RJS-Vol-1-Sept-2006-8.dvi


RUHUNA JOURNAL OF SCIENCE
Vol. 1, September 2006, pp. 67–81
http://www.ruh.ac.lk/rjs/
issn 1800-279X ©2006 Faculty of Science

University of Ruhuna.

Validation of Taguchi design using a quality
parameter of cosmetic soap manufactured in

a local industry

C. P. S. Pathirana
Department of Mathematics, University of Ruhuna, Matara, Sri Lanka, macpsp@maths.ruh.ac.lk

R. A. Dayananda, P. Dias
Department of Statistics and Computer Science, University of Sri Jayewardenepura, Gangodawila,

Nugegoda, Sri lanka, radaya@sjp.ac.lk, dias@sjp.ac.lk

S. B. Nawarathne
Harishchandra Mills (Pvt.) Ltd., Matara, Sri Lanka

The objective of this study is to investigate the applicability of Taguchi method to the
production process of a local industry. Harishchandra Mills (Pvt.) Ltd, Matara, which is
engaged in soap manufacturing process has been selected as the local industry. This process
is entangled with different kinds of variables. Four critical variables - two types of oil,
coconut oil (a1) and palm oil (a0), on the basis of high and low saponification values, two
levels of caustic soda (b0, b1), and two different saponification temperatures, 70�(c0) and
80�(c1), with and without stirring process for saponification (d1, d0) were adopted. The
results obtained for Total Fatty Matter (TFM) was used to calculate optimum value (Yopt)
for each treatment with and without replicates. The results for Yopt for TFM with and
without replicates were 75.98%, and 76.66%, respectively. The best treatment combination
under this method was a1b1c1d1 for the same sequence of quality parameters given above.
The same best treatment combinations were also obtained for the validation test, four-
factor experiment design and block design with and without replicates.

Key words : Soap manufacture, Statistical quality control, Taguchi method, Factorial
experiment design, and Block design.

1. Introduction
Sri Lanka is a developing country, which enjoys a wide spectrum of production
processes using abundant natural resources. With the emergence of global village
concept and free market economy a substantial amount of business establishments
have mushroomed throughout the country. Though there are many kinds of business
establishments’ function in the country, most of these do not posses an adequate
advanced technical know how to cope with the issues encountered by them during
their day today activities.

Aftermath of this development has resulted in releasing different kinds of sub-
standard products, produced under manufacturer’s own standard to the dynamic
market. Hence in order to cope with this situation, the technical term “standard-

67



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68 Ruhuna Journal of Science 1, pp. 67–81, (2006)

ization” has come into light along with regulatory requirement with the view to
protect the consumer.

Since modern market is also dynamic and competitive the entrepreneurs strive
hard to maintain competitive edge on their products while minimizing wastages
occurring in the production process and boosting the productivity.

On the other hand, Sri Lankan business establishments can be categorized into
3 key groups as traditional, semi modern and modern. The majority of them are
coming under traditional and semi modern groups. However they do not posses
adequate resources to face the challenges exerted by the conditions in the dynamic
marketing environment.

Therefore switching on to advanced statistical designs is one of the options for
any type of producer to improve the over all productivity of his business along with
the quality while minimizing wastages.

Professor Genichi Taguchi, an engineer and an eminent scientist from Japan who
encountered with a similar problem was able to introduce a new statistical design,
after deeply studying the “off line quality control” activities of production lines. The
new statistical design called “Taguchi design” is applicable to the modern indus-
trial environment, in order to resolve most issues emerging from wilful errors and
inadvertent errors in a production line. The other advantage of using this statis-
tical design is the maximum utilization of tangible and intangible scarce natural
resources in a production process.

Hence objective of the study was to use Taguchi design in a production process of
a local industry, where production process is carried out amid considerable number
of variables. Outcome of which is to be validated by two other designs to gauge the
accuracy of Taguchi design.

