Made available in DSpace on 2015-03-03T15:04:51Z (GMT). No. of bitstreams: 1 JoeltonFB_DISSERT.pdf: 887273 bytes, checksum: d3d21c6f9340a0a9d396b1c840cef67e (MD5) Previous issue date: 2013-09-19 / The chart of control of Hotelling T2 has been the main statistical device used in monitoring multivariate processes. Currently the technological development of control systems and automation enabled a high rate of collection of information of the production systems in very short time intervals, causing a dependency between the results of observations. This phenomenon known as auto correlation causes in the statistical control of the multivariate processes a high rate of false alarms, prejudicing in the chart performance. This entails the violation of the assumption of independence and normality of the distribution. In this thesis we considered not only the correlation between two variables, but also the dependence between observations of the same variable, that is, auto correlation. It was studied by simulation, the bi variate case and the effect of auto correlation on the performance of the T2 chart of Hotelling. / O grafico de controle T2 de Hotelling tem sido o principal dispositivo estat?stico utilizado no monitoramento de processos multivariados. Atualmente com o desenvolvimento tecnol?gico dos sistemas de controle e automa??o possibilitou uma elevada taxa de coletas das informa??es dos sistemas produtivos em intervalos de tempo muito curto, provocando uma depend?ncia entre os resultados das observa??es. Este fen?meno conhecido como autocorrela??o provoca no controle estat?stico de processos multivariado uma grande quantidade de alarmes falsos, prejudicando no desempenho do gr?fico. Isto acarreta na viola??o do pressuposto de independ?ncia e da normalidade da distribui??o. Nesta disserta??o considerou-se n?o s? a correla??o entre duas vari?veis, mas tamb?m a depend?ncia entre observa??es de uma mesma vari?vel, isto e, a autocorrela??o. Estudou-se, por meio de simula??o, o caso bivariado e o efeito da autocorrela??o no desempenho do gr?fico T2 de Hotelling

Submitted by admin tede (tede@pucgoias.edu.br) on 2018-04-18T12:39:55Z No. of bitstreams: 1 Renato de Souza Gonçalves.pdf: 2338121 bytes, checksum: 85b8036843bc2880b84c59e7336108f9 (MD5) / Made available in DSpace on 2018-04-18T12:39:55Z (GMT). No. of bitstreams: 1 Renato de Souza Gonçalves.pdf: 2338121 bytes, checksum: 85b8036843bc2880b84c59e7336108f9 (MD5) Previous issue date: 2018-03-12 / This research aims to analyze the losses occurring in the production process of a food industry, where statistical methods were used in the milk, peanut and marmalade production line. The case study was carried out at the Doçaria Dois Irmãos, located in Anápolis state of Goiás, where all the data were obtained for the study. The Toyota Production System was used with some quality management tools for the identification and treatment of losses. The data were processed according to the Statistical Process Control, where the stability tests were performed in the production process stages, and this was done through the control charts. After stabilizing the production process with the interventions made in the industry, it was also possible to perform the process capability test, where it was verified that some process steps do not have capacity. Through the results obtained, it was also possible to measure financially the losses that were occurring in the industry, the inherent gains of the investments in the improvement actions and the time of return on the investment made. Thus, it was understood that the time of return on investments justifies the interventions in the productive process of the company in question. It was concluded, therefore, that the losses in the productive process of the industry under study, not only left the processes unstable and incapable statistically, but also was generating unnecessary production costs. By applying improvement actions in the industry, it was possible to raise important information within the production process, as well as increase the profit in the production line of the selected sweets, due to the reduction of losses in the process. / Esta pesquisa visa analisar as perdas ocorrentes no processo produtivo de uma indústria de alimentos, onde foi utilizado métodos estatísticos na linha de produção dos doces de leite, amendoim e casadinho. O estudo de caso ocorreu na Doçaria Dois Irmãos, localizada em Anápolis estado de Goiás, onde obteve-se todos os dados para a concretização do estudo. Foi utilizado o Sistema Toyota de Produção com algumas ferramentas da gestão da qualidade para identificação e tratamento das perdas. Os dados foram tratados segundo o Controle Estatístico de Processo, onde se realizou os testes de estabilidade nas etapas do processo produtivo, sendo isto realizado através das cartas de controle. Após se estabilizar o processo produtivo com as intervenções feitas na indústria, foi possível também realizar o teste de capacidade do processo, onde se verificou que algumas etapas do processo não possuem capacidade. Através dos resultados obtidos, foi ainda possível mensurar financeiramente as perdas que vinham ocorrendo na indústria, os ganhos inerentes dos investimentos nas ações de melhoria e o tempo de retorno sobre o investimento realizado. Sendo assim, entendeu-se que o tempo de retorno sobre os investimentos justifica as intervenções no processo produtivo da empresa em questão. Conclui-se, portanto, que as perdas no processo produtivo da indústria em estudo, não só deixavam os processos instáveis e incapazes estatisticamente, como também estava gerando custos de produção desnecessários. Ao se aplicar ações de melhoria na indústria, foi possível levantar importantes informações dentro do processo produtivo, bem como aumentar o lucro na linha de produção dos doces selecionados, devido à redução de perdas no processo.

