| Multiple Linear Regression Models have been developed for corelating mechanical property characteristics (dependent variables) with processing (independent) variables. After investigating various models, the 'stepwise' technique was chosen as this provided the optimum models. Three families of steels viz. ultra low carbon interstitial free, low carbon formable and microalloyed high strength were chosen covering a wide spectrum starting from extremely formable to less formable high strength groups. The dependent variables chosen were Yield strength, Tensile strength, Total elongation, Yield point elongation, Plastic strain ratio (RBAR) and Strain exponent (NBAR). The processing variables included Chemical composition, Hot rolling temperatures, Tandem reduction, Annealing practice and Skin roll elongation. The standard six step Regression Modelling as developed by many Statisticians was employed for the analyses. Residual analysis, R Square, F test, Mallows statistic C(p), confidence and prediction intervals and residual variances were used to check the integrity of the developed models and regression assumptions. Data was collected over a year's production from five different production lines to come up with generalized models. The validity of these models were further checked by applying these models to previously unused new data from one or two specific production lines. All the above mentioned statistical tests applied to these fully supported the models for each of the three families of steel. Summarizing, this dissertation has paved a new way for using Management Science (Multiple regression in this case) techniques to model and solve applied engineering problems and material development. |
