1822 G Mohanty et al. /Materials Research Bulletin 43(2008)1814-1828 90 0.92 Internally Studentized Residuals Fig. 3. Normal plot of residuals. about process variability. Residual is the difference between the observed response and the value predicted by the model for a particular design point. The residuals should be structureless if the model is adequate 2.9. Diagnostics The normal probability plot is used to determine whether the residuals follow a normal distribution. The residuals seem to follow a normal probability distribution as they lie approximately on a straight line on the normal plot of residuals(Fig 3). In general, moderate departures from normality are of little concern in the fixed effects analysis of variance which Design Expert uses [27]. Fig. 4 shows the plot of residuals versus predicted data points. A random scatter of data points in the residuals versus predicted plot validates our initial assumption of constant variance Random scatter in the plot of residuals versus experimental run order(Fig. 5)eliminates the possibility of a time related variable lurking in the background. The predicted and the actual values also show excellent agreement as can be seen from Fig. 6. Hence, no obvious patterns were found in the analysis of residuals 2.10. Influence plots Influence plots are primarily used for detection of outliers. Externally studentized residual (also called Outlier t) shown in Fig. 7 gives a measure of how many standard deviations the actual value deviates from the value predicted after deleting the point in question. All the data points(Fig. 7)lie within the limits Leverage is a measure of the influence of a point on the model fit. Leverages are numerical value between 0 and 1 that indicate the potential for a design point to influence the model fit. Leverage of I indicates that the model will be forced to go through the point and the point will control the model. Since the leverages of all runs(Fig. 8)are less than l, there is no point which unduly influences the model. DFFITS plot(Fig 9), which measures the influence of each point on the predicted value, suggested four points (corresponding to runs 3, 5, 6 and 18) which influence the regression equation and the response very disproportionately. However, DFBETAS plot(Fig. 10)showed no undue/large influence of each observation on each of the regression coefficients. Cooks distance provides a measure of how much the regression would change if the is omitted from the analysis. Cook's distance plot(Fig. 11)also suggested that the four points lying outside theabout process variability. Residual is the difference between the observed response and the value predicted by the model for a particular design point. The residuals should be structureless if the model is adequate. 2.9. Diagnostics The normal probability plot is used to determine whether the residuals follow a normal distribution. The residuals seem to follow a normal probability distribution as they lie approximately on a straight line on the normal plot of residuals (Fig. 3). In general, moderate departures from normality are of little concern in the fixed effects analysis of variance which Design Expert uses [27]. Fig. 4 shows the plot of residuals versus predicted data points. A random scatter of data points in the residuals versus predicted plot validates our initial assumption of constant variance. Random scatter in the plot of residuals versus experimental run order (Fig. 5) eliminates the possibility of a time￾related variable lurking in the background. The predicted and the actual values also show excellent agreement as can be seen from Fig. 6. Hence, no obvious patterns were found in the analysis of residuals. 2.10. Influence plots Influence plots are primarily used for detection of outliers. Externally studentized residual (also called Outlier t) shown in Fig. 7 gives a measure of how many standard deviations the actual value deviates from the value predicted after deleting the point in question. All the data points (Fig. 7) lie within the limits. Leverage is a measure of the influence of a point on the model fit. Leverages are numerical value between 0 and 1 that indicate the potential for a design point to influence the model fit. Leverage of 1 indicates that the model will be forced to go through the point and the point will control the model. Since the leverages of all runs (Fig. 8) are less than 1, there is no point which unduly influences the model. DFFITS plot (Fig. 9), which measures the influence of each point on the predicted value, suggested four points (corresponding to runs 3, 5, 6 and 18) which influence the regression equation and the response very disproportionately. However, DFBETAS plot (Fig. 10) showed no undue/large influence of each observation on each of the regression coefficients. Cook’s distance provides a measure of how much the regression would change if the case is omitted from the analysis. Cook’s distance plot (Fig. 11) also suggested that the four points lying outside the 1822 G. Mohanty et al. / Materials Research Bulletin 43 (2008) 1814–1828 Fig. 3. Normal plot of residuals