1.1. Objectives� Identification of error variables of Cosmetic Soap manufacturing process using
control charts.� Comparative study of Factorial experiment, confounded blocks design and
Taguchi design.� Manufacturing of cosmetic soap with respect to the 24 designs.� Manufacturing of high quality soap for consumer market by identifying desir-
able limits for important variables of soap manufacturing process with respect to
the advance Taguchi design.

2. Materials and Methods
2.1. Terminology

We shall use the following terminology throughout the paper. Total fatty matter
(TFM), low saponification oil (a0), high saponification oil (a1), NaOH low concen-
tration (b0), NaOH high concentration (b1), low temperature (c0), high temperature
(c1), no stirring (d0), with stirring (d1), Oil (A), NaOH (B), Temperature (C),
Stirring (D), number of replicate (n) and number of variable (f).



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Ruhuna Journal of Science 1, pp. 67–81, (2006) 69

Table 1 Algebraic signs for the Taguchi design

�
�

�
�

�
�

�
�

�

Variable
Test

Treatment
A B C D

combination

(1) a0b0c0d0 - - - -
ad a

1
b
0
c
0
d
1 + - - +

bd a
0
b
1
c
0
d
1 - + - +

ab a
1
b
1
c
0
d
0 + + - -

cd a
0
b
0
c
1
d
1 - - + +

ac a
1
b
0
c
1
d
0 + - + -

bc a
0
b
1
c
1
d
0 - + + -

abcd a
1
b
1
c
1
d
1 + + + +

2.2. Parameters

Four key variables responsible for major quality characteristics of soap were identi-
fied after scrutinizing the soap manufacturing process. They are,� Saponification value of oils,� Concentration of sodium hydroxide (NaOH),� Saponification Temperature, and� Period of stirring.
Quality parameter of the samples,� Total Fatty Matter (TFM)
2.3. Taguchi Method

Taguchi constructed a special set of general designs for factorial experiments that
cover many applications. The special set of designs consists of orthogonal arrays
(OA). The use of these arrays helps to determine the least number of experiments
needed for a given set factors. (Dayananda 1992)

The latest statistical model for design of an experiment, “Taguchi’s advance
design”, was adapted for this study, which has the advantage of less treatment
combinations in compared with other statistical designs. (See Table 1)

Above design was used to analyze the data obtained for TFM of soap samples in
order to determine optimum values for critical variables.

2.3.1. Statistical Analysis of Data: The data obtained for TFM of soap
samples of different treatment combinations were statistically analyzed in order to
determine Yopt using following formula.

Yopt =
T

N
+

4∑

i=1

(k̄i −
T

N
) . (1)

Where,

T = (ā0 + ā1) + (b̄0 + b̄1) + (c̄0 + c̄1) + (d̄0 + d̄1),

k̄i = Mean value of optimum level of each variable, and
N = Number of observations. (Nawarathne 2003)



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70 Ruhuna Journal of Science 1, pp. 67–81, (2006)

Table 2 Algebraic signs for the 24 Experiment Design

X
X

X
X

X
X

X
X

X
Fact effect

run

I A B

A
B

C

A
C

B
C

A
B

C

D

A
D

B
D

A
B

D

C
D

A
C

D

B
C

D

A
B

C
D

(I) a0b0c0d0 + - - + - + + - - + + - + - - +
a a

1
b
0
c
0
d
0 + + - - - - + + - - + + + + - -

b a
0
b
1
c
0
d
0 + - + - - + - + - + - + + - + -

ab a
1
b
1
c
0
d
0 + + + + - - - - - - - - + + + +

c a
0
b
0
c
1
d
0 + - - + + - - + - + + - - + + -

ac a
1
b
0
c
1
d
0 + + - - + + - - - - + + - - + +

bc a
0
b
1
c
1
d
0 + - + - + - + - - + - + - + - +

abc a
1
b
1
c
1
d
0 + + + + + + + + - - - - - - - -

d a
0
b
0
c
0
d
1 + - - + - + + - + - - + - + + -

ad a
1
b
0
c
0
d
1 + + - - - - + + + + - - - - + +

bd a
0
b
1
c
0
d
1 + - + - - + - + + - + - - + - +

abd a
1
b
1
c
0
d
1 + + + + - - - - + + + + - - - -

cd a
0
b
0
c
1
d
1 + - - + + - - + + - - + + - - +

acd a
1
b
0
c
1
d
1 + + - - + + - - + + - - + + - -

bcd a
0
b
1
c
1
d
1 + - + - + - + - + - + - + - + -

abcd a
1
b
1
c
1
d
1 + + + + + + + + + + + + + + + +

divisor 16 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

2.4. Validation Test - Four-Factor Experiment Design

The treatment combination in this design is given in Table 2 (George, William,
Hunter 1978).

