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Vol. 8. Issue 3.
Pages 2865-2879 (May - June 2019)
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Vol. 8. Issue 3.
Pages 2865-2879 (May - June 2019)
Original article
DOI: 10.1016/j.jmrt.2019.02.019
Open Access
Material selection of natural fibre using a stepwise regression model with error analysis
Muhammad Noryania,c,e, Salit Mohd Sapuana,b,
Corresponding author

Corresponding author.
, Mohammad Taha Masturad, Mohd Yusoff Moh Zuhria, Edi Syams Zainudina
a Advanced Engineering Materials and Composites Research Centre, Department of Mechanical and Manufacturing Engineering, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
b Laboratory of Biocomposite Technology, Institute of Tropical Forestry and Forest Products (INTROP), Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
c Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
d Faculty of Mechanical and Manufacturing Engineering Technology, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
e Centre of Advanced Research on Energy, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
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Figures (10)
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Tables (6)
Table 1. Properties of natural fibre [5,11,12,34–39].
Table 2. The condition of forward selection and backward elimination in stepwise regression.
Table 3. The best model of natural fibre suggested by stepwise regression.
Table 4. The coefficient of the regressor into the model.
Table 5. Error analysis using MAE, MSE and RMSE.
Table 6. The ranking for final decision-making.
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The nature of natural fibre such as it is lightweight, recyclable, biodegradable and gives a high performance in relation to its mechanical properties makes this material an excellent alternative to currently used materials in the manufacture of automotive components. The significant mechanical properties are identified using the best statistical model suggested by stepwise regression in this study. The estimation and error analysis of the response variables are discussed to select the best natural fibre for automotive component applications. The results using statistical measurement indicate that tensile strength is the most significant mechanical property for all the selected natural fibres. The final ranking that considered high performance score and minimum error analysis for a hand-brake lever application found that coir, kenaf and cotton are the top three candidates with average scores of 4, 4.5 and 5, respectively. The statistical model presented in this study can be used in multiple applications. In fact, this approach is helpful to the design engineer when huge amounts data are involved.

Material selection
Natural fibre
Stepwise regression
Error analysis
Full Text

Industry wide, mass reduction strategies have become increasingly important in recent years. In the United States, the automotive industry is required to meet the Corporate Average Fuel Economy (CAFE) standard for each car sale [1]. In 2011, 13 large automakers such as Ford, GM, BMW, Honda, Hyundai, Mazda, Nissan, Toyota and Volvo agreed with the regulations for vehicles from model year 2017 until 2025 [2]. This guideline was also implemented in the Kingdom of Saudi Arabia, effective by early 2016 [3]. In recent years, researchers have come up with an innovative idea to use natural fibre as a substitute material in the automotive industry to comply with the global standard. The benefits of this material, such as it is lightweight, recyclable, biodegradable, economical and has good mechanical properties, mean that it is an excellent alternative to the currently used materials to manufacture automotive components in the industry [4–8]. A number of studies have shown that this natural fibre has its own strengths that can fulfil the product design requirements, especially in the automotive industry [9–12]. Not just in the automotive industry, but in other industries the demand for natural fibre composites is also increasing year by year, e.g., in construction, aerospace, textiles, medicine, packaging, and electrical and electronics applications [6,13,14]. To replace steel-based materials with natural fibre in automotive components can overcome or reduce problems such as heavy mass, high cost of materials and manufacturing, high fuel consumption and corrosion issues over a certain period that are always a challenge for the design engineer to consider as a whole in the manufacturing process [15–17].

