Measures of central tendency like process average gives an idea about average staple length of fibre produced in a continuous or batch wise process. Coefficient of variation (CV) of the process signifies about the process control. On the other hand, analysis of time series is helpful in estimating the future production based on the past records. Measures of dispersion such as standard deviation and CV are useful in comparing the performance of two or more fibre-producing units or processes. Significance tests can also be applied to investigate whether significant difference exists between the batches for means or standard
deviations. Analysis of variance can be applied for studying the effect of parameters of fibre production and methods of polymer dissolving.
Textile Testing of Fiber Yarn and Fabrics
Results analysis in textile testing without the applications of statistical tools will be meaningless. In other words every experiment in textile testing include the use of statistical tools like average calculation, computation of SD, CV and application of tests of significance (t-test, z-test and f-test) or analysis of variance (one way, two way or design of experiments). Populations can be very well studied by normal or binomial or Poisson’s distributions. Random sampling errors are used in studying about the population mean and SD at 95% and 99% level of confidence. Application geometric mean for finding out the overall flexural rigidity or Go has an important role in fabric selection for garment manufacture.
A special mention is made in determination of fibre length by bear sorter where all the measures of central tendency and dispersion (mean length, modal length quartile deviation, etc., in the form of frequency distribution) are computed to understand about the cotton sample under consideration for testing its potential in yarn manufacture. On the other hand ball sledge sorter uses weight distribution from which mean and SD are computed. In the case of cotton fibres, the development of cell wall thickening commonly referred as “Maturity” concept can be very well determined using normal distribution and confidence intervals. Several properties are tested for different packages produced from the same material or from the same frame by applying significance tests. Effect of instruments and variables for different types of samples can be
very well studied by using ANOVA. All the fabric properties tested on a single instrument or different instrument can be understood by using design of experiments. In one of the research applications, which include the testing of low stress mechanical properties for nearly 1000 fabrics are studied by ‘Principle Bi component analysis or Bi plot’. Measures of dispersion like coefficient of variation and percentage mean deviation are very much used in evenness measurement.
There are several stages involved in the cotton yarn production. When fibres are mixed and processed through blow room, within and between lap variations are studied by computing mean, SD and CV lap rejection, and production control are studied by p and x charts. Average measure is used to find the hank of silver in carding, draw frame, combing and average hank of roving in roving frame and average count at ring frame. Generally the spinning mill use ‘average count’ as the count specification if it is producing 4–5 counts. On the other hand the weaving section uses ‘resultant count’ which is nothing but the harmonic mean of the counts produced. Control charts are extensively used in each and every process of yarn production (for example, the process control with respect to thin places, neps, etc.). Application of probability distributions like Poisson, Weibull and binomial for various problems in spinning is found very much advantageous to understand the end breakage concept. In ring spinning section several ring bobbins are collected and tested for CSP and difference between the bobbins and within the bobbins is studied using ‘range’ method. In cone winding section the process control can be checked either by using control chart for averages or chart for number defectives.
Design of experiments such as latin square design or randomized block design can be used to identify the effect of different size ingredients on wrap breakages on different looms in fabric formation. Most of the suiting fabric constructions involve the use of double yarn which is nothing but the harmonic mean of different counts. Poisson’s and normal distribution can be applied for loom shed for warp breakages. Using statistical techniques the interference loss can also be studied in loom shed. Various weaving parameters such as loom speed, reed and pick can be correlated with corresponding fabric properties and are interpreted in terms of loom parameters. Control charts are used to study the control of process/product quality in fabric production also. For example, selection of defective cones in a pirn winding from a lot (fixed population) or in a production shift n p and p charts are used. The width of the cloth and its control can be understood by x and defectives per unit length and their control is understood by c charts. The testing process includes determination of average tensile strength (and single thread strength also) and the corresponding CV%.
Chemical processing and Garment Production
The scope of statistics is unlimited. For example the effect of n number washes (identical conditions) on m fabrics on a particular fabric property can be easily found by either tests of significance or analysis of variance. Similarly the effect of different detergents on fabric types can be investigated by two-way analysis of variance. Similarly different types of fabrics and the effect of sewing conditions can be studied by ANOVA.
In garment production the control of measurements and its distribution can be well understood by control and polar charts.