Abstract
Randomization is one of the powerful tools to analyze, construct and draw valid and unbiased conclusions about the factorial design. But in some experimental situations, the technique may not perform equally well to draw valid inferences. These situations may arise due to an influence of external variations like the ageing of catalyst, known as Time-trend or Trend, on the response. Thus, instead of randomizing the run order of the factorial design, systematically arranging the order of treatments that is free of variations, neutralizes the adverse effect of Trend. Such systematic designs are known as Trend Free designs. The design gives not only higher importance to the treatments but also ensures the independence of treatments for further analysis. Methods for constructing trend-free run order of two-level designs have been studied and developed by many authors. The proposed run order for 2k and 2k-p design that are linear and quadratic trend free. Systematic run order has been constructed not only to eliminate the effect of the linear and quadratic trend but also to improve design performance in the presence of a trend. This article provides another technique to develop trend free run order of two-level factorial design using Symmetric Balanced Incomplete Block Design.
Highlights
Randomizing the run order in a factorial experiment does not always give desired results
The randomization technique may not give satisfactory results in the sense that the effects of interest may get affected by some external variations or trend
To avoid any discrepancy that arises due to the external variations, in the output, systematic pattern of level combinations of the factors or runs order with effects free of variations or trends should be constructed
Summary
Randomizing the run order in a factorial experiment does not always give desired results. The new product of the experiment may get affected by the ageing of the chemical used In this case, the randomization technique may not give satisfactory results in the sense that the effects of interest may get affected by some external variations or trend. To avoid any discrepancy that arises due to the external variations, in the output, systematic pattern of level combinations of the factors or runs order with effects free of variations or trends should be constructed. Designs that generate such a run order are called. We provide a technique of generating trend free run order of two-level factorial design using Balanced incomplete block design.
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