoen, and R. R. Sitter. "Designing fractional factorial split-plot experiments with few whole-plot factors." Journal of the Royal Statistical Society: Series C (Applied Statistics) 53, no. 2 (April 2004): 325–39. http://dx.doi.org/10.1046/j.1467-9876.2003.05029.x.

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34

Chen, Chuen-Lung, Muhammad Arshad Khan, and Chyng-Min Wu. "Identify Generators for 2k - p Experiments Using Taguchi Orthogonal Arrays." International Journal of Reliability, Quality and Safety Engineering 05, no. 04 (December 1998): 403–22. http://dx.doi.org/10.1142/s0218539398000339.

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Two-level fractional factorial design is an efficient technique for experiments considering a large number of factors. To evaluate the efficiency and analyze the data for such a design, we need to know the generators for the design, so that, using the generators, we can generate its defining relation and alias structure. Although knowing the generators is important for a two-level fractional factorial design, it is not unusual in actual industrial situations for the generators used in the design to be lost or overlooked while the design is performed. Since Taguchi methods has been widely applied in industry, in this research, an efficient algorithm based on Taguchi orthogonal arrays (OA's) and interaction tables is developed to identify the generators for given designs. Furthermore, with the investigation of the insights of Taguchi OA's and interaction tables, this research may provide ideas for making Taguchi methods a simple tool for developing optimal designs for 2k - p experiments.

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35

Gao, Feng, Rong Fu, Ming Yang Qian, Zhu Min Wang, and Xiang Zhang. "Optimization of Magnesium Separation and Extraction from Boron Slurry Using Response Surface Methodology." Advanced Materials Research 366 (October 2011): 366–69. http://dx.doi.org/10.4028/www.scientific.net/amr.366.366.

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Response surface methodology was used to optimize the soaking Mg leaching ratio from the boron slurry screened by 25 fractional factorial design. Five effective factors such as H2SO4 concentrations, reaction time, reaction temperature and stir velocity were tested by using 25 fractional factorial design criterion and three effective factors H2SO4 concentrations, reaction time and reaction temperature showed significant effect(P2SO4 concentrations of 0.29mol/l, reaction time of 90 min and reaction temperature of 50°C. Three runs of additional confirmation experiments were conducted. The mixture magnesium leaching value was 58.20%.

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36

Bingham, D. R., E. D. Schoen, and R. R. Sitter. "Corrigendum: Designing fractional factorial split-plot experiments with few whole-plot factors." Journal of the Royal Statistical Society: Series C (Applied Statistics) 54, no. 5 (November 2005): 955–58. http://dx.doi.org/10.1111/j.1467-9876.2005.00523_1.x.

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37

AHMED, EJAZ, and SUBOOHI. "ON DETERMINING SPARSE FACTORS FOR CAKE BAKING USING UNREPLICATED FRACTIONAL FACTORIAL EXPERIMENTS." Quality Engineering 5, no. 4 (January 1993): 571–81. http://dx.doi.org/10.1080/08982119308918999.

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38

Echeverría, J. C., M. T. Morera, C. Mazkiarán, and J. J. Garrido. "Competitive sorption of heavy metal by soils. Isotherms and fractional factorial experiments." Environmental Pollution 101, no. 2 (1998): 275–84. http://dx.doi.org/10.1016/s0269-7491(98)00038-4.

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39

Edwards, David J. "Follow-up experiments for two-level fractional factorial designs via double semifoldover." Metrika 77, no. 4 (August 2, 2013): 483–507. http://dx.doi.org/10.1007/s00184-013-0450-z.

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40

Wang, Jian-jun, and Yi-zhong Ma. "Bayesian Analysis of Two-Level Fractional Factorial Experiments with Non-Normal Responses." Communications in Statistics - Simulation and Computation 42, no. 9 (October 2013): 1970–88. http://dx.doi.org/10.1080/03610918.2012.687063.

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41

Zhong, Ming, Li Wang, Pengfei Li, and Zhenya Yan. "Spontaneous symmetry breaking and ghost states supported by the fractional PT-symmetric saturable nonlinear Schrödinger equation." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 1 (January 2023): 013106. http://dx.doi.org/10.1063/5.0128910.

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We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and [Formula: see text]-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole and tripole solitons (i.e., first and second excited states) are also studied numerically. Moreover, we analyze the influences of fractional Lévy index ([Formula: see text]) and saturable nonlinear parameters (S) on the symmetry breaking of solitons in detail. The stability of fundamental symmetric soliton, asymmetric, dipole, and tripole solitons is explored via the linear stability analysis and direct propagations. Moreover, we explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons. Meanwhile, we find the stable excitations from the fractional diffraction with saturation nonlinearity to integer-order diffraction with Kerr nonlinearity via the adiabatic excitations of parameters. These results will provide some theoretical basis for the study of spontaneous symmetry breaking phenomena and related physical experiments in the fractional media with [Formula: see text]-symmetric potentials.

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42

Shen, Zhengwei. "Construction of symmetric fractional over-complete wavelets and applications in image restoration." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 04 (July 2016): 1650020. http://dx.doi.org/10.1142/s021969131650020x.