2.4.1. Statistical Analysis of Data of 24 Design: The data obtained from
the four-factor experiment design were analyzed using Table 2, and the contrast and
the effect with respect to each variable were calculated. The effect for each variable
was calculated using the following formula (Thomas 1998).

Effect =
Contrast

2f−1n
. (2)

The sum of square for any effect of each variables were calculated using,

SS =
(Contrast)2

2f n
. (3)

The high percent contribution values were selected from ANOVA table of which
significant levels of each variable were calculated. A basic model was developed
using significantly different values from the ANOVA table. The function for the
basic model is,

Y =β0 + β1X1 + β2X2 + β3X3 + β4X4 + β12X1X2 + β13X1X3 + β23X2X3 + β14X1X4
+β24X2X4 + β34X3X4 + β123X1X2X3 + β134X1X3X4 + β234X2X3X4
+β124X1X2X4 + β234X2X3X4 + β124X1X2X4 + β1234X1X2X3X4 + ǫ

(4)



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Ruhuna Journal of Science 1, pp. 67–81, (2006) 71

Figure 1 Assignment of the 16 runs to two blocks -without replicate (ABCD confounded).

Figure 2 Partial confounding in the 24 design - with replicates.

The developed model for quality parameter TFM can be used to detect relationship
between significantly different variables. This relationship can be depicted by either
response surface or contour plot. (Douglas 2000)

2.5. Validation Test - Confounded Block Design

Same data obtained for four-factor experiment designs were used for block design
in order to validate Taguchi design again. (Douglas 2000) (See Figure 1, 2)

2.5.1. Statistical Analysis of Confounded Block Design. The effect and
sum of square for ABCD (block) was calculate using,

Block effect = ȳblock1 − ȳblock1 . (5)

SSBlocks =
(y1)

2

8
+

(y2)
2

8
−

(y1 + y2)
2

16
. (6)

where, ȳblocki = average value of each block i and yi = sum of block i.



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72 Ruhuna Journal of Science 1, pp. 67–81, (2006)

Table 3 Comparison of factorial design and Taguchi Design

Factors Level
Total number of experiments Taguchi Design

(factorial Design) Total number of experiments

2 2 4 4
3 2 8 4
4 2 16 8
7 2 128 8
15 2 32,768 16
4 3 81 9

However, the values of SSABC and SSABCD should be calculated using only the
data in replicate I and replicate II, respectively. The effect and sum of square for
the replicate were calculated using,

SSRep =
n∑

i=1

R2i
2k

−

y2...
2kn

(7)

where Ri is the total observation in the i
th replicate. n is the number of replicates,

and k is the number of variable. y... is the sum of total observations.(Richard 1996)

2.6. Comparison of Factorial Design and Taguchi Design

The total number of experiments possible for different number of factors at 2 or 3
levels and the corresponding suggested Taguchi number of experiments is shown in
Table 3. (www.stasoft.com 2004, Pathirana 2005)

Taguchi has established OAs that describes a large number of experimental situ-
ations.

3. Results and Discussion
Results pertaining to the TFM of wet soap manufactured with respect to Taguchi
design were validated by two statistical designs, four- factor experiment design and
block design.

3.1. TFM Value for Samples Prepared from each Design

TFM value was obtained for soap samples prepared with respect to each design,
Taguchi design, four-factor experiment design and block design.

3.1.1. TFM value for Taguchi Design - Without and with Replicate:

The data obtained for TFM value of soap with respect to Taguchi design without
and with replicates (three replicates) are given in Table 4 and Table 5 respectively.

