Evaluation of performance properties in woven Terry towel by multi response optimization

Abstract

This study investigates the influence of various constructional parameters and weave structure on the differential shrinkage (DS) %, tensile strength, absorbency, drape, softness, smoothness and resilience properties of woven terry towels with the goal of optimizing these characteristics for better durability, aesthetic and functionality. This research explores how different variations in constructional parameters and weaves can affect performance of terry woven towels. The results demonstrate that weft density variation significantly influences both differential shrinkage (DS) % and other performance properties. It was concluded that increasing thread density of the towel resulted in lower absorbency, overall moisture management capacity (OMMC), drape, softness, and smoothness. However, the tensile strength, shrinkage, and resilience score increase with increasing thread density of the towel. The differential shrinkage % of the towel can be lowered using proper weave structure and reducing the difference of thread density of body and fancy portions in the towel. The findings also highlight that multi-response optimization can be used for optimization of multiple outcomes. Its implications are far-reaching, impacting efficiency, quality, and competitiveness across various industries. The ability to balance multiple objectives makes it a valuable tool for decision − makers aiming to achieve comprehensive and effective solutions. This research provides practical insights for selecting appropriate thread density and weave combination to achieve both aesthetic and functional comfort, offering valuable guidance for manufacturers aiming to produce woven terry towel on the loom with precise dimensional control and performance. The overall approach is a scientific solution to a complex industrial problem dealing with multiple complex and interrelated parameters especially in the production of high quality terry towels.

Introduction

Terry towels are one of the most widely used home textile products. The terry/loop formation is an important operation of terry fabric production and contributes to about 80% of its efficiency. Terry woven fabric is the most used structure in water absorbency related applications. It is used for wiping or drying and absorbing moisture by direct contact. One of the most popular consumer commodities in the world is terry towel cloth. The market demands for terry towels depend on performance parameters e.g., hand/feel, color, pattern, fashion, and mechanical performance¹. Terry towels are utilized in a variety of settings, such as bathrooms, sports facilities, swimming pools, kitchens, and beaches, among others. There are a variety and sizes of towels depending on the end-use like bathrobes, hand towels etc. In today’s market, manufacturers are obliged to constantly raise the level of usability and aesthetics features of terry woven towels. The end users normally prefer lighter weight, better comfort properties in case of towels due to their direct contact to skin. Comfort related properties of terry woven fabrics are very specific e.g., moisture absorption and soft touch/feel. Terry fabrics, towels, or bathrobes instantly absorb moisture and are used to dry the body^2,3.

A terry towel consists of the basic woven fabric (including the basic warp and the basic weft systems), and the loop pile fastened to this base fabric. The pile is formed by an independent warp − thread system. The pile area is the main part of the terry towel’s body. This portion is responsible for the most important functions of the terry towel, including the absorption and cushioning. This main pile area is split into two or three parts by the border/fancy as shown in Fig. 1. The border is the non − terry portion of the towel typically used for ornamentation purposes. Depending on the size and design of the terry towel, it can have a border on one end or two borders at both ends. The smaller pile areas at both ends of the towel are called the terry bars. The borders are less durable and are likely to shrink more than the main part of the towel (differential shrinkage), causing the sides to pucker⁴.

Fig. 1.

Parts of woven terry towel.

The terry product’s form, look, and properties can be designed in dependence on the raw material used, the kind of yarns, and the way in which the pile is fastened to the base fabric. The material (fiber type, yarn count/fineness, etc.) and structural characteristics (pile height, structure, and stitch density) can have the most significant effects on the absorptive capacity of terry fabrics^4,5. Different researchers have investigated different properties of terry towels. A few researchers have studied the effect of raw material on the properties of terry woven fabrics. Some researchers investigated the comfort properties of terry towels made of cotton yarn in warp and weft of the ground/base structure and pile yarn made of Polypropylene (PP) using different pile heights⁶. Other researchers investigated the water absorption and stiffness properties of bamboo and cotton terry towels and concluded that bamboo pile terry fabric was comparatively softer than cotton pile⁷. Similarly in another study, different blends of cotton and bamboo, 100% cotton greige, 100% dyed cotton, 100% micro cotton terry towel samples were investigated⁸. Researchers investigated the water absorbency and color fastness of woven towels made of ground yarn from cotton and pile yarn from 50/50 blend of cotton/modal⁹. Researchers have studied different parameters of construction of terry towels. They highlighted that the fabric weight, thickness, and kind of pile yarns employed can affect the moisture − absorbing characteristics of terry textiles¹⁰. Some researchers also investigated the factors affecting absorbency e.g., the type of fiber, yarn qualities, and fabric features¹¹. In another research, the effects of yarn structure were investigated. Different yarn count (12’s, 14’s and 16’s Ne) was used, and results indicated that there were positively and highly significant associations between yarn hairiness and overall comfort properties of towels¹². It has been observed that performance of the towels is greatly affected by repeated launderings¹³. It was also proved that the moisture absorption properties of the terry towel generally depend on the fabric weight, thickness, and type of pile yarns used e.g. single, plied, or zero − twist¹⁴.

