E Gondar et al Joumal of the European Ceramic Society 27(2007)2103-2110 y=00138x+9515 00263 R2=0.9945 04000 ● heating time cooling time Fig. 13. Linearity of time influence on mean stress. Fig. 11. Stress progress in a point located on the axis of 2 mm thick specimen. of these input parameters on the mean stress. Low value of the 0.6mm under its heated side R-squared value of cooling time is caused by dispersion of the results, which corresponds also to the dispersion of PI for this The results show a very good linearity--coefficient of deter- case(Fig. 8 and Table 2, rows 13-18). In absolute values, how- mination for this model was 0.999855721 hence the ever, this dispersion is negligil ble. as the maximum difference can be considered reliable without having to"filter out"any between the results is 0.449MPa errors using for example robust models. Graphical represen- High correlation is maintained also when dealing with stress tation of Eq. (3)would require a multidimensional graph. We in a specific cycle. The resulting equations for the 4th and 20th cycle are stated below along with their coefficients of determ parameters influence: a plot of stress versus one input parame- tion. Despite lower coefficient of determination in these cycles ter, while keeping the others constant. The linearity of influence its value is high enough to prove the equations reliable of average temperature(at AT=const)and cooling temperature (at Th=const)is shown in Fig. 12(for mean stress), along with 04thcycle =0.422Th+0.017Tc-0418th-2683te+25.686, the equations of their linear trend models and their coefficients coefficient of determination=0.997279754 of determination. The equations in this figure and the next one contain variables x and y instead of the real physical quantities This is a formal decision to prevent units mismatch. The slope 020th cycle =2.288Th+1.9Te-1 158-9798tc+104.59, of these lines also demonstrates the influence of the parameters. coefficient of determination =0.965192316 Again we must realize that the case of Th=const represents in fact the influence of AT. It proves true again that the influence The linearity of input parameters influence in the fourth cycle of AT is lower than the influence of the absolute values of heat- is shown if Figs. 14 and 15. In this case there is an evident ing and cooling temperature. There is an unexpected influence increase of the influence of cooling time, which corresponds to of increasing cooling temperature(at Th=const)on the mean the results of PI in this cycle(Fig 9). The slope of the cooling stress Increasing of cooling temperatures causes lower temper- time's trend line is negative, but this does not indicate a lower ature difference which should lead to lower values of mean influence-the influence is expressed by deviation of the trend stress line from its horizontal position. The influence of cooling tem- The linearity of influence of heating and cooling time is perature(influence of AD)on stress peaks in the fourth cycle is shown in Fig. 13 and again demonstrates a negligible influence lower than its influence on the mean stress. This corresponds to y=0.0548X+68,203 R2m0.9987 y=0,1166X+28,127 ◆ average temperature△T= const A cooling temperature Th=const A cooing temperature Th=con 00450500550600650700750800850 400450500550600650700750800850 Temperature [C] Temperature{°C Fig. 12. Linearity of temperature influence on mean stress. Fig. 14. Linearity of temperature influence on stress peaks in the fourth cycle2108 E. Gondar et al. / Journal of the European Ceramic Society 27 (2007) 2103–2110 Fig. 11. Stress progress in a point located on the axis of 2 mm thick specimen, 0.6 mm under its heated side. The results show a very good linearity—coefficient of deter￾mination for this model was 0.999855721, hence the equation can be considered reliable without having to “filter out” any errors using for example robust models.21 Graphical represen￾tation of Eq. (3) would require a multidimensional graph. We chose a different approach to demonstrate the linearity of the parameters influence: a plot of stress versus one input parame￾ter, while keeping the others constant. The linearity of influence of average temperature (at T = const) and cooling temperature (at Th = const) is shown in Fig. 12 (for mean stress), along with the equations of their linear trend models and their coefficients of determination. The equations in this figure and the next ones contain variables x and y instead of the real physical quantities. This is a formal decision to prevent units mismatch. The slope of these lines also demonstrates the influence of the parameters. Again we must realize that the case of Th = const represents in fact the influence of T. It proves true again that the influence of T is lower than the influence of the absolute values of heat￾ing and cooling temperature. There is an unexpected influence of increasing cooling temperature (at Th = const) on the mean stress. Increasing of cooling temperatures causes lower temper￾ature difference, which should lead to lower values of mean stress. The linearity of influence of heating and cooling time is shown in Fig. 13 and again demonstrates a negligible influence Fig. 12. Linearity of temperature influence on mean stress. Fig. 13. Linearity of time influence on mean stress. of these input parameters on the mean stress. Low value of the R-squared value of cooling time is caused by dispersion of the results, which corresponds also to the dispersion of PI for this case (Fig. 8 and Table 2, rows 13–18). In absolute values, how￾ever, this dispersion is negligible, as the maximum difference between the results is 0.449 MPa. High correlation is maintained also when dealing with stress in a specific cycle. The resulting equations for the 4th and 20th cycle are stated below along with their coefficients of determina￾tion. Despite lower coefficient of determination in these cycles, its value is high enough to prove the equations reliable: σ4th cycle = 0.422Th + 0.017Tc − 0.418th − 2.683tc + 25.686, coefficient of determination = 0.997279754 (4) σ20th cycle = 2.288Th + 1.9Tc − 1.158th − 9.798tc + 104.59, coefficient of determination = 0.965192316 (5) The linearity of input parameters influence in the fourth cycle is shown if Figs. 14 and 15. In this case there is an evident increase of the influence of cooling time, which corresponds to the results of PI in this cycle (Fig. 9). The slope of the cooling time’s trend line is negative, but this does not indicate a lower influence—the influence is expressed by deviation of the trend line from its horizontal position. The influence of cooling tem￾perature (influence of T) on stress peaks in the fourth cycle is lower than its influence on the mean stress. This corresponds to Fig. 14. Linearity of temperature influence on stress peaks in the fourth cycle.