Multivariate control charts are used to monitor a process when more than one quality variable associated with the process is being observed. The multivariate exponentially weighted moving average (MEWMA) control chart is one of the most commonly recommended tools for multivariate process monitoring. The standard practice, when using the MEWMA control chart, is to take samples of fixed size at regular sampling intervals for each variable. In the first part of this dissertation, MEWMA control charts based on sequential sampling schemes with two possible stages are investigated. When sequential sampling with two possible stages is used, observations at a sampling point are taken in two groups, and the number of groups actually taken is a random variable that depends on the data. The basic idea is that sampling starts with a small initial group of observations, and no additional sampling is done at this point if there is no indication of a problem with the process. But if there is some indication of a problem with the process then an additional group of observations is taken at this sampling point. The performance of the sequential sampling (SS) MEWMA control chart is compared to the performance of standard control charts. It is shown that that the SS MEWMA chart is substantially more efficient in detecting changes in the process mean vector than standard control charts that do not use sequential sampling. Also the situation is considered where different variables may have different measurement costs. MEWMA control charts with unequal sample sizes based on differing measurement costs are investigated in order to improve the performance of process monitoring. Sequential sampling plans are applied to MEWMA control charts with unequal sample sizes and compared to the standard MEWMA control charts with a fixed sample size. The steady-state average time to signal (SSATS) is computed using simulation and compared for some selected sets of sample sizes. When different variables have significantly different measurement costs, using unequal sample sizes can be more cost effective than using the same fixed sample size for each variable. In the second part of this dissertation, control chart methods are proposed for process monitoring when the quality of a process or product is characterized by a linear function. In the historical analysis of Phase I data, methods including the use of a bivariate <i>T</i>² chart to check for stability of the regression coefficients in conjunction with a univariate Shewhart chart to check for stability of the variation about the regression line are recommended. The use of three univariate control charts in Phase II is recommended. These three charts are used to monitor the <i>Y</i>-intercept, the slope, and the variance of the deviations about the regression line, respectively. A simulation study shows that this type of Phase II method can detect sustained shifts in the parameters better than competing methods in terms of average run length (ARL) performance. The monitoring of linear profiles is also related to the control charting of regression-adjusted variables and other methods. / Ph. D.

雙次抽樣平均數和變異數管制圖設計之研究 / Control charts are effective tools for detecting manufacturing processes and service processes. Nowadays, much of the data in manufacturing or service industries comes from processes having non-normal or unknown distributions. The commonly used Shewhart control charts, which depend heavily on the normality assumption, are not appropriately used for this situation. In this paper, we propose a standardized dynamic double sampling asymmetric EWMA mean control chart (SDDS EWMA-AM chart), a standardized dynamic double sampling asymmetric EWMA variance control chart (SDDS EWMA-AV chart), and their combined charts (joint SDDS EWMA-AM and SDDS EWMA-AV charts) to monitor process mean, variance and both shifts, respectively. The charts based on the double sampling procedure and two simple distribution-free transformed statistics are used for non-normal distribution of a quality variable. The performance of the proposed charts and that of some existing distribution-free mean and variance charts are compared. Further, a non-normal service times example from the service system of a bank branch is used to illustrate the applications of the proposed charts and to compare detection performance with the existing distribution-free mean and variance control charts. The charts we proposed show superior detection performance compared to the existing distribution-free mean and variance charts. Thus they are recommended.

<p>In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D).</p><p>In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively.</p><p>In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels.</p><p>Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity.</p><p>These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.</p>

In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D). In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively. In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels. Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity. These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.

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.

This paper represents the most well-known compression methods, which have been published. A Compression of ECG signal is important primarily for space saving in memory cards or efficiency improvement of data transfer. An application of wavelet transform for compression is a worldwide discussed topic and this is the reason why the paper focuses in this direction. Gained wavelet coefficients might be firstly quantized and then compressed using suitable method. There are many options for a selection of wavelet and a degree of decomposition, which will be tested from the point of view of the most efficient compression of ECG signal.

