ABSTRACT
RESEARCH MONOGRAPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 ROBUST REGRESSION DESIGNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 SUMMARY OF THE RESEARCH MONOGRAPH . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Response surface methodology is a collection of mathematical and statistical techniques useful for analyzing problems where several independent variables influence a dependent variable. The independent variables are often called the input or explanatory variables and the dependent variable is often called the response variable. In response surface methodology, a natural and desirable property is that of rotatability, which requires that the variance of the predicted response at a point remains constant at all such points that are equidistant from the design center. The present research monograph confines to first-and second-order regression models with correlated errors. Robust rotatability, slope-rotatability and optimality are described for the first-and second-order designs. Weakly robust rotatable, sloperotatable designs, and their different measures are discussed. Robust first-and second-order optimal and rotatable designs are discussed for different lifetime distributions in quality improvement experiments. Regression analyses are described for correlated observations. Generally, experimental observations are positive, and they are analysed by log-normal and gamma models. These two models are described for constant and non-constant variances. The discrepancy of regression estimates and the model fittings between these two models are described. Some applications of correlated regression analyses in block designs, and positive data analyses (with real data) are illustrated in the different fields of science.
