This paper deals with CUSUM tests based on grouped or classified observations. The computation of average run length is reduced to that of solving of a system of simultaneous linear equations. Moreover a corresponding approximation based on the Wald approximations for characteristics of sequential likelihood ratio tests is presented. The effect of grouping is investigated with a CUSUM test for the mean of a normal distribution based on F-optimal grouping schemes. The considered example demonstrates that hight efficient CUSUM tests can be obtained for F-optimal grouping schemes already with a small number of groups.

This paper deals with CUSUM tests based on grouped or classified observations. The computation of average run length is reduced to that of solving of a system of simultaneous linear equations. Moreover a corresponding approximation based on the Wald approximations for characteristics of sequential likelihood ratio tests is presented. The effect of grouping is investigated with a CUSUM test for the mean of a normal distribution based on F-optimal grouping schemes. The considered example demonstrates that hight efficient CUSUM tests can be obtained for F-optimal grouping schemes already with a small number of groups.

This paper deals with CUSUM tests for monitoring of intensity parameter of a Poisson process if this process can be observed in a restricted manner only at pregiven equidistant time points. In this case the process can be monitored by means of a CUSUM test for the parameter of a corresponding Poisson distribution. For rational reference parameter values the computation of average run length is reduced to that of solving of a system of simultaneous linear equations. The performance of obtained CUSUM tests is discussed by means of corresponding examples.

Double sampling procedure is adapted from a statistical branch called acceptance sampling. The first Shewhart-type double sampling monitoring scheme was introduced in the statistical process monitoring (SPM) field in 1974. The double sampling monitoring scheme has been proven to effectively decrease the sampling effort and, at the same time, to decrease the time to detect potential out-of-control situations when monitoring the location, variability, joint location and variability using univariate or multivariate techniques. Consequently, an overview is conducted to give a full account of all 76 publications on double sampling monitoring schemes that exist in the SPM literature. Moreover, in the review conducted here, these are categorized and summarized so that any research gaps in the SPM literature can easily be identified. Next, based on the knowledge gained from the literature review about the existing designs for monitoring the process mean, a new type of double sampling design is proposed. The new charting region design lead to a class of a control charts called a side-sensitive double sampling (SSDS) monitoring schemes. In this study, the SSDS scheme is implemented to monitor the process mean when the underlying process parameters are known as well as when they are unknown. A variety of run-length properties (i.e., the 5th, 25th, 50th, 75th, 95th percentiles, the average run-length (𝐴𝑅𝐿), standard deviation of the run-length (𝑆𝐷𝑅𝐿), the average sample size (𝐴𝑆𝑆) and the average extra quadratic loss (𝐴𝐸𝑄𝐿) metrics) are used to design and implement the new SSDS scheme. Comparisons with other established monitoring schemes (when parameters are known and unknown) indicate that the proposed SSDS scheme has a better overall performance. Illustrative examples are also given to facilitate the real-life implementation of the proposed SSDS schemes. Finally, a list of possible future research ideas is given with hope that this will stimulate more future research on simple as well as complex double sampling schemes (especially using the newly proposed SSDS design) for monitoring a variety of quality characteristics in the future. / Statistics / M. Sc. (Statistics)