TFM values obtained for Taguchi design with respect to each variable are given in
linear graphs in Figure 3 and Figure 4. These graphs clearly indicate that there is a
positive relationship for TFM value with the increase of magnitude of each variable.
Hence, the best treatment combination in order to enhance TFM value of soap
manufacture is a1b1c1d1. Furthermore, the value of TFM is increased simultaneously
with the increase of each variable. Calculation from the model (using equation 1)
for optimum value of TFM (Yopt) is equal to 75.98% and 76.66% with and without
replicates, respectively. (See Figure 3, 4)



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Ruhuna Journal of Science 1, pp. 67–81, (2006) 73

Table 4 TFM value for Taguchi design - without
replicate

Variable
A B C D

Treatment
Value

Test combination

(1) - - - - a0b0c0d0 63.00
ad + - - + a1b0c0d1 68.25
bd - + - + a0b1c0d1 60.42
ab + + - - a1b1c0d0 66.30
cd - - + + a0b0c1d1 73.90
ac + - + - a1b0c1d0 65.32
bc - + + - a0b1c1d0 72.10

abcd + + + + a1b1c1d1 79.20

Table 5 TFM value for Taguchi Design - with replicates

�
�

�
�

�
�

�
�

�

Variable
Test

Treatment Replicate Replicate Replicate Total
combination I II III Value

(1) a0b0c0d0 62.50 63.00 62.50 188.00
ad a

1
b
0
c
0
d
1 68.20 67.30 68.00 204.00

bd a
0
b
1
c
0
d
1 60.52 60.88 60.86 182.26

ab a
1
b
1
c
0
d
0 66.50 66.20 66.30 199.00

cd a
0
b
0
c
1
d
1 72.70 73.30 74.00 220.00

ac a
1
b
0
c
1
d
0 64.30 64.50 64.20 193.00

bc a
0
b
1
c
1
d
0 70.90 71.40 71.70 214.00

abcd a
1
b
1
c
1
d
1 77.80 78.90 78.30 235.00

69.25 69.19

A
v
e
r
a

e

A
v
e
r
a

e

a a0 1 b1

67.02

g

b

g

0

67.08

(a) (b)

71.83

64.44 66.17

A
v
e
r
a
g
e

A
v
e
r
a
g
e

70.10

(c) (d)

d d0c c 01 1

Figure 3 Relationship of TFM with respect to each variable- with replicates



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74 Ruhuna Journal of Science 1, pp. 67–81, (2006)

A
v
e
r
a
g
e

A
v
e
r
a
g
e

(a)
a a b0 01 b1

69.77

67.36
67.62

69.50

(b)

A
v
e
r
a
g
e

A
v
e
r
a
g
e

(c) (d)

d d0c c 01 1

64.49

72.63

66.68

70.44

Figure 4 Relationship of TFM value with respect to each variable - without replicates

3.1.2. Four Factor Experiment Design With and Without Replicate

for TFM. The data obtained for TFM value for without replicate design are given
in Table 6. A normal probability graph of cumulative value of probability vs effect
is drawn in Figure 5. The data obtained for TFM value for with replicates design
are given in Table 7 Soap samples were prepared with respect to the 24 design and
each treatment combination was replicated 3 times. A normal probability graph of
cumulative value of probability Vs effect is drawn in Figure 6. These graphs (Figure
5 and Figure 6) clearly indicate that the variables C and D are more significant
in compared with A and B. An ANOVA table was developed for further studies
of the significance of variables C and D and the results are given in Table 8 and
Table 9. The ANOVA table clearly indicates that calculated values for variables
C (temperature) and D (stirring) are higher than the F distribution table values
(F1,5(0.10) = 4.06 and F1,32(0.01) = 7.56 ).

From Table.8,

C = 4.16 > 4.06
D = 5.26 > 4.06

and from Table.9,

C = 24.68 > 7.56
D = 70.25 > 7.56.



