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Optimisation of Parboiling Process using Response Surface Methodology

(RSM) to improve the Physical Properties of Parboiled Milled Rice

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 Published by : International Journal of Engineering Research & Technology (IJERT)
http://www.ijert.org ISSN: 2278-0181
Vol. 7 Issue 07, July-2018

Optimisation of Parboiling Process using Response

Surface Methodology (RSM) to improve the
Physical Properties of Parboiled Milled Rice
1 2
Ogunbiyi, M. O., Adejumo, B. A., 2 Gbabo, A.
1 2
Department of Agribusiness and Market Development, Department of Agricultural and Bioresources Engineering,
Federal Ministry of Agriculture and Rural Development, Federal University of Technology, Minna, Nigeria
Abuja, Nigeria

3
Chinma, C. E.
3
Department of Food Science and Technology,
Federal University of Technology, Minna, Nigeria

Abstract— The optimisation of the parboiling conditions of a Nigeria being a multi-ethnic nation has a variety of food
popular rice variety in Nigeria using Response Surface cultures and tastes, but it citizens still share in common, a
Methodology (RSM) was carried out. The parboiling conditions - preference for whole kernel, polished, parboiled long-grain
Initial Soaking Temperature (IST), Soaking Time (ST) and Final rice, free from stone and other foreign matter, fluffy and tender
Moisture Content (FMC) were statistically combined in a Central when cooked [4] [5] [6]. The affinity and consumers’
Composite Design (CCD) with the effects on selected physical acceptability as well as choice of rice in Nigeria are greatly
properties of milled rice of FARO 52 rice variety determined. influenced by the eating and cooking qualities which are
Results obtained were analysed to determine the optimum
mainly controlled by the physicochemical and cooking
parboiling conditions (OPC) to produce milled rice with
properties of the rice grain [6] [7] [8]. This explains why
improved physical qualities. Results showed significant influence
(at 95% confidence level) of IST, ST and FMC on the head rice
imported parboiled rice is preferred against the locally
yield, broken rice ratio, grain hardness and grain colour of the processed rice by Nigerians as imported rice show more high
parboiled milled rice. The optimum paddy parboiling conditions consistency in terms of the desirable quality attributes [7].
for improved physical qualities of milled rice are: Initial soaking The parboiling process as practiced in Nigeria is not
temperature: 67.7°C; Soaking time: 13hrs 18minutes and Final standardized and official parboiling manuals are not available.
moisture content prior to milling: 12.7%. These optimal Hence, the procedure is not uniformly carried out and depends
conditions are expected to produce parboiled milled rice with the
on the method prevalent in the locality and on the experience of
following physical characteristics: Head rice yield, 70%; Broken
the processor. This has resulted to the non-uniformity in the
rice ratio, 2.18%; Grain hardness, 74.7N and Grain colour, 25.8
with a composite desirability of 76.3%.
quality of parboiled milled rice produced in Nigeria.
Parameters such as the initial soaking temperature and soaking
Keywords— Soaking time, soaking temperature, moisture time are important factors in rice parboiling and significantly
content, head rice yield, broken rice ratio. affect the quality of milled parboiled rice [9]. Improper soaking
at low temperature causes microbial contamination while
I. INTRODUCTION soaking at high temperature results in sloughing-off of the
Rice is one of the staple food consumed Sub-Saharan surface before effective hydration is achieved [9]. Prolonged
Africa especially in most part of West Africa [1]. It is however soaking results in leaching loss, fermentation, kernel bursting
a strategic commodity and a policy crop in the Nigerian and colour change [10].
economy. Rice can easily be prepared and consumed in various
ways hence it is a regular item in most diets [2]. Rice is the The quality of milled rice is determined by its physical,
fastest growing commodity in Nigeria’s food basket and its chemical and cooking properties [8]. The physical
demand has considerably increased over the years due to characteristics of the milled rice grains play a very important
increase in population, urbanization and attendant shift in role in determining its market value. Such characteristics like
consumers’ preference [3]. head rice yield, broken rice ratio, grain hardness and grain
colour are major determinants of the acceptability of milled rice
Two types of rice have been mainly cultivated in Nigeria: by consumers [7]. Grain quality differs according to the varietal
the African rice (Oryza glaberrima) and the Asian rice (Oryza composition and the method of postharvest paddy handling,
sativa). However, other improved varieties have been especially paddy parboiling, greatly influences the overall
developed over the years from these two major rice types. quality of the parboiled milled grain [8]. Some quality
These include the West African Rice Development Association characteristics are directly determined by the variety which also
(WARDA) hybrid rice varieties referred to as New Rice for interacts with environment and processing activities to
Africa: NERICA 19, NERICA 34 and NERICA 49 and Federal influence other characteristics indirectly.
Agriculture Research Oryza: FARO 44, FARO 52, FARO 60,
FARO 50 and other varieties.

