Sequenciamento sistemático de experimentos fatoriais como alternativa à ordem aleatória
Systematic sequencing of factorial experiments as an alternative to the random order
Pedro Carlos Oprime; Vitória Maria Miranda Pureza; Samuel Conceição de Oliveira
Resumo
Palavras-chave
Abstract
Abstract:: The current study aims to discuss the use of systematic methods to generate experimental designs with good statistical properties and low costs. The research focuses on the sequence of experiments and on analysis the results of three different approaches used to build (orthogonal and non-orthogonal) two-level factorial designs, wherein sequencing is randomly or systematically performed. The study simulated the design generated by each approach in the context of an actual glass container manufacturing process, with and without the presence of linear trend effects. The results indicate that, in comparison to the random order, systematic sequences may lead to fewer factor level changes and to increased robustness to linear trend effects. Therefore, they may attach design cost and quality.
Keywords
Referências
Addelman, S. (1972). Recent development in the designs of factorial experiments. Journal of the American Statistical Association, 67(337), 103-111. http://dx.doi.org/10.1080/01621459.1972.10481211.
Adekeye, K.S., & Kunert, J. (2005). On the comparison of run orders of unreplicated 2k-p-design in the process of a time-trend. Techinical Report, Universitat Dortmund, (3), 475.
Aggarwal, M. L., Budhraja, V., & Lin, D. K. J. (2003). New class of orthogonal arrays and its applications. IAPQR Transactions, 28(1), 23-32.
Alonso, M. C., Bousbaine, A., Llovet, J., & Malpica, J. A. (2011). Obtaining industrial experimental designs using a heuristic technique. Expert Systems with Applications, 38(8), 10094-10098. http://dx.doi.org/10.1016/j.eswa.2011.02.004.
Angelopoulos, P., Evangelaras, H., & Koukouvinos, C. (2009). Run orders for efficient two level experimental plans with minimum factor level changes robust to time trends. Journal of Statistical Planning and Inference, 139(10), 3718-3724. http://dx.doi.org/10.1016/j.jspi.2009.05.002.
Atkinson, A. C. (1996). The usefulness of optimum experimental designs. Journal of the Royal Statistical Society. Series B. Methodological, 58(1), 59-76.
Atkinson, A. C., & Bailey, R. A. (2001). On hundred year of the design of experiments on and off the pages of Biometrika. Biometrika, 88(1), 53-97. http://dx.doi.org/10.1093/biomet/88.1.53.
Atkinson, A. C., & Donev, A. N. (1996). Experimental designs optimally balanced for trend. Technometrics, 38(4), 333-341. http://dx.doi.org/10.1080/00401706.1996.10484545.
Atkinson, A. C., Donev, A. N., & Tobias, R. D. (2007). Optimum experiments design with SAS. New York: Oxford Press.
Bailey, R. A., Cheng, C. S., & Kipnis, P. (1992). Construction of trend-resistant factorial designs. Statistica Sinica, 2, 393-411.
Bertsimas, D., Johnson, M., & Kallus, N. (2015). The power of optimization over randomization in designing experiments involving small samples. Operations Research, 63(4), 868-876. http://dx.doi.org/10.1287/opre.2015.1361.
Bessant, J., Caffyn, S., & Gallagher, M. (2001). An evolutionary model of continuous improvement behavior. Technovation, 21(2), 67-77. http://dx.doi.org/10.1016/S0166-4972(00)00023-7.
Bessant, J., & Caffyn, S. (1997). High involvement innovation through continuous improvement. International Journal of Technology Management, 14(3), 7-28. http://dx.doi.org/10.1504/IJTM.1997.001705.
Box, G. E. P., Hunter, W. G., & Hunter, J. S. (1978). Statistics for experimenters. New York: Wiley.
Cheng, C.-S. (1985). Run orders of factorial designs. In L. LeCam & R. A. Olshen (Eds.), Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (pp. 619-633). Wadsworth.
