Performance Optimization, Prediction, and Adequacy by Response Surfaces Methodology with Allusion to DRF Technique

Table 3

Comparison of actual and predicted values.

(a)

Ref no.	Weight per square meter					Abrasion cycles					Bursting strength (kg/cm^2)					𝐿-estimation
	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	6	7	8	9	10
1	201	203.50	−1.24	101.24	0.99	1170.00	1233.54	−5.43	105.43	0.95	12.00	11.74	2.17	97.83	1.02	0.96	0.96	1383.00	1448.78	0.95
2	192	194.00	−1.04	101.04	0.99	1230.00	1233.54	−0.29	100.29	1.00	13.00	12.80	1.54	98.46	1.02	1.00	1.00	1435.00	1440.34	1.00
3	196	194.00	1.02	98.98	1.01	1200.00	1233.54	−2.80	102.80	0.97	12.10	12.90	−6.61	106.61	0.94	0.92	0.92	1408.10	1440.44	0.98
4	206	203.50	1.21	98.79	1.01	1150.00	1233.54	−7.26	107.26	0.93	13.05	12.56	3.75	96.25	1.04	0.98	0.98	1369.05	1449.60	0.94
5	186	186.33	−0.18	100.18	1.00	1270.00	1298.33	−2.23	102.23	0.98	13.20	12.50	5.30	94.70	1.06	1.03	1.03	1469.20	1497.16	0.98
6	197	195.79	0.61	99.39	1.01	1195.00	1281.45	−7.23	107.23	0.93	12.20	11.38	6.72	93.28	1.07	1.01	1.01	1404.20	1488.62	0.94
7	193	195.79	−1.45	101.45	0.99	1220.00	1281.45	−5.04	105.04	0.95	13.50	11.74	13.04	86.96	1.15	1.08	1.08	1426.50	1488.98	0.96
8	189	191.29	−1.21	101.21	0.99	1260.00	1315.21	−4.38	104.38	0.96	14.00	11.84	15.43	84.57	1.18	1.12	1.12	1463.00	1518.34	0.96
9	190	191.29	−0.68	100.68	0.99	1240.00	1315.21	−6.07	106.07	0.94	12.85	12.20	5.06	94.94	1.05	0.99	0.99	1442.85	1518.70	0.95
10	188	186.33	0.89	99.11	1.01	1325.00	1298.33	2.01	97.99	1.02	13.05	12.50	4.21	95.79	1.04	1.07	1.07	1526.05	1497.16	1.02
11	197	198.54	−0.78	100.78	0.99	1190.00	1169.16	1.75	98.25	1.02	12.20	11.33	7.13	92.87	1.08	1.09	1.09	1399.20	1379.03	1.01
12	187	189.04	−1.09	101.09	0.99	1280.00	1264.16	1.24	98.76	1.01	14.05	11.79	16.09	83.91	1.19	1.19	1.19	1481.05	1464.99	1.01
13	184	184.54	−0.29	100.29	1.00	1310.00	1297.92	0.92	99.08	1.01	14.35	11.79	17.84	82.16	1.22	1.22	1.22	1508.35	1494.25	1.01
14	193	194.04	−0.54	100.54	0.99	1210.00	1202.92	0.59	99.41	1.01	13.70	12.25	10.58	89.42	1.12	1.12	1.12	1416.70	1409.21	1.01
15	185	186.33	−0.72	100.72	0.99	1300.00	1298.33	0.13	99.87	1.00	13.10	12.50	4.58	95.42	1.05	1.04	1.04	1498.10	1497.16	1.00
Average	192.27	192.95	−0.37	100.37	1.00	1236.67	1263.78	−2.27	102.27	0.98	13.09	12.12	7.12	92.88	1.08	1.06	1.05			0.98
Max	206	203.50	1.21	101.45	1.01	1325	1315.21	2.01	107.27	1.02	14.35	12.90	17.84	106.61	1.22	1.22	1.26			1.02
Min	184	184.54	−1.45	98.79	0.99	1150	1169.16	−7.26	97.99	0.93	12.00	11.33	−6.61	82.16	0.94	0.92	0.86			0.94
𝑅-Factor	0.016					0.002					0.229

(b)

Response surface equations		(𝑅^2)
1	𝑌(weight)=186.33−2.25𝑋3+7.21𝑋^21+5.21𝑋^22+4.75𝑋1𝑋2+4.75𝑋2𝑋3	0.96
2	𝑌(Abrasion)=1298.33+16.88𝑋3−64.79𝑋^22−27.50𝑋1𝑋2−47.50𝑋2𝑋3	0.71
3	𝑌(Bursting)=12.50+0.18𝑋1+0.23𝑋2+0.23𝑋3−0.71𝑋^23−0.35𝑋1𝑋2	0.86

1: actual value; 2: predicted value; 3: difference (%); 4: accuracy (%); 5: actual values/predicted values; 6: product of 1 (all parameters)/product of 2 (all parameters); 7: product of 5 (all parameters); 8: sum of all actual values of parameters; 9: sum of all predicted values of parameters; 10: product (8*9).