Generation of 2n series fractional factorial plans robust against linear-trend

Abstract

agricultural, biological and industrial experiments. However, they occur in experimental situations where the response is dependent on the spatial or temporal position of the experimental units within a block and thus trend in the experimental units becomes an important nuisance factor. In such situations, a common polynomial trend of a specified degree over units within experimental units may be appropriately assumed. Trend-free plans for single factor and at two level factorial experiments (complete and fractional both) are available in literature but trend-free multifactor plans could not be traced in the literature except some discussion by John (1990) where factors are at three levels. Factorial/fractional factorial experiments are often used in various experiments. If there is trend in the experimental units then it is essential to sequence these factorial experiments such that factor effects are orthogonal to the trend. The resulting plans are termed as minimum cost linear trend-free factorial/fractional factorial experiments. Trends may occur in the experimental units when the land is irrigated and the fertilizers supply the nutrients but because of the slope, the distribution of nutrients is not uniform. In the presence of trends, it is desired to allocate the treatment combinations to experimental units in such a manner that the main effects and interactions of interest are estimated free from the linear trend effects. Such fractional factorial plans are called robust against linear trend and the ordered application of treatments to experimental units is called run order (Yeh and Bradley 1983, Cheng 1988, Coster and Cheng 1988, Majumdar and Martin 2002, Lal et al. 2005; 2007, Sarkar et al. 2009, Nguyen 2013).