Composite quality index of silk cocoons--application of discriminant analysis.

ABSTRACT

The quality of silk cocoons is determined by a number of characteristics. Each of these characteristics measures a different aspect of the quality. In the absence of a single measure for the overall quality, the price of the cocoons is based on one or two characteristics, which are deemed to be most important by the buyer or the seller. It is shown that there is very little correlation between these characteristics. A methodology is developed to create a composite quality index (CQI), which encompasses all the important characteristics. The cocoons are graded into three categories, Low, Medium and High quality based on the CQI. Discriminant analysis is used to map the individual characteristics directly on to the three grades of cocoons. It is shown that the discriminant functions are significant and that the functions are able to classify the cocoons into the grades with a high degree of accuracy. Once the cocoons are graded using the discriminant functions, the buyers and the sellers could negotiate the price with complete information about the overall quality of the cocoons.

1. INTRODUCTION

Sericulture occupies a very important position in the Indian economy. Its structure comprising of mulberry cultivation, silkworm rearing, silk reeling and fabric weaving spreads across the agriculture sector, industrial sector as well as cottage industries and export units. Thus it plays a pivotal role in economic development of the country by generating employment, incomes as well as foreign exchange. By the very nature of its structure, sericulture faces the problems associated with both agriculture and industries, especially cottage industries. It is one particular segment of sericulture namely the reeling segment, which faces the brunt of the problems associated with both the sectors, namely the agriculture and industry.

In spite of India being a large producer of raw silk, cocoons are transacted without testing and the cocoon price is purely based on the subjective assessment of quality made by the buyer at the time of purchase. There is neither a system for scientific assessment of the quality of cocoons prior to transaction nor a systematic approach for fixing the price based on their quality and market conditions (Vasumathi, 2000).

It has been established that cocoon quality contributes to the tune of about 80 per cent of the raw silk quality (Shimazaki, 1964). As a result, some form or the other of quality index as a measure of cocoon quality exists in countries more advanced in sericulture especially Japan and China (Somashekar, 1999 and Nakajima, 1999). These countries have realized the importance of cocoon quality in the price fixation and made the cocoon testing mandatory prior to marketing. In addition, the cocoon price in these countries is fixed on the basis of the cocoon quality as well as the price of raw silk, which is fixed on an annual basis.

At the same time, the national standards used by other sericultural countries cannot be adopted as such in the Indian context (Vasumathi, 2000). Therefore, there is a need for developing an objective method of assessing the quality of cocoons based on the parameters so that an organizational mechanism to bring its implementation to cocoon transactions can be set up.

Cocoon quality is governed by several parameters, each of them being associated with a certain level of importance (Anon, 1996). Some of the important quality parameters usually considered are: Shell Ratio percentage, Defective Cocoon Percentage, Average Filament Length, Average Non Broken Filament Length, Denier, and Reelability percentage. Of these, Shell Ratio percentage and Defective Cocoon percentage have been identified as the most significant ones (Sonwalkar, 1982, 1993) especially because these are relatively easy to determine requiring minimum facilities, infrastructure and time.

It has been established that each of the quality parameters has its own relative significance on the reeling efficiency and raw silk quality. The procedures for assessment of a few of these parameters are quite involved, while it is relatively easy for a few others. A few tests are non destructive (as in the case of Defective Cocoon percentage), while a few are destructive (as in the case of Shell Ratio percentage). Thus, each of the parameters is associated with a certain extent of ease or difficulty in assessment.

The important characteristics that define the quality of cocoons are described below:

Single cocoon weight (SCW): This is simply the average weight of a cocoon. This is usually calculated by selecting 25 cocoons at random, then taking the total weight and then calculating the average of a single cocoon weight. This is measured in grams or centigrams.

ii. Shell weight (SW): This is the average of the single shell weight. The shell is that portion of the cocoon after removing the pupae. This is calculated by taking the same 25 cocoons that are used for calculation the single cocoon weight. The pupae are removed from these 25 cocoons and then the average weight of the shells is calculated. The shell yields the raw silk and hence the higher is the shell weight, the higher is the yield of the raw silk. This is also measured in grams or centigrams.

