A comparison of properties of cattail fibres with other commonly used natural fibres, i.e., flax, hemp, sisal, and coir used for composite applications, are shown in
Table 4 [
6,
30,
31]. From the table, it is evident that cattail fibres showed lower tensile strength and modulus of elasticity compared to flax and hemp fibres. However, it showed similar tensile strength as coir fibres, and the modulus of elasticity was found to be higher than coir fibres and almost similar to sisal fibres. Therefore, similar to sisal and coir fibre composites, the cattail fibre composites have potential applications in the automotive and packaging industry [
29].
3.4.1. Optimizing Fiber extraction Process with Desirability Function Analysis
Desirability function analysis (DFA), popularized by Derringer and Suich [
33], is one of the most widely used methods for process optimization having multiple responses. The desirability function transforms each estimated response variable
to a desirability value
where
. The individual desirability is then combined using the geometric mean.
Here, two different types of desirability functions
were used, i.e., desirability function to maximize, and desirability function to minimize. For maximizing a property
, the desirability function
was calculated using the following Equations (4)–(6):
where
C is the upper criteria value or the requirement,
Ymin is the lower tolerance value, and s represents weight. When
equals or exceeds the upper criteria value, which is the requirement, the desirability function equals 1. When
is less than the lower tolerance value, which is unacceptable, the desirability function equals to 0.
For minimizing a property
, the desirability function
was calculated using the following Equations (7)–(9):
where
C is the lower criteria value or the requirement,
Ymax is the upper tolerance value, and
t represents weight. When
Yi is equal to or less than the lower criteria value, which is the requirement, the desirability function equals 1. When
Yi exceeds the upper tolerance value, which is unacceptable, the desirability function equals 0. Therefore, before calculating the individual desirability function, the objective of each property, the criteria value, the tolerance value, and the weights were fixed. The values of
s and
t are specified by the user, and Derringer and Suich [
33] suggested that a large value of weights would be specified if the property (
Yi) is very desirable.
where
,
is the individual desirability of the property
,
is the relative importance of the property
in the composite desirability
shown in Equation (10), w is the sum of the individual importance
, and
is the number of properties. Therefore, this single value of composite desirability represents the overall assessment of the desirability of the combined response levels [
33]. The value of
falls within the range of 0 to 1, and the value of
increases as the combination of properties become more favourable. Moreover, if any
, meaning one of the response variables is unacceptable; the value of
becomes 0, which implies that the overall product is unacceptable.
For bio-composite applications, the objectives of tensile strength and modulus of elasticity of the fibres are to maximize, and the objectives of fibre diameter and moisture regain (%) are to minimize [
34,
35]. The optimum values of the physical and the mechanical properties of extracted cattail fibres obtained from this study are shown in
Table 5.
The cattail fibres showed a relatively low elongation at break (%), and the estimated means ranged between 1.16–2% (
Table 5). Due to the small range, this property was not included in the list of optimized properties. The objectives of fibre properties, the criteria/target values, the tolerance values, weight of individual property, the importance of co-efficient of each property compared to others, and the reference values are listed in
Table 6. The reference values were taken from the properties of commonly used natural fibres used in composite applications [
29,
30].
For composite applications, it is desirable for tensile strength and modulus of elasticity to attain the optimum values, and, therefore, higher weights are given to these properties. Furthermore, higher importance coefficients are given to fibre diameter, tensile strength, and modulus as these are primary characteristics affecting the overall performance of composites [
29].
The desirability index of individual property ( was calculated by selecting Equations (3)–(8). The composite desirability for each treatment by combining all the individual desirabilities were calculated using Equation (9). The highest composite desirability value (0.796, data not shown here) was obtained from the fibres treated with a 7% (w/v) concentration of NaOH at 90 °C treatment temperature for 10 h treatment duration. Therefore, the cattail fibres obtained from this treatment would be most suitable for bio-composite applications, and the optimum values or the estimated treatment means of yield (%), diameter (µm), tensile strength (MPa), modulus of elasticity (GPa), and moisture regain (%) for this treatment are 24.08, 79.83, 165.56, 14.01, and 8.73, respectively.
3.4.2. Sensitivity Test of DFA for Composite Applications
At present, there is no standard that can be used to select or determine the parameters of desirability functions. Therefore, the selection of these parameters is susceptible to bias or arbitrary choices [
37]. In general, these parameters are determined based on applications and manufacturing costs [
33,
38]. However, from a design and quality perspective, the selection of parameters should have some statistical basis so that the optimization results can be analyzed further [
37]. This analysis should examine the robustness of overall desirability to changes in these parameters.
In this study, a sensitivity analysis of desirability functions was conducted by following the approach proposed by Aksezer [
39]. The upper and lower edges of each parameter were assigned as shown in
Table 7. Each parameter was designated by a letter A to O. For sensitivity analysis, 15 factors which are the importance coefficients, weights, and ranges of responses, were analyzed. The selected factors were investigated by a 2-level design. The Plackett–Burman design was selected for this sensitivity analysis as only the main effects are required to be examined to draw relevant conclusions [
39]. Furthermore, this design is very useful for detecting the main effects with a smaller number of experiments as this design can examine up to the N-1 number of factors for N experiments.
For this analysis, the Plackett–Burman design with 20 runs was selected. The experimental setup and the resulting values for overall desirability are shown in
Table 8. All the calculations were conducted using the JMP
® 14.2. software. The resulting ANOVA is given in
Table 9. The overall desirability model is found to be significant with a
p < 0.05 and an acceptable adjusted R-square value of 0.96. The prediction equation on the overall desirability is found as given in Equation (10).
After analyzing the parameter estimates, it was found that the range in (%) yield (Designation: K) is the most sensitive parameter, followed by the weight of (%) yield (Designation: A). The positive sign indicates that any increase in K will increase the overall desirability rapidly, and the negative sign indicates that a decrease in A will increase the overall desirability. Therefore, selecting a moderate range for yield (%) between 20–34% and keeping the weight for moisture regain (%) to 1 while determining the optimum parameters for composites was a prudent decision. Furthermore, the range of tensile strength (Designation: M) and modulus of elasticity (Designation: N) proved to be the least sensitive. The proposed procedure allowed the sensitivity of the important characteristic parameters of the desirability function and their impact on the optimal solution to be analyzed. However, it should be noted that optimum levels of input variables (time, temperature, and concentration of NaOH) obtained from different design points ended up with equal settings with different overall desirability levels, which proved that the higher overall desirability does not necessarily mean a better solution.