Measurement error (ME) in the factor levels of designed experiments is often overlooked in the planning and analysis of experimental designs. A familiar model for this type of ME, called the Berkson error model, is discussed at length. Previous research has examined the effect of Berkson error on two-level factorial and fractional factorial designs. This dissertation extends the examination to designs for second order models. The results are used to suggest optimal values for axial points in Central Composite Designs. The proper analysis for experimental data including ME is outlined for first and second order models. A comparison of this analysis to a typical Ordinary Least Squares analysis is made for second order models. The comparison is used to quantify the difference in performance of the two methods, both of which yield unbiased coefficient estimates. Robustness to misspecification of the ME variance is also explored. A solution for experimental planning is also suggested. A design optimality criterion, called the DME criterion, is used to create a second-stage design when ME is present. The performance of the criterion is compared to a D-optimal design augmentation. A final comparison is made between methods accounting for ME and methods ignoring ME. / Ph. D.