iii. Shell Ratio (SR): This is defined as the ratio average shell weight to the average single cocoon weight and expressed as a percentage. This ratio actually estimates the raw silk content of each cocoon. Thus the higher the shell ratio, the better is the quality.

iv. Filament length (FL): This is the total length of the silk filament reeled from the cocoon. This is measured in meters.

v. Filament size (FS): This is the thickness of the silk filament. This is also expressed as the denier. The denier is expressed as the weight of the silk filament measured in grams for 9000 meters of the filament. A lower denier implies finer silk filament and hence is more desirable.

vi. Reelability (RY): This is a measure of the re-reelability of the silk filament. It is the ratio of the cocoon reeled without break and the total number of cocoons casted, and it is measured as a percentage. This ratio is calculated from the number of times of casting filaments and the number of cocoons reeled. This characteristic actually measures the frequency of breakages of the filament during reeling.

vii. Raw silk (RS): This is a measure of the raw silk expressed as a percentage. It is the ratio of the number of kilograms of cocoons required to produce one kilogram of raw silk and expressed as a percentage.

viii. Neatness (N): This measures the neatness of the silk filament. This is expressed as a percentage. The number of small knots, loops and the frequency of distribution on raw silk are represented as percentage by comparing a sample of 20 panels taken on a seriplane board, with the standard photographs for neatness defects. This characteristic has an impact on the quality of the fabrics woven from the silk.

ix. Boil Loss (BL): Boil loss or degumming loss is the loss of sericin that is used as the gum for binding the silk filaments together in the form of a cocoon. Cocoons selected for reeling are boiled in soap solution for removing the gum or sericin. This is the ratio of the weight of cocoons after degumming, to the original weight of cocoons (green cocoons) and expressed as a percentage.

Percentage of defective cocoons is another characteristic used by reelers in determining the price of cocoons. This is the percentage of defective cocoons in a given lot. Even though it is an important characteristic in determining the price offered for the lot, it is not a determinant of the quality of the cocoons with respect to the reeling aspects.

In addition to these characteristics of the cocoon, three more pre-cocoon characteristics are defined. These three characteristics are observed at the larval stage of the silkworm. These are:

i. Hatching percentage (HP): The number of hatched larvae per dfl (disease free layings). This is expressed as a percentage.

ii. Total larval period (TLP): Total period of the larval stage measured in days from the hatching of the larva from the eggs till the time of spinning the cocoon.

iii. Pupation Percentage (PP): The mature silkworm larvae pass into the pupal stage. Sometimes, some of the matured larvae are unable to stay alive inside the cocoon after cocoon formation. Thus this measure is the ratio of the number of cocoons with live pupae as a percentage of the total larvae. This is expressed as a percentage

iv. Cocoon yield (CY): The total weight of cocoons harvest per 100 dfls. This is measured in grams or Kilograms.

Some of the characteristics such as single cocoon weight and single shell weight can be easily measured. On the other hand, some of the other characteristics can be measured only through a detailed analysis and actual process of reeling.

These characteristics are important in determining the quality of the cocoons. Each of these characteristics has a role to play at different stages of the silk reeling as well as at further stages such as weaving. Consequently, the reelers prefer the cocoons, which exhibit the best levels of all these characteristics. Even though all these characteristics are measurable and quantifiable, there is no single quality index, which takes all these characteristics into account. Even in the cases where more than one characteristic is looked at for evaluating the quality, such an exercise is limited to about 3 or 4 characteristics.

Each of the above cocoon characteristics measure a different aspect of reeling and consequently there is a need to create a composite quality index. Such an index will enable the farmer as well as the reeler to settle a reasonable and appropriate price for the cocoons. The reelers will be in a position to offer an appropriate price with a complete knowledge of the quality of the cocoons. This paper attempts to develop a methodology for creating such a composite quality index.

2. DATA

The creation of a composite quality index for cocoons involves combining all the characteristics detailed earlier. The data with respect to each of these characteristics is obtained from the experiments carried out by the research stations of Central Silk Board (under the Ministry of Textiles, Government of India). The data involves hybrid silkworms (crosses between multi-voltine and bi-voltine strains of silkworms). Data from 1827 different hybrids with 10 replications each was collected. Thus there were 18270 observations on each of the 9 cocoon characteristics.