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The Response Surface Methodology (RSM) has been used TABLE 1. EXPERIMENTAL RANGE AND LEVELS OF THE FACTORS
by many researchers to optimize scientific processes and have Factor Coded levels
been found to be very useful and efficient [11] [12]. RSM is -α Low Medium High +α
essentially useful in experimental design to evaluate responses
-1.68 -1 0 1 +1.68
to independent variables in an experimental process. The
0
methodology combines both mathematical and statistical IST ( C) 61.59 65 70 75 78.40
approaches to determine the optimal conditions at which the ST (Hours) 5.3 8 12 16 18.7
process will produce the best responses. The objective of this
study is therefore to determine the optimum conditions (initial FMC (%) 10.9 12 13.5 15 16.0
soaking temperature, soaking time and final moisture content) IST=Initial Soaking Temperature, ST = Soaking Time, and FMC= Final Moisture Content.

for paddy parboiling to produce milled rice with improved

physical qualities.. TABLE 2. FACTORS WITH CODED AND NATURAL VALUES

Coded form of Independent Actual form of Independent

II. MATERIALS AND METHODS Run variables variables
This study was conducted at the Rice Postharvest X1 X2 X3 X1 X2 X3
Laboratory of the Federal Ministry of Agriculture and Rural 1 -1 -1 -1 65 8 12
Development, Abuja, Nigeria. A hundred kilogram (100kg) 2 1 -1 -1 75 8 12
sample of FARO 52 an improved high yielding irrigated rice 3 -1 1 -1 65 16 12
variety commonly grown in Nigeria, was obtained from the 4 1 1 -1 75 16 12
National Cereals Research Institute (NCRI), Badeggi, Niger
5 -1 -1 1 65 8 15
State, Nigeria and used for this study. Foreign matters such as
stones, straw/chaff and other impurities and contaminants were 6 1 -1 1 75 8 15
removed from the sample. 7 -1 1 1 65 16 15
8 1 1 1 75 16 15
A. Experimental Design
9 -1.68 0 0 61.59 12 13.5
This study used Response Surface Methodology (RSM)
combined with Central Composite Design (CCD) to investigate 10 +1.68 0 0 78.40 12 13.5
the effects of three identified factors: initial soaking 11 0 -1.68 0 70 5.27 13.5
temperature, soaking time and final moisture content prior to 12 0 +1.68 0 70 18.72 13.5
milling on the response of paddy to parboiling process. Based 13 0 0 -1.68 70 12 10.98
on reports in literature and the results of a preliminary study by 14 0 0 +1.68 70 12 16.02
the author, the following test values of the factors were selected 15 0 0 0 70 12 13.5
for the study: Initial soaking temperature: 650C, 700C and
16 0 0 0 70 12 13.5
750C; Soaking time: 8 Hours, 12 Hours and 16 Hours and Final
moisture content: 12%, 13.5% and 15%. 17 0 0 0 70 12 13.5
18 0 0 0 70 12 13.5
A CCD with three factors at five levels was adopted for this
19 0 0 0 70 12 13.5
study. MINITAB 16 Statistical software (Minitab Inc., USA)
was used to design the experiments and to analyse the results. 20 0 0 0 70 12 13.5
The design consisted of 20 experimental runs calculated as 2k X1=Initial Soaking Temperature, X2 = Soaking Time, X3 = Final Moisture Content.