[pt] Os gráficos de controle estão entre as ferramentas indispensáveis para monitorar o desempenho de um processo em várias indústrias. Quando estimativas de parâmetros são necessárias para projetar esses gráficos, seu desempenho é afetado devido aos erros de estimação. Para resolver esse problema, no passado, pesquisadores avaliavam o desempenho desses métodos em termos do valor esperado do número médio de amostras até um alarme falso condicionado às estimativas dos parâmetros (denotado por 𝐶𝐴𝑅𝐿0). No entanto, esta solução não considera a grande variabilidade do 𝐶𝐴𝑅𝐿0 entre usuários. Então, recentemente, surgiu a ideia de medir o desempenho dos gráficos de controle usando a probabilidade de o 𝐶𝐴𝑅𝐿0 ser maior do que um valor especificado – que deve estar próximo do desejado nominal. Isso é chamado de Exceedance Probability Criterion (EPC). Para aplicar o EPC, a função de distribuição acumulada (c.d.f.) do 𝐶𝐴𝑅𝐿0 é necessária. No entanto, para um dos gráficos de controle mais utilizados, o gráfico Xbarra, também conhecido como gráfico x (sob a suposição de distribuição normal), a expressão matemática da c.d.f. não está disponível na literatura. Como contribuição nesse sentido, o presente trabalho apresenta a derivação exata da expressão matemática da c.d.f. do 𝐶𝐴𝑅𝐿0 para três possíveis casos de estimação de parâmetros: (1) quando a média e o desvio-padrão são desconhecidos, (2) quando apenas a média é desconhecida e (3) quando apenas o desvio-padrão é desconhecido. Assim, foi possível calcular o número mínimo de amostras iniciais, m, que garantem um desempenho desejada do gráfico em termos de EPC. Esses resultados mostram que m pode assumir valores consideravelmente grandes (como, por exemplo, 3.000 amostras). Como solução, duas novas equações são derivadas aqui para ajustar os limites de controle garantindo assim um desempenho desejado para qualquer valor de m. A vantagem dessas equações é que uma delas fornece resultados exatos enquanto a outra dispensa avançados softwares de computador para os cálculos. Um estudo adicional sobre o impacto desses ajustes no desempenho fora de controle (OOC) fornece tabelas que ajudam na decisão do melhor tradeoff entre quantidade adequada de dados e desempenhos IC e OOC preferenciais do gráfico. Recomendações práticas para uso desses resultados são aqui também fornecidas. / [en] Control charts are among the indispensable tools for monitoring process performance in various industries. When parameter estimation is needed to design these charts, their performance is affected due to parameter estimation errors. To overcome this problem, in the past, researchers have evaluated the performance of control charts and designed them in terms of the expectation of the realized in-control (IC) average run length (𝐶𝐴𝑅𝐿0). But, as pointed recently, this solution does not account for what is known as the practitioner-to-practitioner variability (i.e., the variability of 𝐶𝐴𝑅𝐿0). So, a recent idea emerged where control chart performance is measured by the probability of the 𝐶𝐴𝑅𝐿0 being greater than a specified value - which must be close to the nominal desired one. This is called the Exceedance Probability Criterion (EPC). To apply the EPC, the cumulative distribution function (c.d.f.) of the 𝐶𝐴𝑅𝐿0 is required. However, for the most well-known control chart, named the two-sided Shewhart Xbar (or simply X) Chart (under normality assumption), the mathematical c.d.f. expression of the 𝐶𝐴𝑅𝐿0 is not available in the literature. As a contribution in this respect, the present work presents the derivation of the exact c.d.f. expression of the 𝐶𝐴𝑅𝐿0 for three cases of parameters estimation: (1) when both the process mean and standard deviation are unknown, (2) when only the mean is unknown and (3) when only the standard deviation is unknown. Using these key results, it was possible to calculate the exact minimum number of initial (Phase I) samples (m) that guarantees a desired in-control performance in terms of the EPC. These results show that m can be prohibitively large (such as 3.000 samples). As a solution to this problem, two new equations are derived here to adjust the control limits to guarantee a desired in-control performance in terms of the EPC for any given value of m. The advantage of these equations (compared to the existing adjustments methods) is that one provides exact results and the other one does not require too many computational resources to perform the calculations. A further study about the impact of these adjustments on the out-of-control (OOC) performance provides useful tables to decide the appropriate amount of data and the adjustments that corresponds to a user preferred tradeoff between the IC and OOC performances of the chart. Practical recommendations for using these findings are also provided in this research work.

