MINITAB Release 15 is the software that gives the statistical analysis of how to form a combination of input parameters and to find out the most significant combination. Process parameters are control factors, and the factors which initiate variability in the process are the noise factors. In a Taguchi designed experiment, the noise factors are manipulated for the variability to occur, and from the results optimal control factors that make the process robust, can be identified. The Signal to Noise ratio indicates the control factors settings that minimize the effects of the noise factors. The Taguchi experiments are carried out in a two-step optimization process.
Step 1: use the S/N ratio to identify those control factors that reduce variability.
Step 2: identify the control factors that bring the mean to target and have little or no effect on the S/N ratio.
Usually, the calculation of the main effect of the S/N ratio and mean response is done by three categories of quality characteristics, as listed below.
(1) The smaller the better:
The Smaller the better criterion is applied to the problems, when a minimization of the response is required for the output characteristics data; (i.e.) if the output result needs to be the minimum in value and the data are non-negative with a target value of zero. Here, in this optimization, maximum tensile strength is required and hence the smaller the better criterion is not applied.
S/N ratio (η) = -10 log10 ((1/n) Σ (yij) 2)
Where n is the number of replications,
yij is the observed response value.
i = 1, 2, 3….n; j = 1, 2, 3…k
(2) The larger the better:
The Larger the better criterion is applied to the problems, when the maximization of the response is required for the output characteristics data. The data of the target value is positive. Here the optimized result needed is higher tensile strength, and hence this criterion is selected to find out the optimum process parameter, which can give better strength.
The following formula is used to find the optimum result,
S/N ratio (η) = -10 log10 ((1/n) Σ (1/ (yij)2))
(3) The nominal the best:
The Nominal the best criterion is applied to target the response, and base the S/N ratio on the mean and standard deviations. The data are non-negative with an absolute zero, in which the standard deviation is zero when the mean is zero.
S/N ratio (η) = -10 log10 (μ2/σ2)
where μ = (y1+y2+y3+…….+yn) / n,
σ = ((yi-y)2 / (n-1))
The greatest advantage of this method is the saving of effort in conducting experiments; saving experimental time, reducing the cost, and discovering significant factors quickly. Taguchi’s robust design method is a powerful tool for the design of a high-quality system. In addition to the S/N ratio, a statistical analysis of variance (ANOVA) can be employed to indicate the impact of process parameters on metal removal rate values. The steps applied for Taguchi optimization in this study are as follows. [11]
- Selection of noise and control factors
- Selection of Taguchi orthogonal array
- Experimental detail
- Adsorption rate measurement
- Analysis of results(Signal-to-noise ratio)
- Prediction of optimum performance
- Confirmation experiment
2.1. EXPERIMENTAL PROCEDURE
2.1.1. Selection of noise and control factors
Taguchi methods which combine the experiment design theory and the quality loss function concept have been used in developing robust designs of processes and in solving problems. The adsorption rate by the desiccant is varied by the parameters such as the desiccant mass, different desiccant and air velocity. Among these input parameters, the desiccant mass, different desiccant and air velocity are taken and the other parameters are maintained constant. The input parameters are entered in the array table with the output characteristics as the adsorption rate. The adsorption rate should be optimized to have a better result, with a suitable process parameter, and hence, the Taguchi technique is applied to a self-analysis of the air dehumidification.
For the purpose of observing the degree of influence of the process parameters in air dehumidification, three factors, each at three levels, are taken into account, as shown in Table 1.
Table 1 Air dehumidification process parameters
|
Factors
|
Levels
|
|
1
|
2
|
3
|
|
A, Desiccant mass in kg
|
2
|
2.5
|
3
|
|
B, Desiccant name
|
Activated Alumina
|
Activated carbon
|
Molecular sieve
|
|
C, Mass flow rate of air in kg/hr
|
72
|
108
|
144
|
2.1.2. Selection of Taguchi orthogonal array
In this research, nine experiments were conducted at different parameters. The degrees of freedom for three parameters in each of three levels were calculated as follows.
Degree of Freedom (DOF) = number of levels -1
For each factor, DOF equal to:
For (A); DOF = 3 – 1 = 2
For (B); DOF = 3 – 1 = 2
For (C); DOF = 3 – 1 = 2
For this, Taguchi L9 orthogonal array was used, which has nine rows corresponding to the number of tests, with three columns at three levels. L9 OA has eight DOF, in which 6 were assigned to three factors (each one 2 DOF) and 2 DOF was assigned to the error.