Material selection is one of the important processes in automotive assembly. The design engineer should select an appropriate suitable material that fulfils the criteria of the design and function of the automotive component. Numerous selection strategies can be used to transfer the inputs to the final output in different multi-criteria decision-making (MCDM) tools, as shown in Fig. 1. It should be noted that there is no specific procedure to select the best natural fibre in automotive applications. The traditional method used manual checking on the product design specification that match to the materials performance. A lot of literature discusses the strengths and limitations of the conventional material selection methods such as analytical hierarchy process (AHP), analytical network process (ANP), technique of ranking preferences by similarity of the ideal solutions (TOPSIS), quality function deployment (QFD), preference ranking organisational method for enrichment evaluation (PROMETHEE) and Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) [18–26]. Just focusing on the weaknesses, the weighting process in AHP is very subjective, based on the judgement of the user. Furthermore, TOPSIS ignores the relationship and interdependency between the attributes throughout the process selection, which can produce inconsistent decision-making. Very simple tools such as PROMETHEE make the final decision not rational and big data is needed for some tools such as VIKOR, which is one of the limitations in MCDM tools. Quality Function Development is one of MCDM tools that can translate customer requirement into design requirement, but the subjective preference also occur in correlation matrix in house of quality matrix diagram [26,27]. Many studies have introduced single and integrated modelling in decision-making [28]; a single model focuses on one criterion, otherwise multiple criteria are considered in the study. With regard to the latter type of model, the effect of each criterion on the model is analysed and the final decision is dependent on the criteria or input considered in the study [29].

Fig. 1.

The process of material selection [30].


The huge number of materials that exist in the world means that it takes up the design engineers’ valuable time and increases costs to select the best material. A novel statistical approach to select a natural fibre composite was introduced by Noryani et al. [20]. By using the statistical package for social science (SPSS) programme, the significant mechanical properties are identified, and the statistical model is constructed for the appropriate data set. This approach can reduce the time and cost throughout the process [31,32]. In the previous study, three types of composites are measured using statistical analysis such as correlation coefficient, coefficient of determination, significant testing, multicollinearity testing and analysis of variance. The present study is motivated by the need to take into consideration the natural fibre itself before it becomes the final composite. In addition, the precision of estimating the performance score for natural fibre is considered compared to the earlier study.

In this study, an improved strategy for the material selection process from the previous work is discussed [20] where another measurement such as error analysis is considered with the estimation values. The performance of alternative natural fibres is analysed by using statistical measurement. The significant mechanical properties are identified to estimate the performance score (PS) for each alternative using the best statistical model suggested by stepwise regression. To select the best natural fibre, the product design specification of a hand-brake lever is used as a case study. Finally, the error analysis for the estimation can increase the trust in the final decision material. In fact, the potential and suitability of this approach can be applied to different automotive components in the industry.


The data collection of mechanical properties for natural fibre in the previous study is an initial stage in this methodology. The screening process is started by using stepwise regression to identify the best statistical model of the natural fibre by excluding the irrelevant models. In this stage, the coefficient of the regressor is expressed by using least squares estimation with significant parameters to the model constructed. The product design specification is used to estimate the PS of the natural fibre. The screening process is performed after calculating the error analysis for all candidates. The errors analysis in this study are mean absolute error (MAE), mean squared error (MSE) and root mean squared error (RMSE). The second stage is ranking the result from the first stage. Identifying the maximum score of the estimation and the minimum score of the error analysis is the objective in this stage. The third stage is supporting information such as final ranking from the second stage and previous result for the application. Figs. 2 and 3 illustrates the three stages of the selection process for the material starting from all materials to the final selection of the specific material in this study. In this methodology, each stage is continuously checked to ensure the decision-makers reach the best final decision [33].

Fig. 2.

The methodology of the material selection process.

Fig. 3.

Quarter selection position of best natural fibre statistical model.

2.1Data collection

Mechanical properties of natural fibre from the previous study are used as secondary data in this study. Here, the implementation of the average value can reduce the dispersion of the data. Twelve types of natural fibre are selected. Table 1 shows the density (x1), tensile strength (x2), Young's modulus (x3) and elongation at break (x4) used in this study. These mechanical properties are the main criteria preferred in material selection for automotive components as mentioned by Noryani et al. [32]. Performance score (PS) is used as the response variable as calculated by using Eq. (1)[20]. Some of the cost of the material is not available (n/a). Therefore, the data is excluded in the analysis.

Table 1.

Properties of natural fibre [5,11,12,34–39].