Cheng, C.-S. (1990). Construction of run orders of factorial designs. In S. Ghosh (Ed.), Statistical design and analysis of industrial experiments (pp. 423-39). New York: Subir Ghosh.
Cheng, C.-S., & Jacroux, M. (1988). On the construction of trend-free run orders of two level factorial designs. Journal of the American Statistical Association, 83(404), 1152-1158. http://dx.doi.org/10.1080/01621459.1988.10478713.
Cook, R. D., & Nachtsheim, C. J. A. (1980). Comparison of algorithms for constructing exact D-optimal designs. Technometrics, 22(3), 315-324. http://dx.doi.org/10.1080/00401706.1980.10486162.
Cordier, C., Marchand, H., Laundy, R., & Wolsey, L. A. (1999). bc-opt: a branch-and-cut code for mixed integer programs. Mathematical Programming, 86(2), 335-353. http://dx.doi.org/10.1007/s101070050092.
Coster, D. C., & Cheng, C.-S. (1988). Minimum cost trend-free run orders of fractional factorial designs. Annals of Statistics, 16(3), 1188-1205. http://dx.doi.org/10.1214/aos/1176350955.
Daniel, C., & Wilcoxon, F. (1966). Factorial 2p-q plans robust against linear and quadratic trends. Technometrics, 8, 259-278.
Davis, O. L. (1956). The design and analysis of industrial experiments. London: Longman. 637 p.
Delbridge, R., & Barton, H. (2002). Organizing for continuous improvement: structures and roles in automotive components plants. International Journal of Operations & Production Management, 22(6), 680-692. http://dx.doi.org/10.1108/01443570210427686.
Dickinson, A. W. (1974). Some run orders requirements a minimum number of factor level changes for the 24 and 25 main effect plans. Technometrics, 16, 31-37.
Draper, N. R., & Stoneman, D. M. (1968). Factor changes and linear trends in eight-run two level factorial designs. Technometrics, 10(2), 301-311. http://dx.doi.org/10.1080/00401706.1968.10490562.
Dykstra, O. (1971). The Augmentation of experimental data to maximize |X′X|. Technometrics, 13(3), 682-688.
Fisher, R. (1926). The arrangement of field experiments. Journal of the Ministry of Agriculture of Great Britain, 33, 503-513.
Galil, Z., & Kiefer, J. (1980). Time- and space-saving computer methods related to Mitchell’s DETMAX for finding D-Optimum designs. Technometrics, 22(3), 301-313. http://dx.doi.org/10.1080/00401706.1980.10486161.
Ganju, J., & Lucas, J. M. (2004). Randomized and random run order experiments. Journal of Statistical Planning and Inference, 133(1), 199-210. http://dx.doi.org/10.1016/j.jspi.2004.03.009.
Garroi, J. J., Goos, P., & Sorensen, K. (2009). A variable-neighborhood search algorithm for finding optimal run orders in the presence of serial correlation. Journal of Statistical Planning and Inference, 139(1), 30-44. http://dx.doi.org/10.1016/j.jspi.2008.05.014.
Gibbons, J. D., & Chakraborti, S. (2011). Nonparametric statistical inference (5th ed.). New York: Taylor & Francis.
Githinji, F., & Jacroux, M. (1998). On the determination and construction of optimal designs for comparing a set of test treatments with a set of controls in the presence of a linear trend. Journal of Statistical Planning and Inference, 66(1), 61-74. http://dx.doi.org/10.1016/S0378-3758(97)00067-0.
Harrison, A. (2000). Continuous improvement: the trade-off between self-management and discipline. Integrated Manufacturing Systems, 11(3), 180-187. http://dx.doi.org/10.1108/09576060010320416.
Hilow, H. (2013). Comparison among run order algorithms for sequential factorial experiments. Computational Statistics & Data Analysis, 58, 397-406. http://dx.doi.org/10.1016/j.csda.2012.09.013.
Hyland, P. W., Soosay, C., & Sloan, T. R. (2003). Continuous improvement and learning in the supply chain. International Journal of Physical Distribution & Logistics Management, 33(4), 316-335. http://dx.doi.org/10.1108/09600030310478793.