2.1.3. Experimental Details
The experiments were conducted during evening hours in the air dehumidifier setup which is shown in Fig. The dehumidifier setup consists of air blower and dehumidification chamber. The desiccant is kept inside the chamber. The initial weight before adsorption and after adsorption were measured to calculate the adsorption rate of desiccant material. Atmospheric air is passed through the dehumidifier chamber in which desiccant material is available. The adsorption rate was measured for three different desiccants, three different masses of desiccant and three different air velocities. The number of experiments along with the significant combination of parameters and level were derived from Taguchi method.
2.1.4. Adsorption rate measurement
Adsorption rate by the desiccant was measured as;
Adsorption rate= (Initial Weight -Final Weight)/Time.
2.1.5. Analysis of results
Regression Analysis
The desiccant mass, different desiccant and air velocity were considered in the development of mathematical models for the adsorption rate. The correlation between factors (desiccant mass, different desiccant and mass flow rate of air) and adsorption rate on the desiccant dehumidifier were obtained by multiple linear regressions.
The regression equation is
Adsorption rate= 0.0838 + 0.0117 A - 0.0193 B + 0.0110 C
R2= 98.19 %, R2 (adj) = 92.75%
In multiple linear regression analysis, R2 is the regression coefficient (R2>0.90) for the models, which indicate that the fit of the experimental data is satisfactory.
Analysis of the S/N Ratio
Taguchi method stresses the importance of studying the response variation using the signal-to-noise (S/N) ratio, resulting in maximization of quality characteristic variation due to uncontrollable parameter. The adsorption rate was considered as the quality characteristic with the concept of "the larger-the-better". The S/N ratio used for this type response is given by [13]
The S/N ratio for the larger-the-better is:
S/N = -10*log (mean square deviation)
S/N ratio (η) = -10 log10 ((1/n) Σ (1/ (yij)2)) …………… (1)
Where n is the number of measurements in a trial/row, in this case, n=1 and y is the measured value in a run/row. The S/N ratio values are calculated by taking into consideration Eqn. 1. The adsorption rate values measured from the experiments and their corresponding S/N ratio values are listed in Table 2.
Table 2 Adsorption rate values and S/N ratio values for experiments
|
Experiment No
|
Dehumidification parameter level
|
Adsorption rate
|
S/N ratio
|
|
A1
|
1
|
1
|
1
|
0.025
|
-32.0412
|
|
A2
|
1
|
2
|
2
|
0.035
|
-29.1186
|
|
A3
|
1
|
3
|
3
|
0.161
|
-15.8635
|
|
B1
|
2
|
1
|
2
|
0.005
|
-46.0206
|
|
B2
|
2
|
2
|
3
|
0.052
|
-25.6799
|
|
B3
|
2
|
3
|
1
|
0.062
|
-24.1522
|
|
C1
|
3
|
1
|
3
|
0.093
|
-20.6303
|
|
C2
|
3
|
2
|
1
|
0.093
|
-20.6303
|
|
C3
|
3
|
3
|
2
|
0.079
|
-22.0475
|
The adsorption rate response table for the desiccant mass, different desiccant and mass flow rate of air was created in the integrated manner and the results are given in Table 3. Regardless of the category of the performance characteristics, a greater S/N value corresponds to a better performance. Therefore, the optimal level of the dehumidification parameters is the level with the greatest S/N value. Based on the analysis of the S/N ratio, the optimal dehumidification performance for the adsorption rate was obtained at 3 kg (level 3), Activated alumina (level 1) and 144 kg/hr (level 3).