Natural fibre  Mechanical properties
  Cost (MYR/kg)  Density (g/cm3Tensile strength (MPa)  Young's modulus (GPa)  Elongation at break (%) 
Bananan/a1.4  721.5  29.5 
1.35  500  12  5.25 
1.35  355  33.8  5.3 
Bagassen/a1.25  256  22.05  1.1 
1.25  256  22.05  1.1 
1.2  290  17  1.1 
1.2  155  23.4  1.01 
Cotton6.45  1.55  543.5  9.05  6.5 
9.68  1.55  543.5  9.25  6.5 
12.9  1.55  543.5  9.05  7.5 
6.45  1.5  442  9.05  6.5 
9.68  1.55  543.5  9.05  6.5 
12.9  1.51  400  12  7.5 
6.45  1.55  442  16.75  6.83 
Ramie6.04  1.28  669  86  4.6 
6.24  1.5  469  86  2.6 
6.14  1.5  669  57  2.6 
6.14  1.28  445  76.25  2.5 
6.14  1.28  700  76.25 
6.14  1.5  700  24.5  2.5 
6.14  1.5  560  44  2.8 
6.14  1.5  500  94.7  2.8 
6.14  1.42  669  68.09  2.8 
Coir0.78  1.2  212  27.5 
1.17  1.2  175.5  33.2 
1.56  1.31  162.5  33.2 
0.78  1.31  162.5  4.4  30 
1.17  1.2  175  4.4  20 
1.56  1.25  220  30 
0.78  1.2  175  27.5 
1.17  1.17  153  28.8 
1.56  1.23  179.4  6.5  28.8 
Pineapplen/a1.74  1020  71  14.5 
1.2  513.5  1.44 
1.5  898.5  82  14.5 
1.2  513.5  1.44  10.3 
Flax9.68  1.5  922.5  25.75  2.4 
10.05  1.5  1087.5  18  2.25 
9.87  1.45  1171.5  53.5  2.25 
9.87  1.5  672  65.3  2.2 
9.87  1.5  690  27  2.95 
9.87  1.45  1172.5  27.6  2.25 
9.87  1.5  690  65.3  2.95 
9.87  1.4  1150  27.6  1.4 
9.87  1.5  690  70  2.95 
9.87  1.45  922.5  27.6  2.6 
9.87  1.48  916.85  63.8  2.42 
Hemp3.24  1.45  690  65  2.8 
6.45  1.5  830  46 
4.67  1.45  585  64  2.25 
4.79  1.48  644.5  56.75  1.6 
4.79  1.45  585  35  1.6 
4.79  1.48  690  56.75  1.6 
4.79  1.48  725  70  1.6 
4.79  1.48  690  70  2.06 
4.79  1.49  805.5  70  2.06 
4.79  1.47  693.9  70  2.06 
Jute2.26  1.38  586.5  21.5  1.9 
2.89  1.4  277  32.5  1.4 
1.17  1.4  596.5  43  1.65 
2.11  1.4  560  55  1.65 
2.11  1.46  596.5  26.5  1.65 
2.11  1.3  583  43  1.65 
2.11  1.4  560  26.5  1.8 
2.11  1.3  583  20  1.65 
2.11  1.46  600  26.5  1.48 
2.11  1.3  583  36.5  1.65 
2.11  1.4  550  33.1  1.65 
Sisal2.03  1.43  495  17.4 
3.89  1.4  681  18.7  4.5 
2.96  1.42  531.5  23.5  2.25 
2.96  1.5  573  15.7  4.5 
2.96  1.42  531.5  23.5  2.25 
2.96  1.5  573  15.7  2.5 
2.96  1.33  650  38  2.25 
2.96  1.5  573  15.7  4.5 
2.96  1.48  575.5  15.7  3.47 
Kenaf1.15  1.5  737.5  40.5  2.55 
1.22  1.19  361  57  2.1 
1.95  1.4  576.5  33.75  1.6 
1.44  1.45  930  53  2.1 
1.44  1.4  576.5  33.75  1.6 
1.44  1.3  930  53  4.25 
1.44  1.3  612.5  53  1.6 
1.44  1.2  930  53  2.25 
1.44  1.34  585  33.5  2.26 
Bamboo2.28  0.75  216.5  29  1.3 
3.60  0.85  470  21.5  3.1 
5.10  0.85  470  21.5  3.1 
3.66  0.85  185  14  2.5 
2.2Stepwise regression

Forward selection and backward elimination are processes in stepwise regression. Forward selection starts with the assumption that there are no regressors in the model except the intercept. The process is followed by inserting the regressors into the model one at a time to find the optimal subset in the model. The largest simple correlation to the response variable (y) is considered into the equation; the second regressor considered into the equation also has a high partial correlation towards y after adjusting the effect of the first regressor entered into the model. The F-statistics in Eq. (2) that illustrate x2 have a high partial correlation when x1 is already in the model [40]:

where SSR is the sum of the square of the regression and MSRES is the mean square of the residual.