+2𝑘+6 comprising of 8 cube points, 6 axial (star) points and 6

centre points; 𝑘 is the total number of factors [11]. The C. Parboiling process optimization and model development
experimental range and levels of the factors are shown in Table The data obtained from the Central Composite Design
1 and the outline of the experimental design with coded and (CCD) for three factors and five level combinations were
uncoded values is shown in Table 2. subjected to regression analysis using Response Surface
B. Paddy parboiling, Drying and Milling Methodology (RSM), to determine the optimum conditions of
The cleaned samples were parboiled using the laboratory the investigated independent variables (Initial soaking
mini rice parboiler [13]. Five hundred grams (500g) paddy, temperature, Soaking time and Final moisture content) for
held in wire mesh basket, was soaked at 75⁰C for 12 hours in parboiling of paddy rice to produce the desired physical
the soaking/steaming chamber of the parboiling equipment qualities milled rice. The models of the response factors (Yi)
according to the method described by [13]. The soaked paddy were developed as a mathematical function of the independent
samples were thereafter withdrawn from the parboiler, allowed variables through the regression analysis of the experimental
to stand for 15 minutes for water to drain off and steamed for result data [15]. Each response (Yi) was represented by a
35 minutes. The steamed paddy was uniformly dried in thin mathematical equation that correlates the response surfaces as
layer under shade in the laboratory [14]. Husking and milling follows:
of the dry parboiled paddy were done with Test Husker (Satake
Corporation, Hiroshima, Japan) and Test Mill (Satake
Corporation, Hiroshima, Japan) respectively. (1)

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Where Y is the predicted response, k is the number of The results of the regression analysis, the polynomial equation
independent variables (factors) Xi (i = 1, 2, 3); while β is a proposed models for head rice yield (HRY), broken rice ratio
constant and regression coefficients of the model (βi, βii and βij (BRR), grain hardness (GH) and grain colour (GC) and the
are the coefficient of linear, square and interaction terms corresponding coefficients of regression R2 and R2 (adjusted)
respectively) and ε is the random error term. are presented in Table 3. The observed responses and the
predicted values of the physical properties are shown in Table
To determine if the models developed correctly describe the 4.
experimental data, the significance of the models were tested
and confirmed through the estimation of the F-ratio through the B. Test of significance and adequacy of the models
ANOVA test. The models were examined for lack of fit and the 1) Head rice yield: The linear terms in the model fitted
coefficients of determination, R2 were also checked. The for HRY as affected by Initial soaking temperature (IST),
adequacy of the model was also checked with the pattern of the Soaking time (ST) and Final moisture content (FMC) are
points on the normal probability plot of the residuals and the positive except the initial soaking temperature indicating that
plots of the residuals versus the predicted response. The increase in the soaking time (ST) and final moisture content
adequacy is confirmed when the pattern of the points on the (FMC) will lead to increase in the HRY. There are also positive
normal probability plot forms a straight line and the plot of the interactive effects of the initial soaking temperature and
residuals versus the fitted values is scattered and has no soaking time (X1X2) and soaking time and final moisture
structured pattern [10]. content (X2X3) on the HRY. Examination of the observed HRY
and the predicted values of the HRY (Table 4) show that there
D. Laboratory analysis of samples are little variations. This confirms that the model can
1) Head rice yield: Milled rice grains longer than three sufficiently predict the HRY for the parboiling factors [11].
quarters of the whole kernel classified as whole grains, were The adequacy of the model was further confirmed by the
separated automatically using a cylinder-type Test Rice Grader Coefficients of Correlation R2 and R2 (adjusted) values of 0.98
TRG 05B (Satake Corporation, Hiroshima, Japan) [16]. The and 0.96 respectively. These coefficients which are between 0
whole grains were collected and weighed. Head rice yield was and 1 should be close to unity [10]. The p-value for all the
calculated as the ratio of the weight of whole grain to the terms also showed significance at 95% confidence level. The
weight of the dry parboiled samples as follows: large F-ratio as shown in the Analysis of variance (ANOVA) in
Table 5 and the p-value for all the terms in the model which
showed significance at 95% confidence level also confirmed
the significance of the model. The normal probability plot of
(2) the residuals as shown in Figure 1 formed a linear graph
(straight line) indicating that neither response transformation
2) Broken rice ratio: The broken rice was collected from was required nor there was any apparent problem with
normality assumption of the regression model [10] [18]. The
the Test Rice Grader and the broken rice ratio (BRR) was also
plot of the residuals versus the predicted response (Figure 2) is
determined in similar manner as the HRY as follows: scattered and showed no structured pattern. This further
confirmed the adequacy of the model for HRY described in
Table 3.
(3)
2) Broken rice ratio: The model fitted for BRR showed
3) Grain hardness: Five whole grains randomly selected the linear terms except that of the soaking time are positive
from a sample were placed on a flat plate of Hardness Tester (Table 3). This indicated that increase in the soaking time (ST)
(Fujiwara Seisakusho Ltd. Japan) and compressed until may lead to the reduction of percentage of broken rice after
rupture. The force at rupture measured in Newtons (N) was milling the paddy. However, increase in the Initial soaking
temperature and Final moisture content of the parboiled paddy
recorded as the hardness.
may cause a corresponding increase in the broken rice ratio.
The significance of the individual terms of the model from the
4) Grain colour: The colour of the grain was determined ANOVA is shown in Table 6. The adequacy of the model is
using a Rice Whiteness Tester C-600 (Kett Electric confirmed by R2 and R2 (adjusted) values of 0.84 and 0.70
Laboratory, Japan). The equipment was first calibrated against respectively. Also, the normal probability plot of the residuals
a standard pure white plate of 85.5 whiteness value. The formed a linear graph and the plot of the residuals versus the
whiteness test was replicated thrice and the mean value was predicted response showed a scattered pattern. The p-value for
recorded as the colour value. the linear and interaction terms showed significance at 95%
confidence level.
III. RESULTS AND DISCUSSION
A. Model development
Paddy parboiling has been reported to significantly increase
head rice yield, reduce broken rice ratio and increase the
nutritional content [9] [10]. Parboiling also offers higher
milling recovery and produces more translucent milled rice
kernels [17]. A number of factors affect the physical properties
of milled rice during the parboiling process. This study
however focused on three factors; initial soaking temperature,
soaking time and final moisture content.

