Designed Experiment for Determining Time-Dependent Polyurethane Foam Characteristics

Figures & data

Table 1. Randomized design used in this study

Run	x5	x1	x2	x3	x4
4	1	1	−1	−1	1
5	−1	−1	1	−1	−1
2	1	−1	−1	−1	−1
11	−1	1	−1	1	1
1	−1	−1	−1	−1	1
7	−1	1	1	−1	1
9	−1	−1	−1	1	−1
6	1	−1	1	−1	1
15	−1	1	1	1	−1
14	1	−1	1	1	−1
12	1	1	−1	1	−1
17	0	0	0	0	0
10	1	−1	−1	1	1
3	−1	1	−1	−1	−1
13	−1	−1	1	1	1
16	1	1	1	1	1
8	1	1	1	−1	−1

Table 2. Results of average IFD25 vs. time (run #11)

Hours	IFD25
4	132.6
8	141.4
24	161.2
48	165.8
96	165.8
168	168.3

Figure 1. Fitted model for average IFD25 vs. time for run #11.

Table 3. Nonlinear regression coefficients for average IFD25

Run	x5	x1	x2	x3	x4	β1	β2	β3
4	1	1	−1	−1	1	177.4	0.472	0.206
5	−1	−1	1	−1	−1	130.7	0.131	0.041
2	1	−1	−1	−1	−1	106.8	0.073	0.035
11	−1	1	−1	1	1	167.3	0.293	0.081
1	−1	−1	−1	−1	1	80.4	0.872	0.327
7	−1	1	1	−1	1	159.5	0.733	0.226
9	−1	−1	−1	1	−1	151.1	0.262	0.111
6	1	−1	1	−1	1	126.5	0.449	0.141
15	−1	1	1	1	−1	279.1	0.404	0.274
14	1	−1	1	1	−1	174.3	0.421	0.472
12	1	1	−1	1	−1	296.9	0.125	0.002
17	0	0	0	0	0	172.6	0.383	0.194
10	1	−1	−1	1	1	140.2	0.288	0.141
3	−1	1	−1	−1	−1	184.8	0.197	0.041
13	−1	−1	1	1	1	125.1	0.506	0.235
16	1	1	1	1	1	267.3	0.396	0.111
8	1	1	1	−1	−1	229.3	0.403	0.426

Table 4. Models for nonlinear coefficients

β1=174.655+45.3983^*x1+11.688^*x2+25.3731^*x3−19.3374^*x4+15.0379^*x5+1.92411^*x1*x2+7.07774* x1*x3−7.98849*x1*x4+7.48249*x1*x5+2.44526*x2*x4−2.18601*x2*x5−5.85886*x3*x4+4.46661*x3*x5+7.35089*x4*x5

β2=0.376878+0.0538553*x2−0.0398739*x3+0.1246*x4−0.0482079*x5+0.0523604*x1*x2−0.0337565*x1*x3−0.02884*x1*x4+0.0193873*x1*x5+0.0410061*x2*x3−0.0339871*x2*x4+0.0350401*x2*x5−0.0907517*x3*x4+0.0188715*x3*x5−0.051647*x4*x5

β3=0.180173−0.00842356*x1+0.0614881x2+0.0124542*x5+0.0269701*x1*x2−0.0528444*x1*x3−0.0189756*x1*x4+0.0331462*x2*x3−0.0665167*x2*x4+0.0344191*x2*x5−0.0405732*x3*x4−0.00919619*x3*x5−0.0461581*x4*x5

Figure 2. Predicted height vs. time plot for coefficients in Table 5.

Table 5. Values of nonlinear coefficients using random values for x1–x5

x5	x1	x2	x3	x4	β1	β2	β3	β
−0.62	−0.94	0.84	0.94	−0.04	152.4	0.415	0.273	Predicted
−0.62	−0.94	0.84	0.94	−0.04	150.6	0.414	0.260	Min
−0.62	−0.94	0.84	0.94	−0.04	154.3	0.420	0.286	Max