Rizvan Erol,
*Aysun Sağbaş
Multiple Response Optimisation
of the Staple-Yarn Production Process
for Hairiness, Strength and Cost
Department of Industrial Engineering, Abstract
Cukurova University, It is generally desirable to reduce yarn hairiness as much as possible since it causes serious
Adana 01330, Turkey problems in both yarn production and use of yarn in subsequent textile operations. On
E-mail: rerol@cu.edu.tr the other hand, the cost of yarn production should be minimised while satisfying yarn
hairiness and yarn strength specifications. In this study, a multiple response optimisation
*Department of Mechanical Engineering,
Mersin University, model based on empirical regression models is developed to determine the best processing
Mersin 33343, Turkey
conditions for spindle speed, yarn twist, and the number of travelers with yarn hairiness,
E-mail: asagbas@mersin.edu.tr yarn strength and production cost being multiple response variables. Experimental levels
for process variables are selected according to a Central Composite Design (CCD) due to
its good statistical properties, such as orthogonality and rotatability. Regression analysis
of experimental results indicates that the second-order regression model adequately
represents yarn hairiness in terms of process variables. Finally, the yarn production cost
model and regression models for yarn hairiness and yarn strength are combined into a
multiple response optimisation model to determine optimum processing conditions for
different yarn quality levels.
Key words: process optimisation, yarn production, hairiness, strength, yarn cost.
n Introduction regression model to analyse the effect of n Optimisation approach
linear density on cotton yarn hairiness in
In yarn production, yarn hairiness is kept ring spinning. The basic steps of the multiple-response
as low as possible except for a few spe- process optimisation approach used in
cial cases. High yarn hairiness causes In this study, an optimisation model this study are summarised in a flowchart,
serious problems in both yarn produc- based on empirical regression models is shown in Figure 1. A pure cotton blend is
tion and use of yarn in subsequent textile developed to determine the best process- prepared to produce 14.75 tex staple yarn
operations [1]. Such problems include ing conditions for spindle speed, yarn on ring machines. Therefore, spindle
higher friction during spinning, greater twist, and the number of travelers with speeds for the ring spinning frame
fly fibre, and increased yarn breakage yarn hairiness, yarn strength and produc- are selected in this study. Higher
during weaving [2 - 4]. A study published tion cost being the multiple responses.
in Textile World (1989) states that 46% Regression analysis is used to build re-
spindle speeds could be used for
of yarn breakages in weaving are due to sponse surface models for yarn hairiness, other types of spinning frames, such
high yarn hairiness. Another adverse ef- yarn cost and yarn strength as a function as open-end. Experimental levels for
fect of hairiness in weaving is greater pill- of the process variables under consid- process variables are selected according
ing in fabric. Differences in the hairiness eration. Finally, the yarn production cost to a Central Composite Design (CCD)
properties of weft yarns result in a band model and regression models for yarn due to its good statistical properties, such
forming in fabric [5]. High hairiness in hairiness and yarn strength are combined as orthogonality and rotatability [9]. This
bobbin machines results in a loss of pro- in a multiple-criteria decision model to design has 15 different design points
ductivity, and dark lines form where high determine optimum processing condi- for all combinations of process vari-
hairiness exists in warp yarn [3, 6]. These tions for different quality levels. ables. Yarns produced are tested on Uster
examples show that it is critical to reduce
yarn hairiness in order to improve the
quality of yarn used in knitting, weaving
and finishing operations. This also brings
significant cost reductions in the produc-
tion of yarn by eliminating additional
operations to reduce hairiness. On the
other hand, the cost of yarn production
should be minimised while maintaining
yarn hairiness and yarn strength within
desirable limits.
Process optimisation through statistical
regression models is common practice
in many industries. Ozkan et al. [7] use
the Box-Wilson optimisation method to
determine the best production conditions Figure 1. Steps of
the multiple response
for partially oriented yarn properties. process optimisation
Altas and Kadoglu [8] build a multiple approach.