Imai, M. (1997). Gemba Kaisen: a common sense, low-cost approach to management. New York: McGraw-Hill.
Jacroux, M. (1994). On the construction of trend-resistant fractional factorial row-column designs. The Indian Journal of Statistics, 56(Pt. 2), 251-258.
Joiner, B. L., & Campbell, C. (1976). Designing experiments when run order is important. Technometrics, 18(3), 249-259. http://dx.doi.org/10.1080/00401706.1976.10489445.
Kume, H. (1993). Métodos estatísticos para melhoria da qualidade (11. ed.). São Paulo: Gente. 245 p.
Marin-Garcia, J. A., Val, M. P., & Martin, T. B. (2008). Longitudinal study of the results of continuous improvement in an industrial company. Team Performance Management, 14(1/2), 56-6.
Mitchell, T. J. (1974). An algorithm for the construction of D-optimal experimental designs. Technometrics, 16, 203-211.
Montgomery, C. D., Runger, G. C., & Hubele, N. F. (2009). Engineering statistics. New York: John Wiley & Sons.
Montgomery, D. C. (1991). Design and analysis of experiments. New York: John Wiley & Sons.
Oprime, P. C., Monsanto, R., & Donadone, J. C. (2010). Análise da complexidade, estratégias e aprendizagem em projetos de melhoria contínua: estudos de caso em empresas brasileiras. Gestão & Produção, 17, 669-682.
Pureza, V., Oprime, P. C., & Costa, A. F. (2014). Some experiments on mathematical programming for experiment sequencing (Documento de pesquisa).
Savolainen, T. I. (1999). Cycles of continuous improvement: realizing competitive advantages through quality. International Journal of Operations & Production Management, 19(11), 1203-1222. http://dx.doi.org/10.1108/01443579910291096.
Street, D. J., & Burgess, L. (2008). Some open combinatorial problems in the design of stated choice experiments. Discrete Mathematics, 308(13), 2781-2788. http://dx.doi.org/10.1016/j.disc.2006.06.042.
Suen, C., & Midha, A. C. K. (2013). Optimal fractional factorial designs and their construction. Journal of Statistical Planning and Inference, 143(10), 1828-1834. http://dx.doi.org/10.1016/j.jspi.2013.05.004.
Tack, L., & Vandebroek, M. (2004). Trend-resistant and cost-efficient cross-over designs for mixed models. Computation Statistics & Data Analysis, (46), 721-746.
Toledo, J. C. (1986). Qualidade Industrial: conceitos, sistemas e estratégias. São Paulo: Editora Atlas.
Triefenbach, F. (2008). Design of experiments: the D-Optimal approach and its implementation as a computer algorithm (Bachelor’s thesis). UMEA University, Umea; South Westphalia University of Applied Sciences, Meschede.
Tsao, H.-S. J., & Liu, H. (2008). Optimal sequencing of test conditions in 2. k factorial experimental design for run-size minimizationComputers & Industrial Engineering, 55(2), 450-464. http://dx.doi.org/10.1016/j.cie.2008.01.006.
Wang, P. C. (1991). Symbol changes and trend resistance in orthogonal plans of symmetric factorials. The Indian Journal of Statistics, 53(Pt. 3), 297-303.
Wang, P. C., & Chen, M. H. (1998). Level changes and trend resistance on replacement in asymmetric orthogonal arrays. Journal of Statistical Planning and Inference, 69(2), 349-358. http://dx.doi.org/10.1016/S0378-3758(97)00168-7.
Wang, P. C., & Jan, H. W. (1995). Designing two-level factorial experiments using orthogonal arrays when the run order is important. The Statistician, 44(3), 379-388. http://dx.doi.org/10.2307/2348709.
Wilmut, M., & Zhou, J. (2011). D-optimal minimax design criterion for two-level fractional factorial designs. Journal of Statistical Planning and Inference, 141(1), 576-587. http://dx.doi.org/10.1016/j.jspi.2010.07.002.