自舒華特發明以管制圖監測製程以來，管制圖在工程的應用日趨重要。在特殊工程中，一個高效的管制圖方法尤為重要。基於此項事實，在文獻中各式各樣的管制圖層出不窮且技術日益完善。但傳統管制圖往往受制于常態分佈，因此在無母數管制圖研究方向仍有大量工作值得探討。於是本文在母體分佈未知情況下，推廣Yang (2015)的無母數平均值管制圖方法建立變動樣本指数加权移动平均管制圖，VSS EWMA-np control chart。新的管制圖將變動樣本大小（VSS）和指數加權移動平均（EWMA）方法結合建立一種新的管制圖方法，並用這種新型管制圖監測未知分佈母體的平均值是否發生變動。而為了監測平均數是否發生變化，也為了減少抽樣損失，本文評估管制圖監測效力的指標為管制圖偵測出異常訊息所需抽樣的樣本數期望值（EN）、平均連串長度（ARL）和平均觀測值總數（ANOS）。從本文的比較結果看出新的變動樣本指數加權移動平均管制圖擁有更好的失控偵測力。 / Since Shewhart invention control chart monitor the process, control charts are increasingly important in engineering applications. In special projects, an efficient control chart is especially important. Based on this fact, the various kinds of control charts in the literature are not poor and the technology is improving. However, traditional control charts are often subject to normal distribution, so there is still a lot of work to be discussed in the direction of the study of non-parametric control charts. So in this paper under unknown distribution in the matrix, Yang (2015) established on the basis of the theory of a non-parametric method of control chart - Exponentially Weighted Moving Average Control Chart with Variable Sampling Sizes (VSS EWMA - np control chart). New control chart will change the sample size (VSS) and exponential weighted moving average (EWMA) method to establish a new control chart, and use new control chart for monitoring the mean of unknown distribution matrix is changed. And whether to monitor the average changes in order to reduce the loss of sampling, this paper mainly evaluate control chart for monitoring the effectiveness of the statistics for the expected value of the sample size (EN), the average run length (ARL) and the average number of observations to signal (ANOS). From the comparison shown in this paper, the new control chart has better detection.

This thesis describes Burrow-Wheeler compression algorithm. It focuses on each part of Burrow-Wheeler algorithm, most of all on and entropic coders. In section are described methods like move to front, inverse frequences, interval coding, etc. Among the described entropy coders are Huffman, arithmetic and Rice-Golomg coders. In conclusion there is testing of described methods of global structure transformation and entropic coders. Best combinations are compared with the most common compress algorithm.

Signal compression is daily-used tool for memory capacities reduction and for fast data communication. Methods based on wavelet transform seem to be very effective nowadays. Signal decomposition with a suitable bank filters following with coefficients quantization represents one of the available technique. After packing quantized coefficients into one sequence, run length coding together with Huffman coding are implemented. This thesis focuses on compression effectiveness for the different wavelet transform and quantization settings.

The first goal of diploma thesis is to study the basic principles of video signal compression. Introduction to techniques used to reduce irrelevancy and redundancy in the video signal. The second goal is, on the basis of information about compression tools, implement the individual compression tools in the programming environment of Matlab and assemble simple model of the video codec. Diploma thesis contains a description of the three basic blocks, namely - interframe coding, intraframe coding and coding with variable length word - according the standard MPEG-2.