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TABLE 3. POLYNOMIAL EQUATION PROPOSED MODELS FOR PHYSICAL PROPERTIES AND REGRESSION
COEFFICIENTS FOR THE DEVELOPED MODELS
Response Regression Equation Regression Coefficient
R2 R2 (adjusted)
HRY Y = 70.29 – 0.311X1 + 1.09X2 + 0.23X3 – 0.28X1 – 0.49X2 –
2 2
0.91X32 + 0.4X1X2 – 0.98 0.96
0.33X1X3 + 0.75X2X3

BRR Y = 2.292 + 0.09X1 – 0.33X2 + 0.003X3 –0.034X12 + 0.16X22 + 0.09X32 – 0.21X1X2 0.84 0.70
– 0.19X1X3 – 0.113X2X3

GH Y = 73.78 – 0.71X1 + 3.67X2 – 0.37X3 +4.18X12 – 3.74X22 – 2.5X32 – 4.08X1X2 0.94 0.89
+2.45X1X3 + 0.25X2X3

GC Y = 25.91 + 0.08X1– 0.39X2 – 0.02X3 – 0.25X12 – 0.27X22– 0.06X32 – 0.038X1X2 + 0.89 0.79
0.26X1X3 – 0.29X2X3

HRY = Head rice yield; BRR = Broken rice ratio; GH = grain hardness; GC = Grain colour
X1 = Initial Soaking Temperature, X2 = Soaking Time, X3 = Final Moisture Content

TABLE 4. OBSERVED AND PREDICTED VALUES FOR THE PHYSICAL CHARACTERISTICS OF MILLED RICE
Run Head Rice Yield Broken Rice Ratio Hardness Colour (Whiteness
(%) (%) (N) value)
Observed Predicted Observed Predicted Observed Predicted Observed Predicted
1 68.30 68.42 2.10 2.25 60.80 59.40 25.60 25.60
2 67.90 67.65 3.30 3.22 62.40 61.23 25.00 25.32
3 68.60 68.31 2.50 2.22 77.70 74.40 25.20 25.47
4 69.10 69.13 2.40 2.35 58.90 59.92 25.30 25.03
5 68.30 68.04 3.00 2.84 54.80 53.26 25.20 25.61
6 65.90 65.97 3.00 3.07 62.10 64.89 26.50 26.37
7 70.90 70.92 2.50 2.37 68.60 69.26 24.50 24.33
8 70.80 70.45 2.10 1.75 63.70 64.58 24.80 24.94
9 69.90 70.03 1.90 2.05 60.10 63.16 25.30 25.06
10 68.80 69.0 2.20 2.34 63.10 60.76 25.30 25.34
11 67.00 67.08 3.40 3.31 56.50 57.04 26.10 25.81
12 70.50 70.74 1.80 2.18 69.20 69.39 24.40 24.49
13 67.20 67.32 2.50 2.55 64.70 67.34 25.90 25.78
14 67.90 68.10 2.30 2.54 68.00 66.09 25.80 25.72
15 69.80 70.29 2.30 2.29 73.80 73.78 25.90 25.91
16 70.40 70.29 2.30 2.29 73.80 73.78 25.90 25.91
17 70.40 70.29 2.30 2.29 73.80 73.78 25.90 25.91
18 70.40 70.29 2.30 2.29 73.80 73.78 25.90 25.91
19 70.40 70.29 2.30 2.29 73.80 73.78 25.90 25.91
20 70.40 70.29 2.30 2.29 73.80 73.78 25.90 25.91

