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

Abstract

The RSM introduces statistically designed experiments for the purpose of making inferences from data. The second-order model is the most frequently used approximating polynomial model in RSM. The most common designs for the second-order model are the 3 factorial, Doehlert, Box-Behnken, and CCD. In this Box and Behnken design of three variables is selected as a representative of RSM and 70 : 30 polyester-wool DRF yarn knitted fabrics samples as a process representative. The survey reveals that secondorder model is the most frequently used approximating polynomial model in RSM. The Box-Behnken is the most suited design for optimization and prediction of data in textile manufacturing and this model is well-suited for DRF technique yarn knitted fabric. The trend was as higher wool fiber length shows higher fabric weight, abrasion, and bursting strength, correlation of TM was not visible; however, role of strands spacing is found dominant in comparison to other variables; at 14 mm spacing it shows optimum behaviors. The optimum values were weight (gms/mt 2 ) 206 at length 75 mm, TM 2.5 and 14 mm spacing, abrasion (cycles) 1325 at length 70 mm, TM 2.25 and 14 mm spacing, bursting (kg/cm 2 ) 14.35 at length 70 mm, and TM 2.00 and 18 mm spacing. A selected variables, fiber length, TM, and strand spacing, have substantial influence. The adequacies of response surface equations are very high. The line trends of knitted fabric basic characteristics were almost the same for actual and predicted models. The difference (%) was in range of 1.21 to −1.45, 2.01 to −7.26, and 17.84 to −6.61, the accuracy (%) was in range of 101.45 to 98.79, 107.27 to 97.99, and 106.61 to 82.16, and the Discrepancy Factor ( -Factor) was noted to be 0.016, 0.002, and 0.229 for weight, abrasion, and bursting, respectively, between actual and predicted data. The -estimation factors for actual and predicted data were that (i) the ratio were in range of 1.01 to 0.99, 1.02 to 0.93, and 1.22 to 0.94 for weight, abrasion, and bursting, respectively, (ii) the multiple-ratio was in range of 1.26 to 0.86, (iii) the ratio product was in range of 1.22 to 0.92, and (iv) the toting ratio was in range of 1.02 to 0.94.

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