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Ruhuna Journal of Science 1, pp. 67–81, (2006) 75

Table 6 TFM value for 24 Factorial
Design (without replicate)

Run Run Treatment
Values

number label Combination

1 (I) a0b0c0d0 66.20
2 a a1b0c0d0 66.00
3 b a0b1c0d0 57.00
4 ab a1b1c0d0 58.00
5 c a0b0c1d0 55.67
6 ac a1b0c1d0 65.32
7 bc a0b1c1d0 71.90
8 abc a1b1c1d0 57.69
9 d a0b0c0d1 69.31
10 ad a1b0c0d1 68.25
11 bd a0b1c0d1 57.42
12 abd a1b1c0d1 56.90
13 cd a0b0c1d1 73.50
14 acd a1b0c1d1 48.20
15 bcd a0b1c1d1 69.39
16 abcd a1b1c1d1 78.20

Figure 5 Normal probability plots for the effects for TFM (without replicate)

Therefore, relatively high temperature and stirring time have a big effect on TFM

of soap manufactured. Since four-factor experiment design also shows that most
important variables for TFM of soap manufacture are C and D and least effect
variables are A and B, Taguchi method can be validated by four-factor factorial
design as Taguchi method was also indicated that C and D variables at higher levels
are critical for soap manufacturing process, in addition to A and B variables.



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76 Ruhuna Journal of Science 1, pp. 67–81, (2006)

Table 7 TFM value for 24 experiment design- with replicates

Run Treatment 1 Replicate Replicate Replicate
Total

Label Combination I II III

(1) a0b0c0d0 69.63 66.50 65.33 201.46
a a

1
b
0
c
0
d
0 67.16 65.55 65.23 197.94

b a
0
b
1
c
0
d
0 58.69 56.72 55.63 171.04

ab a
1
b
1
c
0
d
0 56.72 56.80 57.40 170.92

c a
0
b
0
c
1
d
0 45.56 45.60 45.82 136.98

ac a
1
b
0
c
1
d
0 64.82 64.50 64.43 193.75

bc a
0
b
1
c
1
d
0 70.61 71.50 72.22 214.33

abc a
1
b
1
c
1
d
0 62.33 65.43 66.55 194.31

d a
0
b
0
c
0
d
1 70.20 69.22 68.50 207.92

ad a
1
b
0
c
0
d
1 68.11 67.45 68.22 203.78

bd a
0
b
1
c
0
d
1 58.20 58.40 57.70 174.30

abd a
1
b
1
c
0
d
1 54.42 57.27 58.98 170.67

cd a
0
b
0
c
1
d
1 72.98 73.30 74.40 220.68

acd a
1
b
0
c
1
d
1 45.39 50.34 48.87 144.60

bcd a
0
b
1
c
1
d
1 70.42 69.50 68.24 208.16

abcd a
1
b
1
c
1
d
1 78.30 78.42 78.85 235.57

Figure 6 Normal probability plots for the effect for TFM - with replicates

Similarly out come of the ANOVA tables with and without replicate do not show
any significant difference. Therefore, four-factor experiment design can also be used
to validate Taguchi method.

A regression model can be developed using calculated F values, which should be
more than the F table value. With replicates, the model is as follows.

Y = 63.47 + 0.46X3 + 1.77X4 + 0.64X1X2 − 1.86X1X4 + 5.84X2X3 + 1.13X3X4
+ 3.70X1X2X4 + 1.69X1X3X4 + 3.82X1X2X3X4.

(8)



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Ruhuna Journal of Science 1, pp. 67–81, (2006) 77

