**Abstract**

A novel statistical approach for multiple-stream processes is proposed in this manuscript. As important as quality control in manufacturing is, hypothesis tests are an important part of it if utilized and constructed the most logically to evaluate and decide on a special matter in a production line or a production machine. The proposed statistical approach is explained in detail in a spinning mill having 20 spinning frames. The spinning frames are adjusted according to customers' orders and to the technology of spinning frames first. Then, the result of that adjustment is controlled statistically by means of hypothesis testing, *χ*<sup>2</sup> , *t*-test, and F statistics are used. Later, they are pooled one by one, and at the end, all 20 spinning frames are considered as one machine producing the same yarn, the same variance of yarn count, and the same yarn count. Performed literature review claims that control charts are appropriate for multiple-stream processes. But, the application of this proposed statistical approach guarantees that production starts with correct adjustments on machines, and control charts become more sensitive to the assignable causes. The application area of this proposed statistical approach is wide, leading to higher quality in products, a requirement that is in demand more every day.

**Keywords:** textile engineering, hypothesis tests, spinning mill, spinning frame, chi-square statistics, *t*-tests, F statistics, pooled estimator of sigma, pooled estimate of standard deviation, pooled estimator of variance, pooled *t*-Test, distribution, multiple-stream processes

### **1. Introduction**

Quality is demanded by every customer in the products they purchase in this era of science and technology, claiming for better products and services alike. This demand produces pressure on the manufacturers to conform to customers' wishes by offering products and/or services incorporating increased quality levels, applying quality control methods, practicing statistical quality control, etc. Manufacturers intensely control and improve the quality of their products in order to make them better while also aiming at establishing a competitive edge.

Textiles are regarded as fundamental items in everyday life. They are indeed used in every field of daily life like apparel, home textiles, technical textiles (automotive, aerospace, geological, agriculture, civil, medical, sport, packaging, protective, military, art, etc.). Similar to every engineering branch, quality is the main requirement in textile engineering. The only way to achieve this is the application of quality control tools which are mostly applied in every step of textile production in order to fulfill the demands of consumers.

The main steps in textile manufacturing are yarn production, weaving, knitting, and ready-wear; besides nonwovens, texturing, finishing, dyeing, printing, etc. Yarn production is the primary step among these because if a good yarn is produced at the beginning the rest of the steps will probably end up likewise good. Good yarn provides the properties required for the next step, and for any succeeding step thereafter until the end product is reached, namely the one used in daily life. In a reverse pattern, first, the usage area of that special textile product to be manufactured has to be decided on as well as determining the requirements of properties in that special unit. Then one step backwards, weaving or knitting-specific quality properties are determined, followed by the properties of yarn to meet the properties of fabric. Finally, the latter are determined together with the fibers to be used and thus, production starts. It is very important to keep the quality properties of yarn correct and stable in order for the rest of the steps to be good. This is why quality control tools have to be applied in yarn production. Besides, technology in machinery is another grand field where huge improvements are achieved so as to manufacture products with the aimed properties. Textile machinery is an area where many technological improvements are successfully applied, yielding production of yarn with better properties.

Textile manufacturing is a multiple-stream process where one operation is usually done by more than one machine. The product of every machine is mixed into one lot. In literature, it is stated that in processes consisting of several machines producing the same material which pool their output into a common stream, control charts are appropriate to use in order to keep quality under control. In this case, machines producing the same material form a rational subgroup. Separate control charts are advised for each rational subgroup, each individual machine, or sometimes even for the different heads on the same machine. Therefore, the proper selection of samples is very important within the rational subgroup concept; the process is to be consistent and careful by extracting as much useful information as possible from the evaluation of the control charts. Even more, simultaneous monitoring of all streams is impractical when the streams are large in number, identical, and independent. Also, control charts are sensitive to assignable causes that affect the uniformity across the streams and between-stream variability [1–7].

