OBRABOTKAMETALLOV technology Vol. 27 No. 2 2025 where Pi is the preference value for the i-th response; xi is the raw data obtained from the experiment for the i-th response; x’i is the smallest acceptable value for the i-th response; A is a constant, defined as: 9 log i i A x x (under optimal conditions) After determining the preference values for each response, it is necessary to determine the weightage (Wi, i = 1, 2, ..., n) for each performance indicator, satisfying the condition (7): 1 1 n i i W . (7) Subsequently, for each test condition and repetition, the utility value (U(n,R)) is calculated based on equation (8): ( , ) 1 ( , ) n n R i i i U P n R xW (8) where n is the number of performance metrics (1, 2, 3, ..., 18); R is the number of repetitions of each trial (1, 2, 3). After calculating the utility values, to determine the ideal configurations of process parameters, the S/N ratio is calculated, considering utility as a “Larger-the-Better” type of characteristic. Then, the average response value and confidence interval are calculated using the values of significant parameters. Equations (9) and (10) are used to calculate 95 % confidence intervals for confirmation experiments (CICE) and populations (CIpop): α 1 1 (1, ) CE e e eff CI F f V n R (9) α (1, ) e e pop eff F f V CI n (10) Fα(1, fe) is the F ratio at the confidence level of (1-α) against DOF 1 and error degree of freedom fe; Ve is the error variance; R is the sample size for confirmation trials. 1 ( ) eff N N DOF associated inthe estimate of meanresponse neff is an effective sample size, calculated as N / (1 + DoF), where N is a total number of findings DoF is the total number of degrees of freedom associated with the estimation of the mean response. Specific values: Neff = 54/(1+6) = 7.714; N (total number of results) = 18×3 = 54; R (sample size for confirmatory trials) = 3; Ve (error variance) = 0.05087; fe (error degrees of freedom) = 11. Conduct the validation trials at the optimum process parameter settings and compare the results with the projected mean response values. The assumed weightage of quality characteristics was 0.33 for each MRR, SR and TWR (WMRR, WTWR and WSR), and the utility value was calculated using equation 14. The utility values are calculated for all 18 experimental conditions and three repetitions. Since utility is a quality criterion that favors higher values, the utility values were analyzed based on the average utility at each parameter level as well as the S/N ratio.
RkJQdWJsaXNoZXIy MTk0ODM1