40 Erol R., Sağbaş A.; Multiple Response Optimisation of the Staple-Yarn Production Process for Hairiness, Strength and Cost.
FIBRES & TEXTILES in Eastern Europe 2009, Vol. 17, No. 5 (76) pp. 40-42.
Tester 4 and Uster Tensorapid 3 testing to such levels that the following overall gression models adequately represent
equipment [10]. Table 1 shows experi- desirability function is maximised, yarn hairiness and yarn strength in terms
mental design points and test results for of the process variables considered (p-
D = (d1d2........dm)1/m (2)
the response variables. Since this study values for the model significance are
attempts to find optimal processing con- For yarn hairiness, the desirability func- 0.0087 and 0.0144 for yarn hairiness and
ditions by selecting the region of interest tion is as follows yarn strength, respectively). The analysis
as large as possible, some extreme val- 1 y <T of Variance (ANOVA) in Table 2 shows
ues for the spindle speed and yarn twist r that yarn twist is the most influential
U − y factor for yarn hairiness. Least-square
are also introduced in experimental runs. d = T ≤ y ≤U (3)
Furthermore, central composite designs U − T regression equations estimated for yarn
usually have extreme combinations of 0 y >U hairiness and yarn strength are as fol-
processing variables for complete ex- lows:
where T and U are the target value and the
ploration of the region of interest unless upper limit for yarn hairiness, respective-
there is an infeasibility or safety problem yhairiness = -19.56 - 0.00109x1 +
ly. In Equation 3, r is the weight assigned
during experiments. Design points at the + 0.0762x2 - 0.7655x3 + (5)
to the response variable. Choosing r > 1
centre of the CCD correspond to current - 0.00027x32 + 0.00039x1x3
places greater importance on being close
or more common operating conditions. to the target value, whereas choosing
ystrength = 14.97 - 0.0004x1 +
0 < r < 1 makes this less important.
The yarn production cost at each design + 0.0386x2 + 0.378x3 + (6)
point is estimated using factory data in or- In similar fashion, as the yarn strength - 0.0183x22 + 0.0008x2x3
der to build a regression model that defines should be maximised, the desirability
the relationship between yarn cost and the function should be: However, the following first-order linear
process variables of interest. DesignExpert model is found to be adequate for yarn
1 y <T
software is used for all statistical analysis cost
r
and optimisation in this study [11]. y − L
d = T ≤ y ≤U (4) ycost = 4.135 - 0.00016x1 +
T − L (7)
+ 0.0031x2 - 0.0185x3 +
A useful approach for optimisation of 0 y >U
multiple response variables m proposed Response models for all three response
where L is a lower limit for the yarn
by Derringer and Suich makes use of de- variables are combined into a single
strength.
sirability functions [12]. In this approach, multiple-response optimisation model.
each response yi is expressed in terms of Upper and lower limits for the response Search parameters of the multiple re-
an individual desirability function di that variables are selected from the Uster sta- sponse optimisation approach described
takes its values from the following range tistics published in 2001 for quality of in the previous section are summarised
yarn produced worldwide. in Table 3 for various yarn quality levels.
0 ≤ di ≤ 1 i = 1, 2, ..., m (1)
The spindle speed and yarn twist values
When the response variable is at its in Table 1 are used to build a regression
goal or target, di becomes 1, and if the
Research findings model that will be used to estimate opti-
response variable is outside the accept-
and discussion mal processing conditions, as shown in
able range, di becomes zero. The overall Regression analysis of experimental re- Table 3. The best 10 spindle speed and
objective is to set the process variables sults indicates that the second-order re- yarn twist values are obtained from the
iterative optimisation approach. Actual
Table 1. Central Composite Design(CCD) points and experiment results; x1 - spindle speed experiments are not performed at these
(r.p.m.), x2 - yarn twist (t.p.m.), x3 - number of travellers. values since regression model estimates
are used in the optimisation. However,
Process variables Response variables
Run
x1 x2 x3 yhairiness ystrength, cN/tex ycost, USD/kg
experiments at these values could be run
1 12500 1231 35.5 4.54 17.52 5.10
for further validation of optimisation re-
2 12500 1067 35.5 4.98 19.02 4.85 sults.