[pt] Os gráficos de controle de S(2) são ferramentas fundamentais amplamente utilizados para monitoramento da dispersão do processo em aplicações de CEP. O desempenho na Fase II de diferentes tipos de gráficos de controle, incluindo o gráfico de S(2), com parâmetros desconhecidos pode ser significativamente diferente do desempenho nominal por causa do efeito da estimação de parâmetros. Nos anos mais recentes, este efeito tem sido abordado predominantemente sob a perspectiva condicional, que considera a variabilidade das estimativas de parâmetros obtidas a partir de diferentes amostras de referência da Fase I em vez das típicas medidas de desempenho baseadas na distribuição marginal (incondicional) do número de amostras até o sinal (Run Length-RL), como sua média. À luz dessa nova perspectiva condicional, a análise do desempenho da Fase II e do projeto de gráficos de controle é frequentemente realizada usando o Exceedance Probability Criterion para a média da distribuição condicional do RL (CARL 0), isto é, o critério que garante uma alta probabilidade de que CARL 0 seja pelo menos um valor mínimo tolerado e especificado. Intervalos de tolerância para variâncias amostrais são úteis quando o maior interesse está focado na precisão dos valores de uma característica de qualidade, e podem ser usados na tomada de decisões sobre a aceitação de lotes por amostragem. Motivado pelo fato de que estes intervalos, especificamente no caso dos intervalos bilaterais, não foram abordados na literatura, limites bilaterais de tolerância exatos e aproximados de variâncias amostrais são derivados e apresentados neste trabalho. A relação matemática-estatística entre o intervalo de tolerância para a variância amostral e o Exceedance Probability (função de sobrevivência) da CARL 0 do gráfico de S(2) com parâmetro estimado é reconhecida, destacada e usada neste trabalho de tal forma que o estudo do desempenho na Fase II e o projeto desse gráfico pode ser baseado no intervalo de tolerância para a variância amostral, e vice-versa. Os trabalhos sobre o desempenho e projeto do gráfico de S(2) com parâmetro estimado focaram-se em apenas uma perspectiva (incondicional ou condicional) e consideraram somente um tipo de gráfico (unilateral superior ou bilateral). A existência de duas perspectivas e dois tipos de gráficos poderia ser confusa para os usuários. Por esse motivo, o desempenho e o projeto do gráfico de S(2) de acordo com essas duas perspectivas são comparados, considerando cada tipo de gráfico. Da mesma forma, esses dois tipos de gráficos também são comparados para cada perspectiva. Alguns resultados importantes relacionados ao projeto do gráfico de S(2), que ainda não estão disponíveis na literatura, foram necessários e obtidos neste trabalho para fornecer um estudo comparativo completo que permita aos usuários estarem cientes das diferenças significativas entre as duas perspectivas e os dois tipos de gráficos para tomar decisões informadas sobre a escolha do projeto do gráfico de S(2). Além disso, dado que a distribuição condicional do RL é em geral fortemente enviesada à direita, a mediana e alguns quantis extremos desta distribuição são propostos como medidas de desempenho complementares à sua tradicional média (CARL 0). Finalmente, algumas recomendações práticas são oferecidas. / [en] The S(2) control charts are fundamental tools widely used to monitor the process dispersion in applications of Statistical Process Monitoring and Control. Phase II performance of different types of control charts, including the S(2) chart, with unknown process parameters may be significantly different from the nominal performance due to the effect of parameter estimation. In the last few years, this effect has been addressed predominantly under the conditional perspective, which considers the variability of parameter estimates obtained from different Phase I reference samples instead of the traditional unconditional performance measures based on the marginal (unconditional) run length (RL) distribution, such as the unconditional average run length. In light of this new conditional perspective, the analysis of the Phase II performance and design of control charts is frequently undertaken using the Exceedance Probability Criterion for the conditional (given the parameter estimates) in-control average run length (CARL 0), that is, the criterion that ensures a high probability that the CARL 0 is at least a specified minimum tolerated value. Tolerance intervals for sample variances are useful when the main concern is the precision of the values of the quality characteristic and then they can be used in decision-making on lot acceptance sampling. Motivated by the fact that these tolerance intervals, specifically in the case of the two-sided intervals, have not been addressed in the literature so far, exact and approximate two-sided tolerance limits for the population of sample variances are derived and presented in this work. The mathematical-statistical relationship between tolerance interval for the sample variance and the exceedance probability (survival probability) of the CARL 0 for the S(2) control chart with estimated parameter is recognized, highlighted and used in this work in such a way that the study of the Phase II performance and design of this chart can be based on tolerance interval for the sample variance, and vice versa. Works on performance and design of S(2) chart with estimated parameter generally focused on only one perspective (either unconditional or conditional) and considered only one type of chart (either upper one-sided chart or two-sided chart). The existence of both perspectives and two types of charts may be confusing for practitioners. For that reason, the performance and design of S(2) control chart according to these two perspectives are compared, considering each type of chart. Similarly, these two types of charts are also compared for each perspective. Some important results related to the S(2) chart design, which are not yet available in the literature, were required and obtained in this work to provide a comprehensive comparative study that enables practitioners to be aware of the significant differences between these two perspectives and the two types of charts so that proper informed decisions about the chart design to choose can be made. Furthermore, because the conditional RL distribution is usually highly rightskewed, the median and some extreme quantiles of the conditional RL distribution are proposed as complementary performance measures to the customary mean (CARL 0). Finally, some practical recommendations are offered.