Carefree handling refers to the ability of a pilot to operate an aircraft without the need to continuously monitor aircraft operating limits. At the heart of all carefree handling or maneuvering systems, also referred to as envelope protection systems, are algorithms and methods for predicting future limit violations. Recently, envelope protection methods that have gained more acceptance, translate limit proximity information to its equivalent in the control channel. Envelope protection algorithms either use very small prediction horizon or are static methods with no capability to adapt to changes in system configurations. Adaptive approaches maximizing prediction horizon such as dynamic trim, are only applicable to steady-state-response critical limit parameters. In this thesis, a new adaptive envelope protection method is developed that is applicable to steady-state and transient response critical limit parameters. The approach is based upon devising the most aggressive optimal control profile to the limit boundary and using it to compute control limits. Pilot-in-the-loop evaluations of the proposed approach are conducted at the Georgia Tech Carefree Maneuver lab for transient longitudinal hub moment limit protection. Carefree maneuvering is the dual of carefree handling in the realm of autonomous Uninhabited Aerial Vehicles (UAVs). Designing a flight control system to fully and effectively utilize the operational flight envelope is very difficult. With the increasing role and demands for extreme maneuverability there is a need for developing envelope protection methods for autonomous UAVs. In this thesis, a full-authority automatic envelope protection method is proposed for limit protection in UAVs. The approach uses adaptive estimate of limit parameter dynamics and finite-time horizon predictions to detect impending limit boundary violations. Limit violations are prevented by treating the limit boundary as an obstacle and by correcting nominal control/command inputs to track a limit parameter safe-response profile near the limit boundary. The method is evaluated using software-in-the-loop and flight evaluations on the Georgia Tech unmanned rotorcraft platform- GTMax. The thesis also develops and evaluates an extension for calculating control margins based on restricting limit parameter response aggressiveness near the limit boundary.

傳統的二項累積和(CUSUM)管制圖是監測不合格率變化的有效工具。在本文中，我們考慮了俱有機率管制界線的二項CUSUM管制圖的設計，旨在控制每一期的條件誤報率達到所需的值。與固定的管制界線相比，機率管制界線將會是動態的，且更一般化、更能適應各種複雜的實際情況。在本文中，我們著重在機率管制界線的決定。藉由積分方程式法的發展，以促成動態二項加權CUSUM管制圖的設計與分析。俱有機率管制界線或固定管制界線的二項加權CUSUM管制圖與是否俱有快速起始反應特性的管制圖皆進行了比較。此外，在高良率的情境下，我們互相比較俱有機率管制界線與固定管制界線的二項加權CUSUM管制圖在製程失控時的偵測力表現。舉了一個例子來說明該如何應用所提出的管制圖。比較的結果顯示，動態界線的管制圖優於固定管制界線的管制圖，且在高良率的情況下，若樣本數越大，對動態管制界線的管制圖越有利。 / The conventional binomial CUSUM chart is an efficient tool for monitoring changes in fraction nonconforming. In this paper, we consider the design of Binomial CUSUM charts with probability control limits aimed at controlling the condi- tional false alarm rate at the desired value at each time step. The resulting control limits would be dynamic, which are more general and capable of accommodating more complex situations in practice as compared to the use of a constant control limit. In this paper, We focus on the determination of the probability control limits. An integral equation approach is developed to facilitate the design and analysis of the binomial WCUSUM control chart with probability control limits. The performance of the binomial WCUSUM charts with probability and constant control limits and the binomial WCUSUM charts with and without the fast initial response feature are compared. Besides, we compared the out-of-control detection perfromance of the binomial WCUSUM charts with probability and constant control limits for high yield process. An example is used to illustrate the application of the proposed control chart. Our comparisons show that the binomial WCUSUM chart with probability control limits generally outperforms the WCUSUM chart with constant control limits, and the conventional binomial CUSUM control chart with a constant control limit for high yield process when the sample size is large.