If this F value exceeds FIN, then the regressor is added to the model. In general, the regressor having a high partial correlation with y which considers the effect of another regressor already in the model is entered into the model. The process stops when the F-statistics do not exceed FIN or the last regressor is added to the model. An opposite direction is a practice in backward elimination; the process starts with all regressors being included in the model. FOUT is used to exclude the regressor that has the smallest partial correlation into the model. The summary of the process of forward selection and backward elimination is shown in Table 2.

Table 2.

The condition of forward selection and backward elimination in stepwise regression.

Condition  Forward selection  Backward elimination 
Start  No regressor in the model except intercept  All regressors in the model 
Add and removeExample:→ y, intercept (β0)→ y, β0, x1y, β0, x1, x2y, β0, x1, x2, x3y, β0, x1, x2, x3, x4……  Example:→ y, β0, x1, x2, x3, x4y, β0, x1, x2, x3y, β0, x1, x2y, β0, x1y, β0 
Add the regressor when:  Remove the regressor when: 
F-statistics>FINExample:SSRx2|x1MSRESx1,x2>FIN  F-statistics<FOUTExample:SSRx2|x1MSRESx1,x2<FOUT 
or  or 
P-value<α(0.05)  P-value>α(0.05) 
Stop  No regressor to be added  Until all P-valueα 

F-statistics: F value calculated from Eq. (2), FIN: critical point added, FOUT: critical point remove, P-value: significant value, α: standard error.

2.3Least squares estimation

Here, a standard approach in regression analysis is used. The general form implemented for the stepwise regression is shown in Eq. (3). It can be simple or multiple linear regression; the number of regressors will identify the type of regression.

where yi is the response variable (PS) xi are the regressor variables, β1, β2, …, βn are partial regression coefficient, ɛi is an error term and the subscript i indexes a particular observation.

The variation of the PS is explained by the regressors by calculating R2 and Adj R2 using Eqs. (4) and (5).

where SSR is the sum of the square of the regression; SSRes is the sum of the square of the residual; SST is the sum of the square of the total; df is the degree of freedom (n1 or np1).

2.4Measuring model performance using error analysis

Error analysis of the response variable (PS) is analysed by using three types of error, which are mean absolute error (MAE), mean squared error (MSE) and root mean squared error (RMSE), to identify the minimum error of the estimation of PS for each alternative natural fibre. The minimum error is required to guide the decision-maker in the process of selection with precision, less bias and result in a highly accurate solution.

2.4.1Mean absolute error (MAE)

The simplest error used for assessing the fitness of the model. The advantages of this error are its simplicity, and it is easy to understand and to calculate. This type of error is most preferred compared to the others. MAE can be calculated using Eq. (6).

2.4.2Mean squared error (MSE)

Another common error used to measure the accuracy of the estimation. Large errors may occur in this type of error because of the square function. MSE can be calculated using Eq. (7).

2.4.3Root mean squared error (RMSE)

Another favourite error used in inferential statistics. Mostly, using this type of error produces small errors compared to MSE. RMSE can be calculated by using Eq. (8).

for Eq. (6) until Eq. (8) which ei=yi−yˆi, where yi is the actual observed value, yˆi is the estimated value and n is the number of sample error in the model.

2.4.4Ranking the error score and final rank

Each error score is ranked (R) from small to large for alternative natural fibres. The rank of average score (RAS) and the final rank are calculated using Eqs. (9) and (10), respectively. By using AS score, the final error rank for alternative natural fibres is finalised. Rank number 1 is the best alternative natural fibre with a small number of errors.