3 10500 1231 35.5 4.37 18.78 5.60
4 10500 1067 35.5 4.33 17.19 5.12 As an example, Table 4 shows the best
5 10500 1231 28.0 4.41 18.18 5.81 eight solutions of the optimisation ap-
6 10500 1067 28.0 5.09 17.51 5.40
proach used to determine optimum
7 12500 1231 28.0 4.41 18.29 5.27
8 12500 1067 28.0 5.15 17.39 4.79 processing conditions for the upper 5%
9 11500 1280 31.5 4.03 16.60 5.93 in terms of quality. Achieving a maxi-
10 11500 1143 40.0 4.47 18.96 5.07 mum overall desirability of 0.79 means
11 9768 1143 31.5 4.81 18.70 5.08 that it is not possible to meet all the qual-
12 11500 1000 31.5 4.03 17.19 4.80
ity and cost goals for this quality level
13 11500 1143 25.0 4.89 18.44 5.33
14 13232 1143 31.5 4.92 18.54 4.85
since the quality of cotton fibres is not
15 11500 1143 31.5 4.78 18.49 5.26 high enough for this level. Yarn strength
16 11500 1143 31.5 4.78 18.47 5.23 quality limits for upper quality levels of
17 11500 1143 31.5 4.76 18.48 5.23 75%, 50%, 25% and 5% are taken from
18 11500 1143 31.5 4.79 18.47 5.26 Uster statistics for the year 2001. Table 5
FIBRES & TEXTILES in Eastern Europe 2009, Vol. 17, No. 5 (76) 41
Table 2. ANOVA Table for yarn hairiness; * significant factors at 5% significance level. ditions for different yarn quality levels.
Optimisation runs indicate that a low
Source Sum of squares df Mean square F value p-value
spindle speed and yarn twist along with
Model 1.64 9 0.18 6.18 0.0087*
a high number of travellers should be se-
x1 0.083 1 0.083 2.82 0.1317
x2 0.30 1 0.30 10.04 0.0132*
lected to reduce yarn hairiness and pro-
x3 0.15 1 0.15 5.12 0.0535 duction cost while maintaining high yarn
x12 0.040 1 0.040 1.37 0.2752 strength. Other process variables such as
x22 0.74 1 0.74 25.07 0.0010* applied draw, ring diameter, temperature
x32 0.00027 1 0.00027 0.0089 0.9268 and humidity at the workplace can be
x1 x2 0.034 1 0.034 1.15 0.3145
considered for further optimisation study.
x1 x3 0.76 1 0.76 2.57 0.1479
Moreover, the process optimisation ap-
x2 x3 0.12 1 0.12 4.06 0.0787
Error 0.24 8 0.030 proach used in this study can be extended
Total 1.88 17 for yarn produced in other spinning sys-
tems, such as open-end. Other quality
parameters (e.g., yarn evenness, breaking
Table 3. Iterative determination of optimum conditions for the upper 5% in terms of quality;
x1 - spindle speed (r.p.m.); x2 - yarn twist (t.p.m.); x3 - number of travellers. force, thin places) could be incorporated
into our optimisation model with new ex-
Process variables Response variables
Overall perimental runs.
Best desirability
solutions
x1 x2 x3 yhairiness ystrength, cN/tex ycost, USD/kg D
1 9820 1011 38.05 3.40 20.61 4.96 0.790 References
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42 FIBRES & TEXTILES in Eastern Europe 2009, Vol. 17, No. 5 (76)
