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A D V A N C E D M A T E R I A L S & P R O C E S S E S | O C T O B E R 2 0 1 8 2 4 economics, after which they were im- plemented in a Lumet system (a soft- ware system for facile use of nonlinear models). Besides predictions from nonlinear models, the system has ca- pabilities including plotting the ef- fects of variables in several ways and STATISTICAL CHARACTERISTICS OF MEASUREMENT DATA FROM 38 EXPERIMENTS Output variable 1:.............................................Density [kg/m³] Output variable 2:.............................................Thickness [mm] Output variable 3:.............................................Conductivity, 10°C [W/mK] Output variable 4:.............................................Tensile strength (ED) [MPa] Output variable 5:.............................................Tensile strength (CD) [MPa] Output variable 6:.............................................Elastic modulus (ED) [MPa] Output variable 7:.............................................Elastic modulus (CD) [MPa] rms err of output variable 1:. ...........................0.5049 mean |err| of output variable 1:. ......................0.3190 max |err| of output variable 1:..........................1.6893 at observation 24 Correlation of output variable 1:. ....................0.9998 rms err of output variable 2:. ...........................0.4035 mean |err| of output variable 2:. ......................0.3003 max |err| of output variable 2:..........................1.1752 at observation 27 Correlation of output variable 2:. ....................0.9796 rms err of output variable 3:. ...........................3.1541E-04 mean |err| of output variable 3:. ......................2.4168E-04 max |err| of output variable 3:..........................7.6170E-04 at observation 25 Correlation of output variable.........................3: 0.9969 rms err of output variable 4:. ...........................1.7497E-02 mean |err| of output variable 4:. ......................1.3120E-02 max |err| of output variable 4:..........................4.3160E-02 at observation 25 Correlation of output variable.........................4: 0.9977 rms err of output variable 5:. ...........................1.9430E-02 mean |err| of output variable 5:. ......................1.5513E-02 max |err| of output variable 5:..........................4.7344E-02 at observation 25 Correlation of output variable 5:. ....................0.9966 rms err of output variable 6:. ...........................0.3472 mean |err| of output variable 6:. ......................0.2441 max |err| of output variable 6:..........................1.1597 at observation 7 Correlation of output variable 6:. ....................0.9737 rms err of output variable 7:. ...........................0.3130 mean |err| of output variable 7:. ......................0.2145 max |err| of output variable 7:..........................1.2023 at observation 7 Correlation of output variable 7:. ....................0.9740 optimization calculations, which are necessary for recipe calculations to de- velop products with more demanding combinations of material properties. Figure 5, plotted using the Lumet system, shows the effect of foaming agent on tensile strength in the ex- trusion direction for different amounts of cross-linking agents. MATERIALS DEVELOPMENT Nonlinear models considerably speed up product development. The objective of product development is to make a finished product with a de- sired combination of properties, pref- erably at a suitable production rate and cost. It is easy to mathematically find a solution and confirm it with one exper- iment instead of carrying out several trial-and-error experiments. Another important factor is the wide range of customer requirements. For example, consider the require- ments for a material with a density of 35.5 to 36.5 kg/m 3 , a thickness of 11.8 to 12.2 mm, thermal conductivity at 10°C below 0.04 W/mK, and tensile strength above 0.3 MPa in either direction. The matrix width must be 750 mm. Fur- ther, production wants to operate at 200 kg/h of polymer flow rate. Figure 6 shows the feasible region (green) for this situation in terms of two variables. Other input variables are kept constant for this plot. The feasible region would shift if a variable such as carbon black content were changed. Trial-and-error experiments would require consider- able time and effort to find an accept- able solution. In other instances, a custom- er might require something that is not possible with the available materials and equipment. Experimental time and effort would be wasted before realizing that it is impossible to produce the ma- terial within the framework of the ex- isting equipment and materials used. However, nonlinear models show in seconds or a few minutes if some com- binations are not feasible. If it is feasible, production will want to manufacture it at a healthy line speed (production rate) and cor- porate management will want it to be produced at the lowest cost. These cal- culations are made possible by the use of nonlinear models. Developing mod- els that relate product variables with composition, process, and dimension- al variables makes it easy to determine suitable or best values to achieve the