3Results and discussion

In this part, the result suggested by stepwise regression is discussed. The significant statistical model with the coefficient is shown in the least squares method. The best and consistent natural fibre statistical models are demonstrated in quarter R2 and Adj R2 figures. R2 describes the variation of response variable, (PS) is explained by the regressor and Adj R2 is the measurement for multiple (more than one) regressors. Estimation of performance score of the alternative natural fibres is plotted and the final natural fibre is selected by the comparison of both the estimation of PS and the error analysis.

3.1Best statistical model suggested by stepwise regression

The previous study discussed the ability of stepwise regression to produce a significant statistical model without carrying out all possible simple and multiple linear regression [20]. The significant parameter is identified by constructing this statistical model [41]. In this study, there are 15 possible regression models for each natural fibre, but only the significant models are discussed. The main advantage of this method is that valuable time can be saved. By using stepwise regression, only the significant model is proposed by adding and excluding all the regressors based on the conditions discussed in Table 2. Table 3 shows the significant statistical model for each natural fibre that will be chosen as our best model for further decision-making for manufacturing the hand-brake parking lever. The minimum number of models proposed by the stepwise regression was for bamboo and pineapple. Coir, flax, kenaf, ramie and sisal were the natural fibres that had a maximum number of models suggested by the stepwise regression.

Table 3.

The best model of natural fibre suggested by stepwise regression.

Natural fibre  Model  Regressors in model  SSRES  MSRES  R2  Adj R2  P-value 
Bananax2  285.423  285.423  0.996  0.992  0.041 
x1x2  0.000 
Bagassex2  10.974  5.487  0.999  0.998  0.001 
Bamboo  x2  72.782  36.391  0.999  0.999  0.000 
Coirx2  140.744  20.106  0.965  0.961  0.000 
x2x4  5.088  0.848  0.999  0.998  0.000 
x2x3x4  0.873  0.175  0.000 
Cottonx2  79.264  15.853  0.997  0.996  0.000 
x2x4  26.315  6.579  0.999  0.998  0.000 
Flaxx2  2987.07  331.89  0.992  0.991  0.000 
x2x3  1.216  0.152  0.000 
x2x3x4  0.076  0.011  0.000 
Hempx2  1135.779  141.972  0.982  0.98  0.000 
x2x3  3.824  0.546  0.000 
Jutex2  1093.873  121.541  0.987  0.986  0.000 
x2x3  0.766  0.096  0.000 
Kenafx2  734.109  104.873  0.998  0.998  0.000 
x2x3  3.334  0.556  0.000 
x2x3x4  0.276  0.055  0.000 
Pineapple  x2  579.027  289.514  0.998  0.997  0.001 
Ramiex2  3345.848  477.978  0.955  0.949  0.000 
x2x3  3.261  0.544  0.000 
x2x3x4  0.1  0.02  0.000 
Sisalx2  294.484  42.069  0.99  0.989  0.000 
x2x3  4.8  0.8  0.000 
x2x3x4  0.317  0.063  0.000 
3.1.1Least squares estimates for best model

The sum of squares method is used to find the coefficient of the regressor to the model. An appropriate model can be written for each model by using the coefficient appropriately, as shown in Table 4. Tensile strength (x2) is the most significant regressor in the model, as shown in Table 4, followed by Young's modulus (x3) and elongation at brake (x4). Throughout the process, density (x1) is the only significant parameter for banana.

Table 4.

The coefficient of the regressor into the model.

Natural fibre  Regressors in model  βˆ0  βˆ1  βˆ2  βˆ3  βˆ4 
Bananax2  31.874  –  1.001  –  – 
x1x2  −1328.355  1053.555  0.849  –  – 
Bagassex2  31.861  –  0.965  –  – 
x2x4  −107.578  –  0.85  –  154.889 
Bamboo  x2  24.34  –  1.012  –  – 
Coirx2  38.491  –  0.988  –  – 
x2x4  5.214  –  1.004  –  1.057 
x2x3x4  1.046  –  1.001  1.072  1.027 
Cottonx2  42.369  –  0.971  –  – 
x2x4  −11.998  –  0.989  –  6.712 
Flaxx2  105.879  –  0.946  –  – 
x2x3  15.322  –  0.998  0.999  – 
x2x3x4  11.188  –  1.051 
Hempx2  40.711  –  1.04  –  – 
x2x3  4.660  –  1.008  0.964  – 
Jutex2  41.201  –  0.995  –  – 
x2x3  6.802  –  0.998  0.986  – 
Kenafx2  39.047  –  1.017  –  – 
x2x3  3.552  –  1.002  0.998  – 
x2x3x4  3.335  –  1.001  0.985  0.906 
Pineapple  x2  –832.581  –  1.178  –  – 
Ramiex2  135.727    0.904     
x2x3  8.853    1.001  1.01   
x2x3x4  8.203    0.999  0.998  0.945 
Sisalx2  0.676    1.048     
x2x3  3.941    1.011  0.871   
x2x3x4  1.404    1.008  0.959  0.822 
3.1.2Selection of best statistical model using determination of coefficient score (R2 and Adj R2)

