Minimum Cost Trend-Free Run Orders of Fractional Factorial Designs

Sequenciamento sistemático de experimentos fatoriais como alternativa à ordem aleatória

“…Although the studies conducted by Draper and Stoneman (1968), Dickinson (1974) and Joiner and Campbell (1976) already considered linear trend effects through maximum time count, only in the late twentieth century these criteria were actually used to develop factorial designs, especially in the studies by Cheng and Jacroux (1988), Bailey et al (1992) and Atkinson & Donev (1996). Coster & Cheng (1988), Jacroux (1994), Githinji & Jacroux (1998), and Tsao & Liu (2008), in turn, approached the issue either based on time count or on the number of factor level changes.…”

Trend-free Repeated Measurement Designs

“…However, one may use suitable designs in the presence of trends to avoid the complications of analysis of covariance and increase design efficiencies. Some studies in this direction have been made by Atkinson and Donev (1996), Box (1952), Box and Hay (1953), Bailey, Cheng and Kipnis (1992), Bradley and Yeh (1985), Bradley and Odeh (1988), Chai and Majumdar (1993), Cheng (1985), Cheng and Jacroux (1988), Coster (1993), Coster and Cheng (1988), Cox (1951Cox ( ,1952Cox ( ,1958, Daniel (1976, chapter 15), Daniel and wilcoxon (1966), Githinji and Jacroux (1998), Hill (1960), Jaroux (1993Jaroux ( , 1994, Jacroux and Ray (1990), Joiner and Campbell (1976), Lin and Dean (1991), Mukerjee and Sengupta (1994), Ogilvie(1963), Philips (1964Philips ( ,1968aPhilips ( ,1968b, Prescott (1981), Stufken (1988), Taylor (1967), Yeh and Bradley (1983), Yeh, Bradley and Notz (1985), Whittinghill (1989) and Wilkie (1987). In the present paper, we consider two families of repeated measurement designs (RMDs) and show that efficient/optimal trend-free RMDs exist.…”

Characterization of Six Categories of Systematic 2<sup><i>n</i>－(<i>n</i>－<i>k</i>)</sup> Fractional Factorial Designs

“…For systematic complete 2 n factorial experiments, there are four main algorithms for sequencing their 2 n runs to overcome either of the above mentioned two problems. These algorithms are due to [1][2][3][4]. [5] has conducted a comparison among these algorithms and documented their differences according to three criteria: 1) which algorithm produces run orders in less number of factor level changes, 2) which algorithm produces run orders with more linear/quadratic time trend free main effects and 3) which run order of an algorithm can be generated by another algorithm using either the generalized foldover scheme or the interactions-main effects assignment.…”