The physical properties of towels change because of shrinkage during washing cycles. Sometimes different parts of the towel shrink differentially. This kind of shrinkage is known as differential shrinkage (DS). Differential shrinkage is the different levels of shrinkage in different sections of a fabric unit cell. If the border shrinks too much, the towel will have an undesirable bowed shape. If it is too heavy, then shrinkage is inevitable. It causes the towel’s shape to distort, degrading both its appearance and functionality. Because of this, the towel can exhibit problems including curling of the edges, uneven surface roughness, and decreased absorbency, all of which could reduce customer satisfaction and shorten the life of the product³. Researchers investigated the effect of pile yarn parameters on absorbency, appearance, handle, and shrinkage of terry towels. Their results confirmed that the pile/ground ratio was the most important contributing factor in dimensional change/overall shrinkage of the towel since the shrinkage occurs in the ground of the towel fabric¹⁵. Some others compared the shrinkage properties of woven and warp − knitted terry fabrics and concluded that dimensional changes in warp − knitted towels were lower than that in woven towels¹⁶. Researchers examined the dimensional stability of woven terry textiles constructed from hard core − spun yarns versus standard cotton yarn for terry. The shrinkage values of the border, sides, and hems of the 100% cotton samples varied significantly, resulting in shape distortion¹⁷. Recent advances in digital imaging and analysis have led to more precise measurements of fabric shrinkage. Some researchers used image analysis to develop digitized evaluation methods for assessing the shrinkage, skewness¹⁸, and fabric shape retention for towels and other fabrics¹⁹. This method provides a multi − directional analysis of shrinkage, with more accurate data to help in the development of more durable terry fabrics.

The life of any product is crucial in estimating its cost and sale. The decision to buy the towel is commonly based on touch and evaluation of appearance. A customer may declare a fabric unusable if it is not aesthetically appealing. A fabric may lose its aesthetic appeal much sooner rather than getting worn out. Limiting differential shrinkage is essential for maintaining towel quality and consumer satisfaction. From the literature, most of the research is focused on improving water absorbency, wicking, and overall shrinkage of the towels. There is limited research available on reducing the differential shrinkage (DS) of the towels. The available research lacks understanding of the factors resulting in different levels of shrinkage in different parts of the terry towel. The effect of fiber properties (such as elasticity), weave density, border dobby/jacquard weave, and heat setting on shrinkage of different parts of the towel remains unclear. Sometimes varying weave patterns, yarn types and applied tensions, and finishing processes cause different parts of the fabrics to shrink at different percentages. Common problems that occur in towels are differential shrinkage and comfort properties. Therefore, the aim of this study is to find a solution for reducing the differential shrinkage of terry woven towels. Different factors and sub factors that can affect differential shrinkage were identified using Cause and Effect diagram. Different properties beside differential shrinkage, like tensile strength, thermo − physiological comfort performance e.g., water absorbency and overall moisture management capacity (OMMC) were studied. Tactile comfort properties e.g., smoothness and softness, drape and resilience were evaluated by using Phabrometer. Statistical tool e.g., Weighted Multi − response optimization analysis was employed in order to determine the best construction parameters for the reduction in differential shrinkage% (DS) by giving DS% double the weightage in contrast to other responses. Subsequently, the same technique was used for enhancement of comfort properties without compromising other properties by giving all responses equal weightage.