3) Grain hardness: The model fitted for Grain hardness TABLE 5. ANALYSIS OF VARIANCE (ANOVA) FOR THE FITTED
(GH) was found to be significant and adequately sufficient to QUADRATIC POLYNOMIAL MODEL FOR HEAD RICE YIELD
DURING PARBOILING PROCESS
predict the strength of the parboiled milled rice (Table 3). The
linear terms are negative except that of the soaking time. This
Source of Degree of Sum of Mean sum f- value p-value
indicated that increase in the initial soaking temperature of the variation freedom Square of square
paddy and the final moisture content of the paddy before Regression 9 39.56 4.40 53.00 0.001
milling may cause a reduction in the grain hardness of the Linear 3 18.29 6.10 73.51 0.000
milled rice and increase in the soaking time may improve the Square 3 14.64 4.48 58.87 0.001
hardness of the grain. The significance of the individual terms Interaction 3 6.63 2.21 26.63 0.000
of the model is shown in Tables 7 and the adequacy of the Residual 10 0.829 0.08 * *
model is confirmed by R2 and R2 (adjusted) values of 0.94 and Total 19 40.39 * * *
0.89 respectively. The p-values for all the terms showed
significance at 95% confidence level. The Residual plots are
also shown in Figures 5 and 6.

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99 0.4

0.3
95

90 0.2

80
0.1

R esidual
70
Percent

60 0.0
50
40
-0.1
30
20 -0.2

10
-0.3
5

-0.4

1 2.0 2.5 3.0 3.5

-0.50 -0.25 0.00 0.25 0.50 Fitted Value
Residual

Fig. 1. Normal probability plot of the residual for HRY Fig. 4. Plot of residuals against fitted values for BRR

0.4
TABLE 7. ANALYSIS OF VARIANCE (ANOVA) FOR THE FITTED
0.3
QUADRATIC POLYNOMIAL MODEL FOR GRAIN HARDNESS
0.2
DURING PARBOILING PROCESS
0.1
Source of Degree of Sum of Mean sum f- value p-value
0.0 variation freedom Square of square
Res idual

-0.1
Regression 9 833.096 92.566 17.68 0.000
Linear 3 193.057 64.352 12.29 0.001
-0.2
Square 3 458.674 152.891 29.20 0.000
-0.3 Interaction 3 181.365 60.455 11.54 0.001
Residual 10 52.366 5.327 * *
-0.4
Total 19 885.462 * * *
-0.5

66 67 68 69 70 71

Fitted Value
99

Fig. 2. Plot of residuals against fitted values for HRY 95

90

80
TABLE 6. ANALYSIS OF VARIANCE (ANOVA) FOR THE FITTED 70
Percent

QUADRATIC POLYNOMIAL MODEL FOR BROKEN RICE RATIO 60

DURING PARBOILING PROCESS 50

40
30

Source of Degree of Sum of Mean sum f- value p-value 20

variation freedom Square of square 10

Regression 9 2.893 0.321 6.0 0.005 5

Linear 3 1.65 0.550 10.27 0.002

Square 3 0.50 0.166 3.11 0.076 1
-4 -3 -2 -1 0 1 2 3 4
Interaction 3 0.74 0.248 4.63 0.028 Residual
Residual 10 0.54 0.054 * *
Total 19 3.43 * * *
Fig. 5 Plot of residuals against fitted values for Grain hardness

99

95
2
90
R e sidu a l

80 1

70
Percent

60 0
50
40
-1
30
20
-2

10
-3
5

55 60 65 70 75

1 Fitted Value
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4
Residual Fig. 6. Plot of residuals against fitted values for Grain hardness
Fig 3. Normal probability plot of the residual for BRR