3. ANALYSIS

As a first step in developing a composite quality index, the relationship, if any, between the cocoon characteristics is analyzed. Pearson correlation coefficients between each pair of cocoon characteristics were calculated. The pair-wise correlations are presented in Table 1.

In case some of the characteristics exhibit strong correlation, one of these characteristics could be selected as a proxy to indicate or represent the quality with respect to the other, strongly correlated characteristics. If necessary, one of these characteristics could be selected as the dependent variable and the relationship could be quantified through regression analysis by selecting the other characteristics as explanatory variables. It can be seen from Table 1 that the two characteristics namely cocoon weight and shell weight are closely related. Such high correlation between these two characteristics is rather expected. Other than these two characteristics and the shell ratio, which is a derived characteristic (derived from cocoon weight and shell weight), there is low level of correlation between other variables. Even though few of these correlation coefficients are statistically significant, the values are not high enough to suggest close relationship between the characteristics. For example, the correlation coefficient between filament length and raw silk percentage is 0.5225. It implies that if one of these is taken as a dependent variable and the other as an independent variable, then only about 25 per cent of the variation in dependent variable is explained by the independent variable and the remaining 75 per cent is unexplained (using the concept of R2 which is the square of the simple linear correlation coefficient). This percentage is much lower in case of other pairs of characteristics. Such low values of the correlation coefficients imply that each of these characteristics are actually measuring different aspects of cocoon quality.

Another interesting finding is that the correlation coefficients between the post cocoon and pre-cocoon characteristics are very low. Table 2 presents the Pearson correlation coefficients between the pre-cocoon and post-cocoon characteristics.

The correlation coefficients presented in the above table show that there is very little relationship between the pre-cocoon and post-cocoon characteristics. In other words the four pre-cocoon characteristics do not have any impact on the quality of the cocoons. The quality characteristics develop during the growth phase of the larvae. Thus, it is important that extreme care is taken in the development of the larvae during the growth phase.

3.1 Composite quality index

It has been established in the previous section that each of the cocoon characteristics measures a different aspect that is important for the reeling industry. In addition, the correlation between these characteristics is rather low and hence none of these characteristics could be used a proxy for the overall quality of the cocoon. In addition, the units of measurement for different characteristics are different. It is rather difficult to establish any characteristic as overall important because each characteristic has an important role to play in the subsequent processing of the cocoons or the raw silk. As a result it is important to develop a composite index of quality for the cocoons. The basic requirements of such a composite index are:

i. The composite index should take into account various cocoon characteristics. The reason for this requirement has already been explained in the earlier sections.

ii. It should be possible to rank or grade the cocoons using the composite index. The composite index in itself is not the end. While the index provides an idea about the overall quality of the cocoons, the grading of cocoons into different categories will help the farmers and the reelers to arrive at the right price. Thus, ranking or grading is important in order to price the cocoons according to the quality

iii. It should be possible to translate the actual measurements of the cocoon characteristics into different cocoon grades without actually calculating the values of the composite index. The ultimate objective is to relate the overall quality with the price. It will facilitate the price fixation immensely if the cocoon characteristics can be used to identify the grade of cocoons without actually having to go through the process of calculating the composite index and then identify the corresponding grade.

The following methodology is proposed for the creation of the composite quality index (CQI) and then to grade the cocoons based on the CQI. After the grades are identified, discriminant analysis is used to map the cocoon characteristics directly on to the grades of cocoons.