Methodology

Cause − and − effect diagram

A Cause − and − Effect Diagram, also known as a Fishbone Diagram or Ishikawa Diagram, is a visual representation used to identify, explore, and display the possible causes of a specific problem or effect²⁰. It is a useful tool in problem − solving and quality improvement processes. The diagram is called a Fishbone Diagram due to its appearance, resembling the skeleton of a fish. The possible factors and sub − factors which could affect the differential shrinkage process in different sections of a terry fabric unit cell were identified. Shrinkage behavior of terry fabric depends on the structure, orientation, and elasticity of the fibers, the yarn and fabric construction, the finishing processes, and the laundering methods, fiber content/raw materials, fiber properties (e.g., strength, elongation, elasticity), yarn elasticity, yarn Count/fineness, yarn twist, fabric construction (float length and number of interlacements per unit length), thread density (per cm), finishing process (Heat setting), laundering (temperature, type of wash, chemicals), etc., are included in the Fishbone Diagram shown in Fig. 2. Some of the key factors have been considered in the present study i.e., weave design and construction parameters.

Fig. 2.

Cause & Effect Diagram.

Materials

Four types of 100% cotton yarns were used for making terry towel samples. The yarns were bought from local manufacturers. For pile warp, English counts of 10/1, 10/1 with Zero Twist, 10/1 Carded, and 12/1 with Zero Twist were taken. For Ground warp, English count 10/1 was used. For weft, the yarn of English counts of 10/1 and 12/1 were used.

Methods

Samples of terry towels were prepared with a size of 75 cm × 75 cm each according to the design of experiment (DOE) as shown in Tables 1 and 2 respectively. Towel samples were made on air jet loom (Toyota, Japan). 3 pick terry design was used for all the samples for body of the towel as shown in Fig. 1, while for fancy segments, 4/1 Satin (5 end satin) weave was used for sample S2. For sample S1, 3 × 3 matt and for S3 and S4 plain weave was used. These structures were selected based on the varieties available in the market and produced typically in the manufacturing industry.

Table 1.

Factors and their level.

Sample ID	Weave	Warp density (ends/cm)	Body Weft density (Picks/cm)	Weft count (Ne)	Warp count (Ne)
					Pile	Ground
S1	3-pick terry for terry portion	22	12	10/1	10/1, 12/1 Zero twist (ZT)	10/1
S2			14	12/1
S3			16	16/1
S4			14	16/1

Table 2.

Design of experiments (DOE).

	Sample	Weave	Ends/cm	Wefts/cm	Weft fineness (Ne)	Warp fineness (Ne)
						Pile	Ground
For Body	B1	3-pick terry 3 Pick Terry	22 22	12	10/1	10/1, 12/1 ZT	10/1
	B2			14	12/1
	B3			16	16/1
	B4			14	16/1
For Fancy	F1			12	10/1	10/1, 12/1 ZT	10/1
	F2			14	12/1
	F3			16	16/1
	F4			14	16/1

The process flow for developing the towels is demonstrated in Fig. 3.

Fig. 3.

Flow process of terry towel manufacturing.

To test the various parameters properties of the body, the warp count/fineness (ground and pile yarn) and warp density were kept constant for both body and fancy part of the terry towels, while weft parameters were variable. Same samples were used to test the properties of the body and fancy.

The Fig. 4 shows 3D images of the 3-pick terry design created using Microsoft Paint 3D on Windows 11, Version 24H2 (Washington, 98052 − 6399, USA). Figure 5 shows the images of the developed terry fabric samples.

Fig. 4.

3-pick terry design created using Microsoft paint 3D on Windows 11, Version 24H2 (Washington, 98052 − 6399, USA.). https://apps.microsoft.com/detail/9nblggh5fv99.

Fig. 5.

Images of developed samples.

Testing and evaluation

Yarn testing

Yarn linear density/Count (Ne) was determined according to ASTM D1059 − 17²¹. The count lea strength product (CLSP) testing was performed on Lea Strength Tester as per ASTM − D1578²². The lea strength of yarn is an indicator of the suitability of the yarn for a specific application. This is a standard and defined method for the calculation of yarn strength. Resistance per kilometer (RKM) is also investigated. It is calculated from the data of single yarn strength tests performed on Uster^® Tensorapid as per ASTM D 2256²³. Yarn twist tester was used to calculate the twist per inch (2.54 cm) (TPI) as per ASTM 1422²⁴.