The main concept of control charts is: Sampling the material of which the property/properties to be investigated, testing the property/properties, obtaining the results, plotting the values on the control charts, and interpreting the charts. Production is under control while the plot falls between the upper and lower control limits. If not, then the precautions needed are taken and adjustments to the machines are done. Not only one machine produces the same product but there may be more than one machine producing the same material which will be mixed and shipped into one lot, and every machine producing the same material will have to do so. The customer does not need to know which machine produced which constitutes the lot; it is the responsibility of the factory to ship a lot containing the same properties in every piece [8].

In this manuscript, it is worth noting at this point that before constructing the control charts for rational subgroups, the adjustments on the subgroups have to be

#### *Practicing Hypothesis Tests in Textile Engineering: Spinning Mill Exercise DOI: http://dx.doi.org/10.5772/intechopen.105643*

controlled statistically first. The subgroups are machines in this case. Control charts may keep the control limits after the correct adjustments on the machines are successfully done. It is thought that controlling the adjustments of the machines to produce the right material is different than keeping it under control with control charts. If the adjustments of the machines are correct at the beginning, then the purpose of the control charts will only be sensitive to assignable causes. Otherwise, it may be as if it is expected too much from the control charts; however, in this proposed novel statistical approach the purposes are separated and may help to understand processes better and keep quality under control. When quality will be set at the beginning and tested statistically then control charts will help to carry it forward in a stable manner. In this study, a different approach will be presented which is applying hypothesis tests to the adjustment of the multiple-stream machines prior to them starting production. A novel method for this kind of statistical control is proposed and explained in detail based on an example of a textile engineering spinning mill.

Hypothesis testing is a process of drawing conclusions on the collected data of statistical testing and is a specific approach for testing means or averages of that data. The purpose of statistical inference is to draw conclusions about a population on the basis of data obtained from a sample of that population. Hypothesis testing evaluates the strength of evidence from the sample and gives the basis to determine the relation to the population. Hypothesis testing equally indicates the chance about how reliably the observed results in a sample can be extrapolated to the larger population of collected samples. A specific hypothesis is formulated, the data from the sample is evaluated and if they support the specific hypothesis a statistical inference about the population is reached. Hypothesis testing is a dominant approach for data analysis in many fields of science [9].

In literature, it is discussed that there is a close connection between hypothesis testing and control charts. It is considered that if the obtained value of *x* is plotted and values fall in-between the control limits then it is expressed that the process mean is in control, and it is equal to a value *μ*0. If *x* falls out of the upper or the lower control limits then it will have a value other than *μ*0, it is concluded that the control chart is a kind of hypothesis testing and shows that the process is under statistical control. If the plots are in-between the control limits, this means the hypothesis is not rejected; if they are out of the control limits, this means the hypothesis is rejected [10].

On the other hand, there are some differences between hypothesis tests and control charts. The validity of assumptions, like the form of the distribution, independence, etc., are tested in hypothesis testing but not in control charts. Instead, the departures from *x* are seen in control charts so that the process variability may be reduced. There may be assignable causes in production and they result in different types of shifts in the process parameters. An assignable cause can result in an increase or a decrease to a new value but return quickly. It can have ups and downs in-between the control limits, and can shift to a new value but remain there; this is called a sustained shift. It is recognized in literature that only the sustained shift fits the statistical hypothesis testing model.

This chapter suggests that adjustment of the machines in a multiple-stream should be done with hypothesis testing at the beginning and then continuing production should be observed with control charts so that the quality will be under control at the beginning and will be kept stable during production. This proposed method will be done just at the beginning of production for once in order to confirm that the adjustments to produce the same lot are the same all throughout the lot, as well as considering that every centimeter of yarn will exactly be the same in the tons of guaranteed

yarn production. Then, while the production continues the control charts will monitor that quality is kept stable. This novel approach of a statistical control method will be explained in detail given in an example of a textile engineering spinning mill. In this case, the type of the yarn, the properties of the yarn, the type of fibers used to produce the yarn will not be considered except for yarn count. Yarn count property will be mentioned in the proposed hypothesis testing method. One may bear in mind that the same application can be done for every property of yarn like twist, breaking strength, breaking elongation, elasticity, abrasion resistance, hairiness, unevenness, imperfection (thick place, thin place, neps), etc.