It may be recalled that the two characteristics namely single cocoon weight and the shell weight are highly correlated. In addition, the shell ratio is derived from these two characteristics. Hence shell ratio is used to represent both these two characteristics. Thus, the 9 cocoon characteristics mentioned earlier are reduced to only 7. As a first step, the 18,270 observations are sorted in the ascending order of shell ratio. Then, these observations are binned into 5 groups using the equi-depth method. Even though it was desired to have equal depth in each bin, it was not possible to have exactly equal depth because of the overlap of common values of the characteristic across contiguous bins. After allowing for such overlaps, equi-depth binning was carried out. These 5 bins are labeled from 1 to 5 starting from the lowest SR values. Thus these bin labels are synonymous to ranking of the cocoons on a 5-point scale based on the SR values. Since higher SR values are more preferable, higher the ranking based on SR values, higher is the quality of the cocoons based on this characteristic. This process is repeated with each of the other 6 characteristics. Thus, at the end of the process, each observation (lot of cocoons) has a rank between 1 and 5 with respect to each of the 7 cocoon characteristics. These ranks are added to obtain a composite rank, which could be viewed as the composite quality index. Interestingly while the lowest value for the CQI is 7, as expected, none of the observations had an index of the highest possible value namely 35. This again substantiates the point that each of the characteristics is different from the others.

In order to make sure that the rankings of the cocoons based on different characteristics are as independent of each other as the characteristics themselves, a correlation analysis was carried out on these rankings. Since these are qualitative rankings, Spearman rank correlation coefficients were calculatred and presented in Table 3. The correlation coefficients in Table 3 indicate that the ranks based on each of the cocoon characteristics are highly correlated with the quality index. At the same time the correlation coefficients between the rankings are much closer to zero, with a few exceptions such as filament length and raw silk. In other words, while the individual rankings based each of the cocoon characteristics are unrelated to a large extent, the CQI is able to capture these individual rankings in the form of a single index.

The composite quality index is used to grade the cocoon lots into 3 different categories. It was decided to use only three categories because it is the general practice to classify the cocoon lots into low, medium and high quality at the cocoon markets. Here again, an attempt is made to create these three categories by binning the cocoons into equi-depth bins. Thus, all the 18,270 cocoon lots were graded into 3 categories namely low, medium and high quality.

The next step is to map the individual cocoon characteristics on to the three grades as defined by the CQI. It should be noted that the independent variables are the cocoon characteristics and these are measurable and continuous in nature. On the other hand, the dependent variable is the grade of the cocoons, which is categorical in nature. Needless to say, the dependent variable can take on only one of the three values, namely Low, Medium or High. Under these conditions, discriminant analysis is one of the best possible techniques for classifying the cocoons into the three grades based on various cocoon characteristics. Discriminant analysis involves deriving a "variate" which is a linear combination of a set of independent variables and the derived variate is used to discriminate between the pre-defined groups (Hair et al, 2003).

3.2 Application of Discriminant Analysis

When there are only two groups, a single discriminant function can be derived. On the other hand when there are three groups, two discriminant functions can be derived. The first function has the largest ratio of between groups to within groups sums of squares. The second function is uncorrelated with the first and has the second largest ratio. The discriminant functions were fitted using the cocoon grade (Low, Medium and High) as the dependent variable and the various cocoon characteristics as the independent variable, using the step-wise method of SPSS. The standardized coefficients of the discriminant functions are presented in Table 4.

The standardized coefficients are used when the variables are standardized with a mean of 0 and variance of 1. It is often suggested that the value of the standardized coefficient can be interpreted as the relative importance of the particular variable. In that sense, the shell ratio, filament length and reelability are the major determinants of the grade. For practical use, it is convenient to use the unstandardized coefficients. These coefficients are multipliers of the variable when they are expressed in their original values. The unstandardized coefficients are presented in Table 5. The significance level of the discriminant functions is determined by the value of Wilk's Lambda. In this case the value of Wilk's Lambda was 0.191 with a significance level of 0.000. This implies that the mean values of the three groups (cocoon grades) are significantly different from each other.

Using the above discriminant function and the prior probabilities, each of the cocoon lots (each observation) is classified into one of three grades. Since there are two discriminant functions, two different scores are calculated and these two values are considered simultaneously for classifying each lot into the three grades. This classification is achieved by the territorial map as shown in Figure 1. In Figure 1, the value of the "variate" calculated based on discriminant function 1 is plotted on the X-axis and that based on the discriminant function 2 is plotted on the Y-axis. The corresponding point on the XY space is located. In this figure, the area between the origin and the line marked by a series of "1s" denotes the territory of the low quality cocoons. Similarly the area to the right of the line marked by a series of "3s" denotes the territory of the high quality cocoons. This predicted grade is compared with the actual grade observed to estimate the predictive efficiency of the model. The results of the analysis are presented in Table 6.

