Experimental design for non‐statisticians

Abstract

Many of us were taught that if more than one variable were changed at a time, the cause of some end result could never be determined. This is certainly true if the experiment is not planned to accommodate analysis of the data. The complex problems faced by modem scientists and engineers can not be solved efficiently using one-at-a-time methods. Good experimental design promotes broader exploration of the variables studied, produces more results from fewer experiments, and validates results by comparing them against measured experimental error. This is done by deliberately varying all variables from run-to-run in systematic patterns. Timely product development and problems solving bears directly on profitability. A systematic approach can pay handsome dividends. The basis of good experimental design and several simple designs for everyday use are presented.

Comparative study of Box–Behnken, central composite, and Doehlert matrix for multivariate optimization of Pb (II) adsorption onto Robinia tree leaves

“…Conventionally, the classical method (one-at-a-time) provides for changing one independent variable while maintaining all others at a fixed level, which is extremely time-consuming and expensive for a large number of variables. Owing to its powerful efficiency, response surface methodology is now being routinely used for optimization of widely various systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. However, it could not lead to real optima in many cases.…”

“…The major disadvantage is the lack of inclusion of the interactive effects among variables. Among the various response surface approaches, it was found that three common multilevel designs such as central composite design (CCD), Box-Behnken design (BBD), and Doehlert matrix (DM) have been frequently utilized for the final optimization of desired processes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Consequently, procedures for optimization of factors by multivariate techniques have been encouraged, as they are faster, more economical, and effective and allow more than one variable to be optimized simultaneously [5][6][7][8][9][10][11].…”

“…However, it could not lead to real optima in many cases. Ferreira et al and other researchers [2][3][4][5][6][7][8][9][10][13][14][15][16][17], although the experimental approaches are quite rare. Owing to its powerful efficiency, response surface methodology is now being routinely used for optimization of widely various systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…In recent years, response surface methodology has been widely used as an optimization tool in various kinds of analytical chemistry, applied chemistry, and industrial and biological process [1][2][3][4][5][6][7][8][9][10][11][12][13]. In fact, optimization is the crucial step to find out the best conditions and maximize the desired responses in any experimental subject [14][15][16][17][18][19][20]. Conventionally, the classical method (one-at-a-time) provides for changing one independent variable while maintaining all others at a fixed level, which is extremely time-consuming and expensive for a large number of variables.…”

“…Consequently, procedures for optimization of factors by multivariate techniques have been encouraged, as they are faster, more economical, and effective and allow more than one variable to be optimized simultaneously [5][6][7][8][9][10][11]. Owing to its powerful efficiency, response surface methodology is now being routinely used for optimization of widely various systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Among the various response surface approaches, it was found that three common multilevel designs such as central composite design (CCD), Box-Behnken design (BBD), and Doehlert matrix (DM) have been frequently utilized for the final optimization of desired processes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”