Performance properties of Terry towel

• Tensile strength of towel samples: Tensile strength was determined according to ASTM D − 5035²⁵ by strip test method on the universal tensile strength tester TITAN TNT 0086, Japan.

• Shrinkage test/Dimensional stability: Shrinkage is also an important factor influencing the dimensional stability during washing. Shrinkage test was performed according to AATCC 135²⁶ standard. For this purpose, the original widths of towel samples were measured from body and fancy parts. Then, the samples were washed and again their width at body and fancy parts were measured. The percentage shrinkage in body and fancy segments were calculated by using widths before wash and after wash for each sample. Then the difference of both dimensions was calculated as shrinkage (%).

• Water absorbency: Absorbency is an important factor that determines the suitability of a fabric for a particular use and is defined as the propensity of a material to take in and retain a liquid, usually water, in the pores and interstices of the material. Especially in the case of terry towels, it is one of the most important characteristics. Water Absorbency rate was determined as per standard AATCC − 79 − 200²⁷ by drop test.

• Moisture Management Testing (MMT): Moisture Management Testing was performed based on AATCC 195²⁸ on Moisture management tester (M290, SDL Atlas) 33. MMT tester provides different measurements such as wetting time on top and bottom surface, absorption rate on top and bottom side, overall moisture management capability (OMMC) etc.

• Tactile comfort/hand feel: Softness, Smoothness, Drape and Resilience attributes were tested on Phabrometer according to AATCC TM − 202²⁹. It is a system developed by Nu Cybertel, Inc, USA.

Our DOE approach (Table 2) prioritized testing multiple parameter combinations (4 samples × 3 replicates = 12 total tests per property) within manufacturing constraints, aligning with ASTM/AATCC standards., and their average was calculated. All the experiments were performed under standard atmospheric conditions i.e., 65 ± 4% relative humidity and 20 ± 2 °C temperature according to standard ISO − 139:2005³⁰.

Statistical analysis/data analysis techniques

Multi − response optimization refers to the process of simultaneously optimizing multiple outcomes or responses in a system or process³¹. In various fields such as engineering, manufacturing, and quality control, it is quite common to have several interrelated factors that influence the overall performance. Instead of optimizing each response individually, multi − response optimization seeks to find a set of input variables that collectively optimize all responses, taking into account their interdependencies³².

Results and discussion

Yarn and fabric performance

The results of yarn performance are given in Table 3.

Table 3.

Yarn properties.

Yarn source	A mill	B mill	C mill	D mill
Blend	100% cotton	100% cotton	100% cotton	100% cotton
Twist multiplier (TM)	3.8 TM	Auto coro	3.8 TM	3.8 TM
Actual count (Ne)	10.22	10.21	16.14	12.23
Count C.V. (%)	1.35	1.27	1.27	1.34
Lea strength	223	192	155	197
Strength C.V. (%)	3.38	2.88	3.32	3.24
CLSP	2279	1960	2502	2409
RKM	14.58	12.54	16.01	15.41
Average Twist/cm	12.28	15.99	16.09	12.93
Moisture (%)	5.40	6.25	5.13	5.70

The results/response of all the performance properties for the terry fabrics are given in Table 4.

Table 4.

Sample ID and responses.

Sample ID	Y1: Differential Shrinkage %	Y2: Tensile Strength (Kg)	Y3: OMMC	Y4: Drape Coefficient	Y5: Resilience Score	Y6: Softness Score	Y7: Smoothness Score	Y8: Water absorbency (s)
S1	5.070	21.500	0.210	13.980	35.810	76.880	62.520	0.670
S2	2.820	20.000	0.170	16.310	38.790	74.380	61.850	1.260
S3	6.557	39.130	0.046	18.327	40.395	66.166	55.938	3.340
S4	6.500	29.000	0.090	25.190	51.840	69.140	61.710	3.240

The scatter plot shown in Fig. 6 reveals critical nonlinear relationships between yarn count (Ne) and strength metrics (CLSP/RKM) across mills (A, B, C & D), directly impacting terry towel performance.