[FIGURE 1 OMITTED]

On average, the discriminant function was able to predict more than 86 per cent of cases correctly. The best performance was with respect to the medium grade cocoons where the prediction was correct almost to 90 per cent. Similarly, the function was able to predict the high-grade cocoons correctly to about 88 per cent. Even among the low-grade cocoons, the misclassification was to the extent of only 18 per cent.

4. CONCLUSION

The quality of silk cocoons depends on many characteristics and each of these measure different aspects of quality of cocoons. Each of these aspects are important at different stages of further processing such as reeling, weaving etc. But, there is no single measure for determining the overall quality of the cocoons. Consequently, the cocoons are priced based on just one or two of the characteristics. It is important that the price of cocoons should be based on the overall quality of cocoons. Under such circumstances, it is necessary to develop a composite quality index for the cocoons. The composite quality index as proposed in this paper is tested using discriminant analysis. It is possible to grade the cocoons into three categories namely Low, Medium and High quality based on the composite quality index. Using the coefficients of the discriminant function, a given cocoon lot can be easily mapped directly on to one of the three grades. The level of misclassification is only about 15 per cent. Once the grade of the cocoons is identified using the discriminant function, the price of the cocoons can be determined by the buyer and the seller with very little ambiguity. This process will be helpful to both the buyer and seller since each has a clear idea of the overall quality of the cocoons and not based on just one or two characteristics.

TABLE 1: PEARSON CORRELATION COEFFICIENTS BETWEEN COCOON
CHARACTERISTICS

           SCW      SW       SR       FL       FS       RY

SCW      1.0000   0.8787   0.1817   0.7061   0.5452   0.1252
SW       0.8787   1.0000   0.6229   0.7266   0.5386   0.0786
SR       0.1817   0.6229   1.0000   0.3330   0.2333   -0.0309
FL       0.7061   0.7266   0.3330   1.0000   0.3483   0.4174
FILSIZE  0.5452   0.5386   0.2333   0.3483   1.0000   0.1343
RY       0.1252   0.0786   -0.0309  0.4174   0.1343   1.0000
RS%      0.3066   0.3985   0.3317   0.5225   0.4419   0.4153
NEAT     0.0005   0.0251   0.0456   0.1181   -0.0420  0.1173
BL       -0.2560  -0.1479  0.1159   -0.2994  0.0461   -0.1754

           RS      NEAT      BL

SCW      0.3066   0.0005   -0.2560
SW       0.3985   0.0251   -0.1479
SR       0.3317   0.0456   0.1159
FL       0.5225   0.1181   -0.2994
FILSIZE  0.4419   -0.0420  0.0461
RY       0.4153   0.1173   -0.1754
RS%      1.0000   0.1907   -0.0064
NEAT     0.1907   1.0000   -0.1251
BL       -0.0064  -0.1251  1.0000

TABLE 2: CORRELATION COEFFICIENTS BETWEEN PRE-COCOON AND POST-COCOON
CHARACTERISTICS

                                  Pre-cocoon Characteristics

                                        Total
                             Hatching  Larval   Population  Cocoon
Post-cocoon Characteristics  per cent  Period    Per cent    Yield

Single Cocoon Weight (SCW)   -0.0254   -0.0078   -0.0128    0.1165
Shell Weight (SW)            -0.0110   0.0154    -0.0100    0.1101
Shell Ratio (SR)              0.0164   0.0437     0.0004    0.0259
Filament Length (FL)         -0.0302   0.0036     0.0046    0.0708
Filament Size (FS)           -0.0143   0.0104     0.0039    0.0386
Reelabilit (RY)              -0.0221   -0.0072    0.0108    0.0384
Raw silk (RS)                -0.0158   0.0357     0.0015    -0.0240
Neatness (NEAT)               0.0030   0.0303     0.0047    -0.0138
Boil Loss (BL)                0.0123   0.0069     0.0021    -0.0339