The variation of the dependent variable in this study, which is PS, is measured by R2 for a single regressor and Adj R2 for multiple regressors in the model. The score of R2 and Adj R2 for all possible statistical models for some natural fibres is shown from Figs. 4–9. The area of each figure is divided into quarters, as shown in Fig. 3, to select the best model for estimation purposes. The selection is based on the highest value of R2/Adj R2 with minimum number of regressors. This condition can benefit the industry as less cost and time is required to estimate the performance of natural fibre in the industry with a reliable statistical model. The model is selected based on the position in the figure. The first quarter in Fig. 3 is the best condition, with a high score of R2/Adj R2 with fewer regressors, while the fourth quarter is the worst model, with the lowest score of R2/Adj R2 with more regressors.

Fig. 4.

The score of R2 and Adj R2 for cotton natural fibre.

Fig. 5.

The score of R2 and Adj R2 for coir natural fibre.

Fig. 6.

The score of R2 and Adj R2 for flax natural fibre.

Fig. 7.

The score of R2 and Adj R2 for hemp natural fibre.

Fig. 8.

The score of R2 and Adj R2 for jute natural fibre.

Fig. 9.

The score of R2 and AdjR2 for kenaf natural fibre.


Most of the best statistical models for natural fibre show x2 (tensile strength) is the significant consistent mechanical property in the model with the highest R2 value. The optimal parameter is identified; other studies used Taguchi design of experiments to optimise the parameters for experimental work [42]. For example, 99.7% of the variation of PS for cotton is explained by tensile strength. Tensile strength also explained the variation of the PS for coir, flax, hemp, jute and kenaf by 96.5%, 99.2%, 98.2%, 98.7% and 99.8% respectively. The consistent finding that concludes x2 (tensile strength) is the most significant parameter in this study can help the estimation process compared to the previous study that found multiple significant mechanical properties for the composite [20,43]. Another study working on the variation of tensile strength using R2 by Weibull statistics also found a high variation of sisal fibre of different gauge lengths [44]. Tensile properties of the materials are an important regressor to study, as shown in Table 4 where x2 is the most significant regressor in the statistical models.

Previous studies on tensile strength of natural fibre performance show the significance of this mechanical property [45,46]. The performance of the tensile strength of natural fibre is affected by the process parameter, chemical treatment, chemical composition, fibre loading and fibre orientation [47–50].

3.1.3Natural fibre selection using estimation of performance score (PS)

A statistical framework by Noryani et al. [51] is referred to. The process to select the most suitable material is essential after evaluation the performance of the different natural fibres. The estimation of the PS based on the product design specification for a hand-brake lever mentioned by Patel and Sarawade [52] is used in this study. Estimation and prediction by using a model can cut the cost and time in the manufacturing industry [53,54]. To manufacture the hand-brake lever, 460MPa is required for tensile strength. This value is used in the statistical model proposed in Table 4. The final score of PS of the alternative natural fibre is shown in Fig. 10. This quantitative measurement can increase the accuracy in the decision-making and overcome the bias and subjective preference [55]. The best natural fibre for the hand-brake lever in this study was ramie, which scored the maximum value of PS, which is 551.57, compared to other fibres. Flax, hemp, kenaf and jute are the other top fibres for manufacturing a hand-brake lever, scoring 541.04, 519.11, 506.87 and 498.90 respectively.

Fig. 10.

The performance score (PS) for the natural fibres.