Fig. 6.

Scatter plot of different yarns count (Ne) and strength product (CLSP/RKM) from different mills (A, B, C & D).

Strength vs. fineness trade-off

It can be observed from Fig. 6 that the finer yarn (16.14 Ne) obtained from C mill achieved peak CLSP (2502) and RKM (16.01), aligning with the high tensile strength of samples S3 and S4 (shown in Table 4). This confirms that finer yarns enhance structural integrity but reduce comfort (e.g., lower absorbency/longer time 3.34 s for sample S3). The coarser yarn (10.21 Ne) obtained from B mill shows the lowest strength (CLSP = 1960, RKM = 12.54), correlating with the superior comfort but moderate strength (21.5 Kg) in sample S1. An optimal mid-range yarn was obtained from D mill. The moderate yarn with fineness 12.23 Ne from D mill exhibited a balanced CLSP (2409) and RKM (15.41), mirroring an intermediate performance for sample S2 (Table 4: 20.0 Kg strength, 2.82% shrinkage). This suggests mid-range yarn counts/fineness optimize the strength-comfort equilibrium for terry towels.

Implications on Terry fabric performance

The evaluated characteristics of the terry towels are also compared in the Fig. 7(a-h).

Fig. 7.

Performance characteristics of terry towels.

From the Table 4; Fig. 7(a), a superior performance can be observed for sample S2 in terms of lower differential shrinkage (2.82%, DS%) as compared to samples S3 & S4 (> 6.5%), while sample S1 shows a DS of 5.07% with reference to the AATCC 135 threshold of 5%. It is attributed to the higher stitch density and stability of sample S2.

In the woven towel fabric, shrinkage % in fancy portions is usually higher as compared to other zones due to difference in weave and thread density. As the extent of interlacement in the weave increases, the yarn crimp increases³³. The no. of interlacements of the fancy zone, in case of samples S1, S3 and S4 is quite high as compared to sample S2. Hence, greater shrinkage % is observed in fancy segments as compared to that in body part of the towel. The shrinkage in the body part of samples S1, S2, S3, and S4 is 7.79%, 7.79%, 7.6%, and 7.6% respectively. The shrinkage in the fancy part of samples S1, S2, S3, and S4 is 12.46%, 10.38%, 13.6%, and 13.6% respectively. The minimum difference in shrinkage between body and fancy was observed in sample S2 followed by sample S1.

It can be seen from Fig. 7(b) that tensile strength of towel sample of S3 is the highest followed by samples S4, S2 and S1. Tensile strength is the force required to break majority of the yarns at the same time. Greater the fabric density, greater is the force required to break the yarns. Such effects are also observed by others and reported in literature³⁴.

Sample S1 shows the highest water absorbency or lowest absorbency time (s) (as shown in Fig. 7(c)) due to its loose structure which allows easy penetration of water to the ground/base fabric of the towel. As weft density increases, the compactness of the fabric structure increases. Compact fabric shows lower water absorbency or higher absorbency time due to higher level of yarn interlacements per unit area and smaller size of pores³⁴. As the water absorbency increases, OMMC of the fabric increases. Hence, sample S1 shows highest OMMC value and sample S3 shows the lowest OMMC value, as depicted in Fig. 7(d).

Greater the thread density of the fabric, lower will be its drapeability due to its increased stiffness. Higher drape coefficient/score represents lower drapeability of the fabric as shown in Fig. 7(e). Hence, sample S1 shows lowest drape coefficient value due to loose structure. Increasing weft density and yarn count/fineness increases the compactness which results in lowest drapeability in case of sample S4, representing highest drape coefficient. Greater the stiffness of the fabric, smaller will be its resilience. As the density of fabric increases from sample S1 to sample S4, the stiffness increases. Hence, sample S1 shows lowest and sample S3 shows highest resilience (Fig. 7(f)). Sample S1 shows the highest value of softness due to loose structure and sample S3 shows lowest softness due to compact structure (Fig. 7(g). Smoothness is the degree of roughness of the surface. Greater the no. of bumps per unit area, greater will be the roughness of the surface. By increasing the weft density, the no. of interlacements per unit area increases. Sample S1, being loose, shows highest smoothness while sample S3, having the highest compactness show lowest smoothness score depicted in Fig. 7(h).