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In this work, a novel design scheme is proposed for the construction of symmetric fractional over-complete wavelet filter banks. We first provide solutions to the open problem of designing low-pass filters that are symmetric and of minimum-length. We then obtain the high high-pass filters via Toeplitz matrix factorization which is of less computational complexity than existing methods. The resulting filter banks are approximately shift-invariant. The designed filter banks are applied in image restoration that uses an analysis based model solved by split Bregman algorithms. The experiments show the constructed symmetric fractional over-complete wavelet transforms (FOWTs) allow better restoration results than some other wavelet transforms in the literature.

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43

Nair, Vijay, Victor Strecher, Angela Fagerlin, Peter Ubel, Kenneth Resnicow, Susan Murphy, Roderick Little, Bibhas Chakraborty, and Aijun Zhang. "Screening Experiments and the Use of Fractional Factorial Designs in Behavioral Intervention Research." American Journal of Public Health 98, no. 8 (August 2008): 1354–59. http://dx.doi.org/10.2105/ajph.2007.127563.

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44

Gilmour, S. G., and R. Mead. "Fixing a factor in the sequential design of two-level fractional factorial experiments." Journal of Applied Statistics 23, no. 1 (February 1996): 21–30. http://dx.doi.org/10.1080/02664769624323.

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45

Ben-Gal, Irad, and Lev B. Levitin. "An application of information theory and error-correcting codes to fractional factorial experiments." Journal of Statistical Planning and Inference 92, no. 1-2 (January 2001): 267–82. http://dx.doi.org/10.1016/s0378-3758(00)00165-8.

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46

Faisal, Saira, Aurelio Tronci, Muhammad Ali, Long Lin, and Ningtao Mao. "Pretreatment of silk for digital printing: identifying influential factors using fractional factorial experiments." Pigment & Resin Technology 49, no. 2 (October 18, 2019): 145–53. http://dx.doi.org/10.1108/prt-07-2019-0065.

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Purpose The purpose of this study is to identify the most influential factors affecting the printing properties and print quality of digitally printed silk fabrics in terms of colour strength and fixation percentage. Design/methodology/approach In this study, five factors (concentration of thickener, concentration of urea, concentration of alkali, pH of pretreatment liquor and steaming duration) were investigated using a blocked 25−1 fractional factorial experiment. The type of thickeners [polyacrylic acid and polyacrylamide (PAM)] were considered as a block. Findings Linear models were obtained and statistically tested using both analysis of variance and coefficient of determination (R2), and they were found to be accurate at 90 per cent confidence level. It was revealed that concentration of alkali, concentrations of urea and pH of the pretreatment liquor had an increasing effect on colour strength, whereas concentration of thickener and steaming duration showed decreasing effect on colour strength of digitally printed silk fabrics. Furthermore, concentration of alkali, concentrations of urea had increasing effect on dye fixation percentage, whereas steaming duration showed decreasing effect on dye fixation percentage of digitally printed silk fabrics. In addition, PAM thickener based pretreatment recipe exhibited better printing properties for the digitally printing of silk fabrics. Originality/value The main influences and significant two-factor interactions were discussed in detail to gain a better understanding of the printing properties of digitally printed silk fabrics. The findings of this study are useful for further optimisation of pre- and post-treatment processes for digital printing of silk fabrics.

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47

HURLEY, PAUL D. "THE CONSERVATIVE NATURE OF THE EFFECT SPARSITY ASSUMPTION FOR SATURATED FRACTIONAL FACTORIAL EXPERIMENTS." Quality Engineering 7, no. 4 (January 1995): 657–71. http://dx.doi.org/10.1080/08982119508918814.

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48

Pan, Guohua, and Thomas J. Santner. "Theory of screening procedures to identify robust product designs using fractional factorial experiments." Journal of Statistical Planning and Inference 125, no. 1-2 (October 2004): 59–84. http://dx.doi.org/10.1016/j.jspi.2003.10.007.

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49

Jaynes, Jessica, Weng-Kee Wong, and Hongquan Xu. "Using blocked fractional factorial designs to construct discrete choice experiments for healthcare studies." Statistics in Medicine 35, no. 15 (January 28, 2016): 2543–60. http://dx.doi.org/10.1002/sim.6882.

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50

Rodríguez-Loaiza, Pilar, Salvador Namur, and Mario González-de la Parra. "Application of Design of Experiments (DOE) to the Development and Validation of a Swab Sampling Method for Cleaning Validation." Asian Journal of Chemistry and Pharmaceutical Sciences 2, no. 1 (April 17, 2017): 16. http://dx.doi.org/10.18311/ajcps/2017/8460.

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Cleaning validation is one of the key elements of the validation program of an active pharmaceutical ingredient (API) manufacturer. One of the most important aspects of cleaning validation is the sampling methods. Swabbing or surface sampling is the subject of this article. The application of sequential experimental designs for the efficient development of a swab sampling method, based on a fractional factorial design followed by full factorial design, is illustrated in this article.

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