Table 8 TFM (without replicate)-Analysis of the
variance

Source of Sum of Degree of Mean F0
Variation Square Freedom Squares Value

C 27.01 1 27.01 4.16
D 34.19 1 34.19 5.26

AB 15.98 1 15.98 2.46
BC 350.91 1 350.91 53.99
CD 12.31 1 12.31 1.89
AC 25.68 1 25.68 3.95
AD 12.80 1 12.80 1.97

ABD 215.89 1 219.85 33.82
BCD 34.02 1 34.02 5.23

ABCD 214.84 1 214.84 33.05
Error 32.52 5 6.50

Total 976.15 15

Table 9 TFM (with replicates)-Analysis of the vari-
ance

Source of Sum of Degree of Mean F0
Variation Square Freedom Squares Value

A 11.63 1 11.63 5.43
B 10.26 1 10.26 4.79
C 52.82 1 52.82 24.68
D 150.34 1 150.34 70.25

AB 19.52 1 19.52 9.12
AC < 0.01 1 < 0.01 < 0.01
AD 167.07 1 167.07 78.07
BC 1639.50 1 1639.50 766.12
BD 1.60 1 1.60 0.75
CD 61.49 1 61.49 28.73

ABC 10.82 1 10.82 5.06
ABD 655.57 1 655.57 306.34
ACD 137.66 1 137.66 64.33
BCD 2.01 1 2.01 0.94

ABCD 698.98 1 698.98 326.63
Error 68.45 32 2.14

Total 2390.96 47

Significant F values are highlighted.

3.1.3. Confounded Block Design with and without replicate for TFM.

The data obtained for TFM value of soap base, prepared in accordance with the
block design are given in Figure 7. (ABCD confounded - without replicate).

Thus, each replicate of 24 designs must be run in two blocks. Two replicates are
run, with ABCD confounded in replicate I and ABC confounded in replicate II. The
data are given in Figure 8.

An ANOVA table was made with respect to the variables and interactions that
are given in Table.10 and Table.11.



Pathirana et al.,: Validation of Taguchi design ...

78 Ruhuna Journal of Science 1, pp. 67–81, (2006)

Figure 7 TFM value (without replicate) - 16 runs in two blocks

Figure 8 TFM - Partial Confounding in the 24 design

Table 10 TFM (without replicate) - Analysis of variance
for block design

Source of Sum of Degree of Mean F −
Variation Squares Freedom Squares Value

Block(ABCD) 642.25 1 642.25 98.81
C 27.01 1 27.01 4.16
D 34.19 1 34.19 5.26

AB 15.98 1 15.98 2.46
AD 12.80 1 12.80 1.97
BC 350.91 1 350.91 53.99
CD 12.30 1 12.30 1.89
AC 25.68 1 25.68 3.95

ABD 215.89 1 213.89 32.91
BCD 34.02 1 34.02 5.23
Error 32.52 5 6.50

Total 1403.55 15

Significant F values are highlighted.

Since the ANOVA Table.10 and Table 11 revealed that calculated F values for C
and D variables are higher than the table values, F1,5 (0.01) = (4.06) and F1,13(0.01)
= 9.07, these variables are more important than others.



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Ruhuna Journal of Science 1, pp. 67–81, (2006) 79

Table 11 ANOVA for Block design - TFM (with replicates)

Source of Sum of Degree of Mean F0
Variation Squares Freedom Squares Value

Replicates 0.27 1 0.27 0.13

Block within
Replicates 258.41 2 129.20 61.82

A 18.03 1 18.03 8.63
B 9.48 1 9.48 4.54
C 24.43 1 24.43 11.68
D 90.45 1 90.45 43.28

AB 7.33 1 7.33 3.51
AC 0.54 1 0.54 0.26
AD 116.36 1 116.36 55.67
BC 1135.50 1 1135.50 543.30
BD 0.07 1 0.07 0.03
CD 57.24 1 57.24 27.39

ABC (replicate I only) 5.20 1 5.20 2.49
ABD 439.83 1 429.83 205.67
ACD 91.46 1 91.46 43.76
BCD 4.52 1 4.52 2.16

ABC (replicate II only) 204.78 1 204.78 97.98
Error 27.18 13 2.09

Total 2491.08 31

Significant F values are highlighted.

Table 10:

C = 4.16 > 4.06

D = 5.26 > 4.06.

Table 11:

C = 11.68 > 9.07,

D = 43.28 > 9.07.

As block design indicates that C and D variables at higher levels are significantly
contributed for the increase of TFM value, this can be used to validate Taguchi
design, because Taguchi design is also showing similar results. Same results were
obtained for variables with and without replicates.