Comparative analysis of construction parameters

A comparative analysis of the construction parameters is depicted in the Heatmap shown in Fig. 8.

Fig. 8.

Comparative analysis of construction parameters with a heatmap.

The heatmap, first introduced by Toussaint Loua in 1873 for Parisian social statistics, has evolved into a vital scientific visualization tool^35,36. In this study, this color-based matrix works by assigning gradient intensities (light to dark) to quantitative values, enabling instant pattern recognition across multidimensional data. This technique has been employed to decode terry towel construction-performance relationships, where color-coding reveals how warp density (constant 22 ends/cm), variable weft density (12–16 picks/cm), and weft count/fineness (10–16 Ne) govern terry fabric performance. The visualized chromatic logic shows darker cells for sample S3 (16 picks/cm) correlating with peak tensile strength (39.13 Kg) but poor absorbency (longer time 3.34s). The lighter cells for sample S1 (12 picks/cm) indicate optimal comfort even at a lower strength. Significantly, the mid-tone cells corresponding to sample S2 (14 picks/cm) reflect its balanced performance − 2.82% differential shrinkage (DS) while maintaining optimal comfort. This modern adaptation of Loua’s original concept validates the optimization methodology, demonstrating how density adjustments engineer fabric properties: darker hues (higher densities) favor durability, lighter zones enhance comfort. By transforming complex parameter interactions into intuitive color logic, Loua’s legacy has been advanced while providing manufacturers and researchers with scientific textile design insights.

The inverse trend between yarn fineness and comfort (seen in samples S1–S4) is validated: finer yarns (right side of plot) favor strength but require higher weft density (16 picks/cm in S3) to maximize durability, while coarser yarns (left side) prioritize absorbency at 12 picks/cm (S1).

Weighted multi − response optimization analysis

Weighted multi − response optimization (WMR) method is particularly valuable in fields such as engineering, manufacturing, and quality control, where optimizing various factors can impact multiple outcomes. The methodology of WMR discussed earlier was employed in a step − by − step manner to get the results.

Step1: Signal − to − noise ratio (SNR) is a critical parameter in the context of multi − response optimization. In the realm of optimization, particularly in experimental design and quality improvement, SNR is employed to quantify the quality of a process or system. The SNR represents the ratio of the signal, which is the desired or target outcome, to the noise, which encompasses variability or undesirable deviations from the target. In the context of multi − response optimization, SNR serves as a performance metric that accounts for the variability in multiple responses simultaneously. It helps evaluate the effectiveness of a set of input variables by considering both the desired signals and the undesirable noise across different responses. There are three types of SN ratio—the lower the better, the higher the better and the nominal the better and can be expressed as follows (Eqs. 1 − 3):

For lower − the − better:

1

For higher − the − better:

2

For nominal − the − better:

3

where, , , n is the number of runs, is the SN ratio of j^th response and i^th trial, is the observed value of the i^th experimental run, j^th response and k^th repetition, the unit of SN is dB and T is the targeted value. In this study, The S/N ratios were expressed as lower−the− better in the case of DS while higher the better in case of other responses. Results are shown in Table 5.

Table 5.

S/N ratio values at all runs of the responses.

Sample ID	Y1	Y2	Y3	Y4	Y5	Y6	Y7	Y8
S1	−14.139	26.531	−13.673	22.793	30.963	37.599	35.803	−3.596
S2	−9.044	25.903	−15.509	24.132	31.657	37.312	35.709	1.890
S3	−16.373	31.837	−26.853	25.249	32.113	36.399	34.941	10.461
S4	−16.297	29.130	−21.033	27.907	34.176	36.677	35.690	10.093

Step 2: Normalized Signal − to − Noise Ratio (NSNR) is a metric used in the context of multi − response optimization to evaluate the quality of a system or process by considering both desired signals and undesired noise across multiple responses³⁷. It is an extension of the traditional Signal − to − Noise Ratio (SNR) that takes into account the scale differences between various responses, ensuring a fair comparison. In multi − response optimization, where different variables may have distinct units or scales, NSNR normalizes the SNR values, making them comparable. This normalization ensures that each response contributes proportionally to the overall optimization goal, preventing biases due to differences in measurement units. Its importance lies in providing a balanced approach to optimization and facilitating informed decision − making, ultimately leading to more robust and reliable solutions. The normalized equation for SN ratios lower − the − better, higher − the − better, and nominal − the − better respectively are as follows (Eqs. 4 − 6).

