Incomplete equivalent estimation split plot designs

Agricultural, post-harvest, processing, engineering and industrial experiments often involved factors which are expensive or time consuming to change from one experimental run to another, they are known as hard-to-change factors. These factors restrict the use of complete randomization because it may make the experimentation expensive and time consuming. One cost effective alternative for these situations to use split plot designs that reduces the number of independent settings of the hard-to-change factors by allocating them to whole plots or main plots and the easy-to-change factors to subplots. In general model estimation of split plot designs requires the use of generalized least squares (GLS). However for some split-plot designs ordinary least squares (OLS) estimates are equivalent to generalized least squares (GLS) estimates. These types of designs are known as equivalent-estimation split-plot designs in literature. This is because split-plot designs for which OLS and GLS produce the same factor-effect estimates offer the advantage that the estimates of the effects do not depend on the estimates of the variance components in the split-plot model. They possess the property that the OLS estimator of the fixed effects in the split-plot model is equivalent to the GLS estimator. Here, we have obtained the equivalent estimation split-plot designs for different experimental situation.