Systematic sequencing of factorial experiments as an alternative to the random order

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.

[1]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[2]  J. Kiefer,et al.  Time- and Space-Saving Computer Methods, Related to Mitchell's DETMAX, for Finding D-Optimum Designs , 1980 .

[3]  Toby J. Mitchell,et al.  An Algorithm for the Construction of “D-Optimal” Experimental Designs , 2000, Technometrics.

[4]  James M. Lucas,et al.  Randomized and random run order experiments , 2005 .

[5]  A. Atkinson.  The Usefulness of Optimum Experimental Designs , 1996 .

[6]  Hisham Hilow.  Comparison among run order algorithms for sequential factorial experiments , 2013, Comput. Stat. Data Anal..

[7]  Jean Dickinson Gibbons,et al.  Nonparametric Statistical Inference , 1972, International Encyclopedia of Statistical Science.

[8]  Mike Jacroux,et al.  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 , 1998 .

[9]  Brian L. Joiner,et al.  Designing Experiments When Run Order is Important , 1976 .

[10]  Alan Harrison,et al.  Continuous improvement: the trade‐off between self‐management and discipline , 2000 .

[11]  Christos Koukouvinos,et al.  Run orders for efficient two level experimental plans with minimum factor level changes robust to time trends , 2009 .

[12]  Michael Jacroux,et al.  RUN ORDERS OF TREND RESISTANT 2-LEVEL FACTORIAL DESIGNS* , 2016 .

[13]  Taina Savolainen,et al.  Cycles of continuous improvement , 1999 .

[14]  R. D. Cook,et al.  A Comparison of Algorithms for Constructing Exact D-Optimal Designs , 1980 .

[15]  John Bessant,et al.  An evolutionary model of continuous improvement behaviour , 2001 .

[16]  Mike Jacroux,et al.  The construction of trend-free run orders of two-level factorial designs , 1988 .

[17]  P. C. Wang,et al.  Designing Two‐Level Factorial Experiments Using Orthogonal Arrays When the Run Order is Important , 1995 .

[18]  José A. Malpica,et al.  Obtaining industrial experimental designs using a heuristic technique , 2011, Expert Syst. Appl..

[19]  J. Bessant,et al.  High-involvement innovation through continuous improvement , 1997 .

[20]  Laurence A. Wolsey,et al.  bc–opt: a branch-and-cut code for mixed integer programs , 1999, Math. Program..

[21]  Deborah J. Street,et al.  Some open combinatorial problems in the design of stated choice experiments , 2008, Discret. Math..

[22]  Joachim Kunert,et al.  On the Comparison of Run Orders of Unreplicated 2k–p Designs in the Presence of a Time Trend , 2005 .

[23]  Martina Vandebroek,et al.  Trend-resistant and cost-efficient cross-over designs for mixed models , 2004, Comput. Stat. Data Anal..

[24]  Claudine Soosay,et al.  Continuous improvement and learning in the supply chain , 2003 .

[25]  P. Goos,et al.  A variable-neighbourhood search algorithm for finding optimal run orders in the presence of serial correlation and time trends , 2006 .

[26]  R. A. Bailey,et al.  One hundred years of the design of experiments on and off the pages of Biometrika , 2001 .

[27]  Pedro Carlos Oprime,et al.  Análise da complexidade, estratégias e aprendizagem em projetos de melhoria contínua: estudos de caso em empresas brasileiras Analysis of complexity, strategies, and learning organization in continuous improvement processes: case studies in brazilian companies , 2010 .

[28]  Eric R. Ziegel,et al.  Engineering Statistics , 2004, Technometrics.

[29]  P. C. Wang,et al.  Level changes and trend resistance on replacement in asymmetric orthogonal arrays , 1998 .

[30]  O. Dykstra.  The Augmentation of Experimental Data to Maximize [X′X] , 1971 .

[31]  Anthony C. Atkinson,et al.  Experimental designs optimally balanced for trend , 1996 .

[32]  David M. Stoneman,et al.  Factor Changes and Linear Trends in Eight-Run Two-Level Factorial Designs , 1968 .

[33]  Harry Barton,et al.  Organizing for continuous improvement: Structures and roles in automotive components plants , 2002 .

[34]  Anthony C. Atkinson,et al.  Optimum Experimental Designs, with SAS , 2007 .

[35]  Ashish Das,et al.  Optimal fractional factorial designs and their construction , 2013 .

[36]  Juan A. Marin-Garcia,et al.  Longitudinal study of the results of continuous improvement in an industrial company , 2008 .

[37]  Rory A. Fisher,et al.  The Arrangement of Field Experiments , 1992 .

[38]  Masaaki Imai,et al.  Gemba Kaizen: A Commonsense, Low-Cost Approach to Management , 1997 .

[39]  Sidney Addelman,et al.  Recent Developments in the Design of Factorial Experiments , 1972 .

[40]  Jacob H.-S. Tsao,et al.  Optimal sequencing of test conditions in 2k factorial experimental design for run-size minimization , 2008, Comput. Ind. Eng..

[41]  Krishna B. Athreya,et al.  Inference for heavy tailed distributions , 1998 .

[42]  Julie Zhou,et al.  D-optimal minimax design criterion for two-level fractional factorial designs , 2011 .

[43]  Dimitris Bertsimas,et al.  The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples , 2015, Oper. Res..

[44]  F. Wilcoxon,et al.  Factorial 2 p–q Plans Robust Against Linear and Quadratic Trends , 1966 .

[45]  Daniel C. Coster,et al.  Minimum Cost Trend-Free Run Orders of Fractional Factorial Designs , 1988 .

[46]  J. S. Hunter,et al.  Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. , 1979 .

[47]  A. W. Dickinson.  Some Run Orders Requiring a Minimum Number of Factor Level Changes for the 24 and 25 Main Effect Plans , 1974 .