3.1.4Error analysis

Minimum error in estimation is used to help the decision-maker to select the final material in the automotive industry. The accuracy of the measurement is determined by calculating the error [56]. Analysis of error for the statistical model can produce trustworthy estimation results for the application. Table 5 shows the score of MAE, MSE and RMSE for the natural fibres.

Table 5.

Error analysis using MAE, MSE and RMSE.

Natural fibre  yi  yˆi  ei  ei2  MAE  MSE  RMSE  AS 
Banana759.4  754.09  5.30  28.14  9.10  95.15  9.75  38.0 
518.6  532.37  −13.77  189.72         
395.45  387.30  8.22  67.58         
Bagasse280.4  249.21  31.20  973.13  27.7  803.94  28.35  286.6 
280.4  249.21  31.20  973.13         
309.3  278.07  31.23  975.25         
180.61  163.46  17.15  294.26         
Bamboo249.83  243.44  6.39  40.86  3.36  18.21  4.27  8.61 
499.05  499.98  −0.93  0.86         
500.55  499.98  0.57  0.32         
206.01  211.56  −5.55  30.80         
Coir246.48  247.95  −1.47  2.15  2.78  15.64  3.95  7.46 
216.07  211.89  4.19  17.51         
203.57  199.04  4.53  20.51         
198.99  199.04  −0.05  0.00         
201.77  211.39  −9.62  92.56         
257.81  255.85  1.96  3.84         
210.48  211.39  −0.91  0.83         
189.14  189.66  −0.51  0.27         
217.49  215.74  1.75  3.07         
Cotton567.05  570.11  −3.06  9.35  2.75  11.34  3.37  5.81 
570.48  570.11  0.37  0.14         
574.5  570.11  4.39  19.29         
465.5  471.55  −6.05  36.61         
570.28  570.11  0.17  0.03         
433.91  430.77  3.14  9.87         
473.58  471.55  2.03  4.12         
Flax961.83  978.56  −16.73  280.03  14.59  271.62  16.48  100.9 
1119.3  1134.65  −15.35  235.75         
1238.57  1214.12  24.45  597.90         
750.87  741.59  9.28  86.10         
731.32  758.62  −27.30  745.24         
1213.67  1215.06  −1.39  1.94         
769.62  758.62  11.00  121.02         
1190.27  1193.78  −3.51  12.31         
774.32  758.62  15.70  246.52         
964.02  978.56  −14.54  211.53         
994.42  973.22  21.20  449.48         
Hemp762.49  758.31  4.18  17.46  8.97  113.62  10.66  44.4 
886.95  903.91  −16.96  287.68         
657.37  649.11  8.26  68.21         
709.12  710.99  −1.87  3.50         
627.84  649.11  −21.27  452.46         
754.62  758.31  −3.69  13.62         
802.87  794.71  8.16  66.57         
768.33  758.31  10.02  100.38         
883.84  878.43  5.41  29.26         
772.22  762.37  9.85  97.08         
Jute613.54  624.77  −11.23  126.08  8.17  99.48  9.97  39.2 
315.19  316.82  −1.63  2.64         
643.72  634.72  9.00  81.03         
620.16  598.40  21.76  473.45         
628.22  634.72  −6.50  42.23         
631.06  621.29  9.77  95.53         
591.81  598.40  −6.59  43.44         
608.06  621.29  −13.23  174.93         
631.55  638.20  −6.65  44.24         
624.56  621.29  3.27  10.72         
588.26  588.45  −0.19  0.04         
Kenaf783.2  789.08  −5.88  34.63  8.07  81.60  9.03  32.9 
422.51  406.18  16.33  266.54         
615.2  625.35  −10.15  102.97         
987.99  984.86  3.13  9.82         
614.69  625.35  −10.66  113.58         
989.99  984.86  5.13  26.35         
669.84  661.96  7.88  62.10         
987.89  984.86  3.03  9.20         
623.54  633.99  −10.45  109.24         
Pineapple1107.24  368.98  368.98  545,029.30  752.21  565,966  752.3  18,915 
518.14  −227.68  −227.68  556,244.49    .52 
996.5  225.85  225.85  593,898.34         
526.44  −227.68  −227.68  568,693.96         
Ramie766.92  740.50  26.42  697.86  16.23  371.77  19.28  135.7 
565.34  559.70  5.64  31.78         
736.24  740.50  −4.26  18.17         
531.17  538.01  −6.84  46.74         
785.67  768.53  17.14  293.88         
734.64  768.53  −33.89  1148.33         
614.44  641.97  −27.53  757.74         
605.14  587.73  17.41  303.21         
747.45  740.50  6.95  48.26         
Sisal520.86  519.44  1.42  2.03  4.90  32.72  5.72  14.5 
709.49  714.36  −4.87  23.76         
561.63  557.69  3.94  15.54         
597.66  601.18  −3.52  12.39         
561.63  557.69  3.94  15.54         
595.66  601.18  −5.52  30.47         
694.54  681.88  12.66  160.38         
597.66  601.18  −3.52  12.39         
599.11  603.80  −4.69  22.00         
3.1.5Comparison for final selection of natural fibre