For lower − the − better:

4

For higher − the − better:

5

For nominal − the − better.

6

where, and are signal to noise and normalized SN value of the i^th experiment and j^th trial, and are the minimum and maximum values of , and targeted value. Results are shown in Tables 6, 7 and 8 respectively.

Table 6.

Normalized S/N ratio values at all runs of the responses (Shrinkage has double weightage than other responses).

Sample ID	Y1	Y2	Y3	Y4	Y5	Y6	Y7	Y8
S1	0.610	0.106	1.000	0.000	0.000	1.000	1.000	0.000
S2	2.000	0.000	0.861	0.262	0.216	0.761	0.891	0.390
S3	0.000	1.000	0.000	0.480	0.358	0.000	0.000	1.000
S4	0.021	0.544	0.442	1.000	1.000	0.232	0.869	0.974

Table 7.

Weightages at all runs of the responses (Shrinkage has double weightage than other responses).

Sample ID	W1	W2	W3	W4	W5	W6	W7	W8	MRPI	Rank
S1	0.232	0.064	0.434	0.000	0.000	0.502	0.362	0.000	1.447	3
S2	0.760	0.000	0.374	0.150	0.137	0.382	0.323	0.165	2.554	1
S3	0.000	0.606	0.000	0.276	0.227	0.000	0.000	0.423	1.243	4
S4	0.008	0.330	0.192	0.574	0.635	0.116	0.315	0.412	2.175	2

Table 8.

Normalized S/N ratio values at all runs of the responses (All responses have equal weightage).

Sample ID	Y1	Y2	Y3	Y4	Y5	Y6	Y7	Y8
S1	0.305	0.106	1.000	0.000	0.000	1.000	1.000	0.000
S2	1.000	0.000	0.861	0.262	0.216	0.761	0.891	0.390
S3	0.000	1.000	0.000	0.480	0.358	0.000	0.000	1.000
S4	0.010	0.544	0.442	1.000	1.000	0.232	0.869	0.974

Step 3: Multi − response optimization using the “Assignment of Weights” approach is a systematic methodology employed to address situations where multiple, often conflicting, responses need to be considered simultaneously in a decision − making process. Weightages are assigned to each response variable based on its importance. These weightages are usually normalized to ensure that they collectively sum to 1, simplifying the optimization process. These weightages are typically determined through a combination of expert judgment, stakeholder input, or statistical analysis. The obtained results are shown in Tables 7 and 9 respectively. The ranking of the samples is also shown in Tables 7 and 9.

Table 9.

Weightages at all runs of the responses (All responses have equal weightage).

Sample ID	W1	W2	W3	W4	W5	W6	W7	W8	MRPI	Rank
S1	0.232	0.064	0.434	0.000	0.000	0.502	0.362	0.000	1.376	3
S2	0.760	0.000	0.374	0.150	0.137	0.382	0.323	0.165	1.794	2
S3	0.000	0.606	0.000	0.276	0.227	0.000	0.000	0.423	1.243	4
S4	0.008	0.330	0.192	0.574	0.635	0.116	0.315	0.412	2.175	1

In this study, the weightages are determined as follows. For response Y₁ (Smaller—the better characteristic), reverse normalization procedure is used. That is, for each response data, 1/Y₁ is obtained and then WY₁ is computed the individual response (data) is divided by the total response value (). In the case of responses Y₂ to Y₈ (larger—the better characteristic) is computed and the individual response (data) is divided by the total response value (), WT1 is computed as follows.

For example, in first trial  = 0.196

The order of the multi − response performance index (MRPI) is shown in Table 7 when DS % has double the weightage as compared to the other responses, which shows that the sample S2 has minimum DS % followed by sample S4.

The normalized S/N ratios at all runs of the responses are shown in Table 8. All responses have equal weightage in this analysis.

Table 9 shows weightages at all runs of the responses when all responses have equal weightage.