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4) Grain colour: The models fitted for Grain colour as C. Response Optimisation
affected by the parboiling factors shows that increase in the The results of the optimised responses of the physical
soaking time of paddy may lead to reduced whiteness value and properties of the parboiled milled rice as well as the criteria
hence darker grains (Table 3). This is expected as soaking has are as presented in Table 9 and the quality desirability in
been reported to cause discolouration due to enzymatic Figure 9.
reactions and transfer of pigments into the grain [19].
According to [20], prolonged soaking activates enzymes that TABLE 9. CRITERIA AND RESULTS OF OPTIMISATION OF
PARBOILING CONDITIONS
will influence the staining activities to discolour the rice Response Goal Response Desirability
kernels. However, increase in the initial soaking temperature Head rice yield (%) Maximum 70% 100%
may cause a corresponding increase in the whiteness value Broken rice ratio (%) Minimum 2.18% 63.9%
(lighter grain colour). Grain hardness (N) Maximum 74.7N 89.5%
Grain colour Maximum 25.8 59.2%
TABLE 8. ANALYSIS OF VARIANCE (ANOVA) FOR THE FITTED
QUADRATIC POLYNOMIAL MODEL FOR GRAIN COLOUR DURING Composite Desirability – 76.3%
PARBOILING PROCESS
Source of Degree of Sum of Mean sum f- p-
variation freedom Square of square value value
Regression 9 1.576 0.575 8.86 0.001
Linear 3 2.197 0.732 11.28 0.002
Square 3 1.756 0.585 9.01 0.003
Interaction 3 1.224 0.408 6.28 0.011
Residual 10 0.649 0.065 * *
Total 19 5.826 * * *

The normal probability plot of the residuals and the plot of the
residuals versus the predicted response as shown in Figures 7
and 8 confirmed the adequacy of the model. The adequacy of
the model is also confirmed by the R2 and R2 (adjusted) values
of 0.89 and 0.79 respectively. The p-values for all the terms
showed significance at 95% confidence level (Table 8).
99
Fig. 9. Optimisation plot for physical properties
95
From the optimisation result and plot (Figure 9), the optimum
90
conditions for paddy parboiling for a desirable physical
80

70
qualities of milled rice grain are Initial Soaking Temperature:
P e rc e n t

60 67.7°C; Soaking Time: 13.3 hours, and Final Moisture

50
40 Content: 12.7%. These optimal conditions are expected to
30

20
produce parboiled milled rice with: Head rice yield, 70%;
10
Broken rice ratio, 2.18%; Grain hardness, 74.7N and Grain
5
colour, 25.8.
1
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 The individual desirability of the responses indicated that the
Residual optimal combinations of the factors as shown in Figure 9 is
Fig. 7. Plot of residuals against fitted values for Grain colour effective in maximizing the Head rice yield and the Grain
hardness and also in minimizing the Broken rice ratio. The
composite desirability of 76.3% (Table 9) showed how the
0.3
settings optimize all the four quality responses when they are
0.2
considered as objective response functions simultaneously
0.1 [21].
R e sidu a l

0.0
IV. CONCLUSION
-0.1
It can be concluded that the optimum parboiling conditions for
-0.2 desirable physical qualities of FARO 52 rice variety are: Initial
-0.3
soaking temperature: 67.7°C; Soaking time: 13hrs 18minutes
and Final moisture content: 12.7%. These optimal conditions
-0.4
are expected to produce parboiled milled rice with the
-0.5 following desired physical characteristics: Head rice yield,
24.5 25.0 25.5 26.0 26.5

Fitted Value
70%; Broken rice ratio, 2.18%; Grain hardness, 74.7N and
Grain colour, 25.8. The composite desirability for the optimal
Fig. 8. Plot of residuals against fitted values for Grain colour settings is 76.3% and showed favorable results for all
responses when considered simultaneously as objective
response functions.

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Struct., 24, 23–30. 1993
[2] United States Department of Agriculture (USDA)..Nigeria grain and
feed update..USDA Foreign Agricultural Service, Global Agricultural [20] Ayamdoo, A. J., Demuyakor, B., Saalia, F. K. and Francis, A. Effect of
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characteristics of Jasmine 85 and NERICA 14 rice varieties. American.
[3] Federal Ministry of Agriculture and Rural Development (FMARD). A
Journal of Food Technology, 9: 1-14.2014
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