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Data as well as hardware characteristics are two key aspects for efficient data management. This holds in particular for the field of in-memory data processing. Aside from increasing main memory capacities, efficient in-memory processing benefits from novel processing concepts based on lightweight compressed data. Thus, an active research field deals with the adaptation of new hardware features such as vectorization using SIMD instructions to speedup lightweight data compression algorithms. Following this trend, we propose a novel approach for run-length encoding, a well-known and often applied lightweight compression technique. Our novel approach is based on newly introduced conflict detection (CD) instructions in Intel's AVX-512 instruction set extension. As we are going to show, our CD-based approach has unique properties and outperforms the state-of-the-art RLE approach for data sets with small run lengths.

<p>The multivariate cumulative sum (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA) control charts are the two leading methods to monitor a multivariate process. This thesis focuses on the MEWMA control chart. Specifically, using the Markov chain method, we study in detail several aspects of the run length distribution both for the on- and off- target cases. Regarding the on-target run length analysis, we express the probability mass function of the run length distribution, the average run length (ARL), the variance of run length (V RL) and higher moments of the run length distribution in mathematically closed forms. In previous studies, with respect to the off-target performance for the MEWMA control chart, the process mean shift was usually assumed to take place at the beginning of the process. We extend the classical off-target case and introduce a generalization of the probability mass function of the run length distribution, the ARL and the V RL. What Prabhu and Runger (1996) proposed can be derived from our new model. By evaluating the off-target ARL values for the MEWMA control chart, we determine the optimal smoothing parameters by using the partition method that provides an easy algorithm to find the optimal smoothing parameters and study how they respond as the process mean shift time changes. We compare the ARL performance of the MEWMA control chart with that of the multivariate Shewhart control chart to see whether the MEWMA chart is still effective in detecting a small mean shift as the process mean shift time changes. In order to apply the model to semiconductor manufacturing processes, we use a bivariate normal distribution to generate sample data and compare the MEWMA control chart with the multivariate Shewhart control chart to evaluate how the MEWMA control chart behaves when a delayed mean shift happens. We also apply the variation transmission model introduced by Lawless et al. (1999) to the semiconductor manufacturing process and show an extension of the model to make our application to semiconductor manufacturing processes more realistic. All the programming and calculations were done in R</p> / Master of Science (MS)

Orientador: Marcela Aparecida Guerreiro Machado Freitas / Resumo: O controle de qualidade, principalmente por meio do uso de gráficos de controle, torna-se essencial na indústria para garantir um processo livre de causas especiais de variabilidade. Como os dados amostrais podem incluir incertezas advindas da subjetividade humana e dos sistemas de medição, a teoria dos conjuntos fuzzy pode ser aplicada aos gráficos de controle quando dados precisos não estiverem disponíveis. Para tal feito, os valores da característica de qualidade são fuzzificados a partir da inserção de incertezas e transformados em valores representativos para uma melhor comparação com o gráfico de controle tradicional. Este trabalho propõe o uso da lógica fuzzy aos gráficos de controle para monitorar a média e a amplitude de processos univariados, assim como dois gráficos de controle fuzzy baseados nas regras especiais de decisão: Synthetic e Side Sensitive Synthetic. O desempenho do gráfico de controle é medido pelo número médio de amostras até sinal (NMA). Verificou-se neste trabalho que os gráficos de controle fuzzy possuem maior eficiência que os gráficos de controle tradicionais para menores valores de α-cut, ou seja, maior incerteza inserida no processo e para cenários onde se tem uma maior diferença entre os limitantes de incerteza dos números fuzzy. / Abstract: Quality control, mainly through the use of control charts, becomes essential in the industry to ensure a process free from special causes of variability. As sample data may include uncertainties arising from human subjectivity and measurement systems, fuzzy set theory can be applied to control charts when accurate data is not available. For this purpose, the quality characteristic values are fuzzified from the insertion of uncertainties and transformed into representative values for a better comparison with the traditional control chart. This work proposes the use of fuzzy logic to control charts to monitor the mean and range of univariate processes, as well as two fuzzy control charts based on the special run rules: Synthetic and Side Sensitive Syntehtic. The performance of the control chart is measured by the average run length (ARL). It was verified in this work that the fuzzy control charts have higher efficiency than the traditional control charts for lower values of α-cut, that is, greater uncertainty inserted in the process and for scenarios where there is a greater difference between the limiting uncertainties of fuzzy numbers. / Mestre