In the second scenario, where all responses have equal weightage as shown in Table 9, MRPI value of sample S4 is the highest and thus it ranks as the best followed by Sample S2.

Conclusions

The present study utilized the cause − and − effect diagram to display the possible causes of a specific problem or effect in terry towels. It is an approach of utilizing the simultaneous optimization of properties by weighted multi − response optimization technique. There are two scenarios discussed, in first scenario, investigation of the optimal constructions parameters was undertaken to reduce the differential shrinkage % in terry towels without compromising other essential properties. While in the second scenario, all responses were weighted equally to achieve optimal construction parameters. This study comprehensively examined the effects of different weave structures and construction parameters on shrinkage of woven terry towels, emphasizing the pivotal role of weave structure/interlacement pattern and construction parameters in determining the performance properties of towel fabrics. The following conclusions were drawn based on the detailed analysis:

• The higher crimp% results in greater shrinkage. If the no. of interlacements in the fancy zone of the terry towel is higher as compared to that in body part, then greater shrinkage % is observed in fancy zones as compared to that in body. This difference can be reduced/controlled by keeping the minimum difference between the two zones or by using appropriate weave, and also by reducing the difference between thread densities in the body and fancy portion of the towel.

• The higher the fabric density, the higher is the force required to break the yarns. The strength of sample S1 was maximum, followed by strength of sample S4 and then sample S2 and S3.

• Sample S1 showed highest water absorbency due to looser structure which allowed easier penetration of water to the ground/base fabric surface of the towel. Sample S3 showed the lowest water absorbency. As the water absorbency increases, OMMC of the fabric increases. Hence, sample S1 showed the highest OMMC value and S3 showed the lowest OMMC value.

• Sample S1 showed the highest drape value due to loose structure and sample S4 showed the lowest drape value. As the density of fabric increased from sample S1 to sample S4, the stiffness score increased. Hence, sample S1 showed the lowest and sample S3 showed the highest resilience score. Sample S1 showed the highest softness score due to loose structure and sample S3 showed the lowest softness due to compact structure. Sample S1, being loose, showed the highest smoothness while sample S3, having maximum compactness showed the lowest smoothness score.

• Optimization requires balancing weft density and yarn count/fineness: higher weft density improves strength but compromises the comfort, as evidenced by the heatmap analysis.

• The simultaneous optimization, in first scenario, suggested that sample S2 was ranked as the best sample, while samples S4 and S1 were ranked as 2nd and 3rd respectively.

• The simultaneous optimization, in second scenario, suggested that sample S4 was ranked as the best sample, while S2 and S1 were ranked as 2nd and 3rd respectively.

The goal of this study was to elucidate the relationship between weave structures, and construction parameters on performance properties in woven terry towels. The findings will help manufacturers and researchers to optimize differential shrinkage and other performance properties through precise control of weave and construction parameters.

Author contributions

Conceptualization: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad, Ambar Shah, Miroslav Muller, Petr Jirku, Jiri Urban, Petr Hrabe, Vijay Chandan; methodology: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad, Ambar Shah, Miroslav Muller, Petr Jirku, Jiri Urban, Petr Hrabe, Vijay Chandan; software: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad, Ambar Shah and Miroslav Muller; data analysis: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad, Ambar Shah and Miroslav Muller; writing—original draft preparation: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad, Ambar Shah, Miroslav Muller, Petr Jirku, Jiri Urban, Petr Hrabe, Vijay Chandan; Writing—review: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad, Ambar Shah, Miroslav Muller, Petr Jirku, Jiri Urban, Petr Hrabe, Vijay Chandan; resources: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad, Ambar Shah and Miroslav Muller; supervision: Hafsa Jamshaid, Rajesh Kumar Mishra, Naseer Ahmad and Miroslav Muller. All authors agreed to the submitted version of the article.

Funding

The authors are grateful to the Internal Grant Agency of Faculty of Engineering, Czech University of Life Sciences Prague, grant no.s 2025:31140/1312/3104: “Research into the production of composite polymer materials with a focus on improving performance” and 2025:31140/1312/3108: “Research on the recyclability of PUR foam in the application of polymer composite systems”.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Conflict of interest

All the authors declare that they have no conflicts of interest related to the data presented in this manuscript.

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