An improved material selection process with consideration of the error analysis of the estimation can improve decision-making. An ascending order is used to rank the highest value of PS while, for the error analysis, the minimum error is prioritised. Table 6 shows the final ranking to select the best natural fibre for manufacturing the hand-brake lever application. Three types of error show a consistent measurement of the error from the estimation and observed value. Most of the ranking is constant, such as cotton is ranked as the lowest error for all types of error; the values of the error are 2.75, 11.34 and 3.37, as shown in Table 5. The same goes for other natural fibres such as coir, bamboo, sisal, kenaf, flax, ramie, bagasse and pineapple.

Table 6.

The ranking for final decision-making.

Natural fibre  Method of selection
  MAE  MSE  RMSE  RAS  RPS  Final rank 
Bagasse  11  11  11  11  11  11 
Pineapple  12  12  12  12  12  12 
Ramie  10  10  10  10 
Sisal  10  10 

As shown in Table 6, the best natural fibre suggested for manufacturing the hand-brake lever was the coir. The second-best candidate is kenaf fibre, followed by cotton fibre. Flax, hemp, jute, bamboo and ramie are placed in the same rank as the fourth most suitable candidate material for this application. In contrast, using the Analytic Hierarchy Process, kenaf was found to be the best natural fibre to be hybridised with glass fibre reinforced polymer composites for a similar automotive component application [11]. Based on error analysis, cotton, coir and bamboo fibres are the top three that score minimum error on the estimation process of PS. Pineapple and bagasse score the highest error in the estimation of PS. A high number of errors may occur due to insufficient data on these types of materials.


Selection of the best natural fibre for the automotive component of a hand-brake lever was performed using a new statistical approach based on the best statistical model suggested by stepwise regression. The consideration of both high score of estimation on PS using best statistical model and minimum error analysis using MAE, MSE and RMSE through the material selection process in this study can increase precision in the decision-making process. The human error and bias in preference that may occur can also be reduced during the selection process. Twelve types of natural fibre were evaluated, considering four mechanical properties: density, tensile strength, Young's modulus and elongation at break. It was found that the tensile strength is the major parameter that influences the performance score of the alternative natural fibres in the statistical models constructed. The product design specification to manufacture a hand-brake lever was used to estimate the performance score for each natural fibre. Coir, kenaf and cotton fibre were highlighted as the top three candidate materials with maximum PS score and minimum error for the hand-brake lever application. Consistent findings were shown in three different types of error in the error analysis. Error analysis was used to increase the confidence level and trust in the final result through the stepwise regression. The major advantage of this method is the time and cost saving where the important parameter is considered with a strengthened statistical model. In addition, stepwise regression also gives more than one significant statistical model that can be used in different applications and allows systematic and detailed analysis with appropriate product design specification information. The most suitable natural fibre is finalised quickly using this statistical optimisation, especially when larger mechanical properties are involved.

Conflicts of interest

The authors declare no conflicts of interest.


The authors would like to thank Universiti Putra Malaysia for the opportunity to conduct this study as well as Universiti Teknikal Malaysia Melaka and Ministry of Education of Malaysia for providing the scholarship award and grant scheme Hi-COE (6369107) to the principal author in this project.

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