4. Conclusion
Based on the results obtained under Taguchi method, we can conclude the following:

1. The optimal combination of four variables for highest TFM is high saponifica-
tion value of oil (coconut oil), high concentration of NaOH (18%), high saponification
temperatures (80�) and with stirring. This was the case for both with and without
replicates. The highest TFM obtained under this combination with and without
replicates were 75.98% and 76.66% respectively. This is almost similar to the Sri
Lanka standards value of 76.5% (Ceylon - Standard 27:1968).



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80 Ruhuna Journal of Science 1, pp. 67–81, (2006)

2. When soap is manufactured with respect to advanced Taguchi design after the
identification of critical variables, the quality parameters are easily falling in line
with regulatory requirements (TFM).

3. Since the results for all quality parameters of soap have shown only a slight-
est difference with and without replicates, the experiment could be conducted even
without replicates and achieve very precise results. Therefore, we can recommend
that the advanced Taguchi Design could be applicable for some industrial environ-
ments at low cost with other high quality comparative designs as they need more
treatment combinations to evaluate the effect of each variable or their combinations.

4. Taguchi method is an advance statistical design. It is most sensitive in terms
of finding the effect of variation of variables. Taguchi method was able to find a
little improvement when the variables A and B are increased from low level to high
level (a0 to a1 and b0 to b1). However, the other two designs do not strong enough
to find the variation of these two variables.

References
Box G, Bisgard S, Fung C 1987 : An Explanation and Critique of Taguchi’s Con-

tributions to Quality Engineering, Supplements to the Journal of the University
of Wisconsion, U.S.A, 126-128.

Dayananda R.A 1992 :Fifty Year of Quality Technology, University of Sri Jayewar-
denepura.

Douglas C.M 2000. Design and Analysis of Experiment, fifth edition, Arizona.

George E.P.Box, William G.Hunter, Hunter J.S 1978 : Statistics for Experiments,
John Wiley & Sons. http://kernow.curtin.edu.av/www/Taguchi/CAE204.html,
20.03.2004. Methods of Analysis of Soap, Ceylon - Standard 27:1968, Bureau of
Ceylon Standards.

Nawarathne SB 2003. M.Phil thesis. Extraction of adible grade sesame oil by Con-
trolling acid value and free fatty acid level in seeds and oil.

Pathirana C.P.S 2005. M.Sc thesis Validation of Taguchi Design Using Quality
Parameters of Toilet Soap Manufactured in a Local Industry, University of Sri
Jayewardenepura.

Richard R. Johnson 1996: Miller & Freund’s Probability and Statistics for Engineers.
Fifth edition, Prentice Hall of India private limited, New Delhi.

Ronald E.W, and Raymond H.M.: Probability and Statistics for Engineers and
Scientists, Collier Macmillan Publisher, London.

Thomas P.R 1998: Statistical Methods for quality Improvement. Wiley Series

Acknowledgments

C. P. S. Pathirana would like to thank Dr. L. A. L W. Jayasekara, Senior Lecturer, Depart-
ment of Mathematics at University of Ruhuna for introducing me to the subject and pro-
viding the guidance for the success of this project.



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Ruhuna Journal of Science 1, pp. 67–81, (2006) 81

C. P. S. Pathirana, also gratefully recalls the sincerity of Mr. Senaka Samarasesinghe,
Managing Director of Harishchandra Mills (Pvt.) Ltd., for kindly permitting to carry out
the research work in his establishment. Special words of gratitude go to Mrs. Sujeewa Rath-
nayake, Miss Devika Preshanthi, Miss Dammika Wijesekera and the other staff members of
the research lab of Harishchandra Mills (Pvt.) Ltd., for their kind cooperation.

The authors, also, grateful to MSc course coordinator, Dr. S. K. Boralugoda, for his
guidance, advice and the encouragement to proceed with this research project. Finally,
we thank the Department of Mathematics, University of Ruhuna Matara, for the facilities
provided for the success of this project.