TABLE 3: SPEARMAN RANK CORRELATIONS BETWEEN
RANKS BASED ON VARIOUS COCOON CHARACTERISTICS

         SR        FL        FS        RY

SR      1.0000    0.3108    0.2782    0.0115
FL      0.3108    1.0000    0.4245    0.4457
FS      0.2782    0.4245    1.0000    0.1751
RY      0.0115    0.4457    0.1751    1.0000
RS      0.3133    0.5452    0.4474    0.4348
NEAT    0.0473    0.1002   -0.0734    0.0989
BL     -0.0738    0.3739    0.0612    0.2275
CQI     0.4758    0.8038    0.5799    0.6011

         RS       NEAT       BL        CQI

SR      0.3133    0.0473   -0.0738    0.4758
FL      0.5452    0.1002    0.3739    0.8038
FS      0.4474   -0.0734    0.0612    0.5799
RY      0.4348    0.0989    0.2275    0.6011
RS      1.0000    0.1171    0.0582    0.7329
NEAT    0.1171    1.0000    0.1041    0.3496
BL      0.0582    0.1041    1.0000    0.4398
CQI     0.7329    0.3496    0.4398    1.0000

TABLE 4: STANDARDIZED COEFFICIENTS OF THE DISCRIMINANT FUNCTION

                      Function

Characteristic       1        2

SCW                 .360    5.347
SW                 -.301   -5.965
SR                  .637    2.989
FL                  .518    -.321
FS                  .413    -.402
RY                  .439    -.018
RS                  .350     .685
NEAT                .383     .119
BL                  .488    -.016

TABLE 5: UNSTANDARDIZED COEFFICIENTS OF THE DISCRIMINANT FUNCTION

                      Function

Characteristic       1        2

SCW                1.506   22.369
SW                 -.054   -1.075
SR                  .337    1.579
FL                  .004    -.003
FS                 1.406   -1.370
RY                  .106    -.004
RS                  .104     .203
NEAT                .058     .018
BL                 -.209    -.007
(Constant)       -25.730  -35.135

TABLE 6: COMPARISON BETWEEN THE ORIGINAL AND PREDICTED
CLASSIFICATION BASED ON THE DISCRIMINANT FUNCTION

                         Predicted Group Membership

                                Cocoon Grade

Cocoon Grade                Low    Medium   High

                 Low        82.21   17.79    0.00
Original         Medium      4.21   89.31    6.48
                 High        0.00   12.17   87.83

REFERENCES

Anon, Manual on bi-voltine Silk Reelinq, JICA Bi-voltine Sericulture Technology Development Project, CSTRI, Central Silk Board, Bangalore, 1996.

Hair, Joseph F., R. E. Anderson, R. L. Tatham and W. C. Black, Multivariate Data Analysis, 5th Edition, Pearson Education (Singapore) Pte Ltd, 2003

Nakajima, K., Report on Bivoltine Silk Reeling Technology, International Sericulture Expert Group, Indian Bivoltine Sericulture Development Project, Central Silk Board, Bangalore, 1999

Shimazaki, A., Filature Technology Lecture: Published by Sericulture Association, Tokyo, 89-93, 1964

Somashekar, T.H., Report on the visit to Sericultural Areas in China Central Silk Board, Bangalore, 1999

Sonwalkar, "Relationship between Shell Percentage and Renditta/Raw Silk Percentage", Indian Silk, XXI, 14-16, 1982

Sonwalkar, Handbook on Silk Technology, Wiley Eastern ltd., New Delhi, 1993

Vasumathi B.V., An Analytical Study of the Silk Reeling Operations in Karnataka Unpublished Ph. D. Dissertation, Department of Management Studies, Indian Institute of Science, Bangalore, 2000

Yamamoto T., Report on Silkworm Rearing, International Sericulture Expert Group, Indian Sericulture Technology Development Project, Central Silk Board, Bangalore, 1999

Author Profiles:

Dr. Vishnuprasad Nagadevara earned his Ph D from Iowa State University, Ames Iowa. He is currently Professor in the Quantitative Methods and Information Systems Area at the Indian Institute of Management Bangalore. His current research interests are Data Mining, Application of Management Techniques to Education and Entrepreneurship.