In 2015 the global fibre consumption was 96.7 million tonnes, which is an increase of 3.1% from the year before. Our high textile consumption has led to an increasing demand of raw materials and generation of textile waste. Only in Europe, a total amount of 4.3 million tonnes of apparel waste each year is sent to either incineration or landfills. Approximately 50% of the clothes we discard and donate are composed of cotton. In the future, the cotton production is predicted to stagnate since the world population is increasing and arable land to greater extent will be needed for food production. Thereby, it is important that we utilize the cotton waste generated. One of the most commonly used processes for recycling textile waste is the shredding process. In this method, textile waste is shredded back into their constituent fibres. The drawback with the shredding process is that the fibre length is reduced. The fibre length is an important property since it has a high influence on textile processing such as yarn production and final product quality. The aim of this thesis was to investigate how post-consumer cotton garments with different degree of wear affects the fibre length obtained in the shredding process. This was performed by analysing the input fibre length as well as the output fibre length. Additionally, several parameters were investigated: fabric construction and yarn structure. Degree of wear was categorized into two levels: low and high degree of wear. The fabric constructions used in this study were single-jersey and denim. The yarn structure were analysed in terms of yarn count, yarn twist and manufacturing process.  The result showed that the fibre length before shredding was statistically significant longer for the materials with low degree of wear compared to high degree of wear. After shredding, it was shown that the fibre length reduction was lower for the materials with high degree of wear. This indicates that longer fibres give higher fibre length reduction. In addition, it was found that finer yarn gives higher fibre length reduction. The result also showed that the yarn manufacturing process has a great influence on the ease of shredding and the fibre length obtained in the end.  Based on the result in this thesis it can be concluded that the shredding process needs to be improved in order to preserve the fibre length. The area of post-consumer textile waste is complex and the result showed that there is many underlying parameters that need to be taken into account to further develop the shredding process.

<p>The motivating forestry background for this thesis is the need for fast, non-destructive, and cost-efficient methods to estimate fibre length distributions in standing trees in order to evaluate the effect of silvicultural methods and breeding programs on fibre length. The usage of increment cores is a commonly used non-destructive sampling method in forestry. An increment core is a cylindrical wood sample taken with a special borer, and the methods proposed in this thesis are especially developed for data from increment cores. Nevertheless the methods can be used for data from other sampling frames as well, for example for sticks with the shape of an elongated rectangular box.</p><p>This thesis proposes methods to estimate fibre length distributions based on censored mixture data from wood samples. Due to sampling procedures, wood samples contain cut (censored) and uncut observations. Moreover the samples consist not only of the fibres of interest but of other cells (fines) as well. When the cell lengths are determined by an automatic optical fibre-analyser, there is no practical possibility to distinguish between cut and uncut cells or between fines and fibres. Thus the resulting data come from a censored version of a mixture of the fine and fibre length distributions in the tree. The methods proposed in this thesis can handle this lack of information.</p><p>Two parametric methods are proposed to estimate the fine and fibre length distributions in a tree. The first method is based on grouped data. The probabilities that the length of a cell from the sample falls into different length classes are derived, the censoring caused by the sampling frame taken into account. These probabilities are functions of the unknown parameters, and ML estimates are found from the corresponding multinomial model.</p><p>The second method is a stochastic version of the EM algorithm based on the individual length measurements. The method is developed for the case where the distributions of the true lengths of the cells at least partially appearing in the sample belong to exponential families. The cell length distribution in the sample and the conditional distribution of the true length of a cell at least partially appearing in the sample given the length in the sample are derived. Both these distributions are necessary in order to use the stochastic EM algorithm. Consistency and asymptotic normality of the stochastic EM estimates is proved.</p><p>The methods are applied to real data from increment cores taken from Scots pine trees (Pinus sylvestris L.) in Northern Sweden and further evaluated through simulation studies. Both methods work well for sample sizes commonly obtained in practice.</p>

The motivating forestry background for this thesis is the need for fast, non-destructive, and cost-efficient methods to estimate fibre length distributions in standing trees in order to evaluate the effect of silvicultural methods and breeding programs on fibre length. The usage of increment cores is a commonly used non-destructive sampling method in forestry. An increment core is a cylindrical wood sample taken with a special borer, and the methods proposed in this thesis are especially developed for data from increment cores. Nevertheless the methods can be used for data from other sampling frames as well, for example for sticks with the shape of an elongated rectangular box. This thesis proposes methods to estimate fibre length distributions based on censored mixture data from wood samples. Due to sampling procedures, wood samples contain cut (censored) and uncut observations. Moreover the samples consist not only of the fibres of interest but of other cells (fines) as well. When the cell lengths are determined by an automatic optical fibre-analyser, there is no practical possibility to distinguish between cut and uncut cells or between fines and fibres. Thus the resulting data come from a censored version of a mixture of the fine and fibre length distributions in the tree. The methods proposed in this thesis can handle this lack of information. Two parametric methods are proposed to estimate the fine and fibre length distributions in a tree. The first method is based on grouped data. The probabilities that the length of a cell from the sample falls into different length classes are derived, the censoring caused by the sampling frame taken into account. These probabilities are functions of the unknown parameters, and ML estimates are found from the corresponding multinomial model. The second method is a stochastic version of the EM algorithm based on the individual length measurements. The method is developed for the case where the distributions of the true lengths of the cells at least partially appearing in the sample belong to exponential families. The cell length distribution in the sample and the conditional distribution of the true length of a cell at least partially appearing in the sample given the length in the sample are derived. Both these distributions are necessary in order to use the stochastic EM algorithm. Consistency and asymptotic normality of the stochastic EM estimates is proved. The methods are applied to real data from increment cores taken from Scots pine trees (Pinus sylvestris L.) in Northern Sweden and further evaluated through simulation studies. Both methods work well for sample sizes commonly obtained in practice.