Table.3 Signal to Noise Ratio values for adsorption rate by factor level
|
Level
|
Desiccant mass
|
Desiccant name
|
Mass flow rate of air
|
|
1
|
-21.69
|
-19.17a
|
-21.07
|
|
2
|
-22.86
|
-22.62
|
-23.76
|
|
3
|
-19.51a
|
-22.28
|
-19.23a
|
|
Delta
|
3.35
|
3.45
|
4.53
|
|
Rank
|
3
|
2
|
1
|
a optimum level
2.1.6. Prediction of optimum performance
The effect of process parameters on the adsorption rate values was shown in Figure 1. The adsorption rate increases with increasing in mass flow rate of air, type of desiccant and desiccant mass in order. Lowering mass flow rate of process air more time for the air to contact the desiccant, so more moisture is removed. However, lower mass flow rate mean larger equipment for a given air flow, so dehumidifiers are generally selected at the highest process air mass flow rate that the application will allow. Each desiccant has unique sorption characteristics which affect the performance of the dehumidifier. At constant temperature, each desiccant has a fixed capacity to absorb moisture. Its capacity is a function of relative humidity. Along with other factors, the amount of moisture removed from the air depends on how much desiccant the air contacts as it moves through the dehumidifier-more desiccant means more moisture removed.
Analysis of Variance (ANOVA)
ANOVA is a statistically based, objective decision-making tool for detecting any differences in the average performance of groups of items tested. The ANOVA results are illustrated in Table 4.ANOVA helps in formally testing the significance of all main factors and their interactions by comparing the mean square against an estimate of the experimental errors at specific confidence levels. First, the total sum of squared deviations SST from the total mean S/N ratio nm can be calculated as [14]
n
SST =∑ (ni-nm)2
i=1
where n is the number of experiments in the orthogonal array and ηi is the mean S/N ratio for the ith experiment.
The percentage contribution can be calculated as: P =SSd / SST
where SSd is the sum of the squared deviations.
Statistically, there is a tool called an F test, named after Fisher [15], to see which design parameters have a significant effect on the quality characteristic. In the analysis, the F-ratio is a ratio of the mean square error to the residual error, and is traditionally used to determine the significance of a factor. The P-value reports the significance level (suitable and unsuitable) in Table 4. Percent (%) is defined as the significance rate of the process parameters on the metal removal rate. The percent numbers depict that the applied voltage, feed rate and electrolyte concentration have significant effects on the metal removal rate. It can observed from Table 4 that the desiccant mass (A), desiccant type (B) and air velocity (C) affect the adsorption rate by 25.21%, 34.74 % and 38.31% in the air dehumidification process, respectively. A confirmation of the experimental design was necessary in order to verify the optimum cutting conditions.
Table 4 ANOVA results for adsorption rate for the dehumidification process
|
Source
|
DF
|
Seq SS
|
Adj SS
|
Adj MS
|
F
|
P
|
Percentage of contribution
|
|
Desiccant mass
|
2
|
0.0022389
|
0.0022389
|
0.0011194
|
3.13
|
0.242
|
25.21
|
|
Desiccant name
|
2
|
0.0030969
|
0.0030969
|
0.0015484
|
70.58
|
0.014
|
34.74
|
|
Air velocity
|
2
|
0.0034149
|
0.0034149
|
0.0017074
|
36.52
|
0.027
|
38.31
|
|
Error
|
2
|
0.0001616
|
0.0001616
|
0.0000808
|
|
|
1.81
|
|
Total
|
8
|
0.0089122
|
|
|
|
|
|
DF- Degrees of Freedom, Seq SS – Sequential Sum of Squares, Adj SS – Adjusted Sum of Squares, Adj MS – Adjusted Mean Square, F test of hypothesis, P value of hypothesis.
Table.5 Optimized result obtained from ANOVA – Minitab
|
Method
|
Desiccant mass
|
Desiccant name
|
Air velocity
|
Adsorption rate
|
|
Taguchi method
|
3 kg
|
Activated alumina
|
0.04 kg/sec
|
0.1629 kg/hr
|
2.1.7. Confirmation test
The experimental confirmation test is the final step in verifying the results drawn based on Taguchi’s design approach. The optimal conditions are set for the significant factors (the insignificant factors are set at economic levels) and a selected number of experiments are run under specified cutting conditions. The average of the results from the confirmation experiment is compared with the predicted average based on the parameters and levels tested. The confirmation experiment is a crucial step and is highly recommended by Taguchi to verify the experimental results. In this study, a confirmation experiment was conducted by utilizing the levels of the optimal process parameters (A3B1C3) for adsorption rate in the air dehumidification process and obtained as 157.17 kg/hr at an air flow rate of 144 kg/hr.