When monitoring a binary process proportion p, it is usually assumed that the binary observations are independent. However, it is very common that the observations are correlated with p being the correlation between two successive observations. The first part of this research investigates the problem of monitoring p when the binary observations follow a first-order two-state Markov chain model with p remaining unchanged. A Markov Binary GLR (MBGLR) chart with an upper bound on the estimate of p is proposed to monitor a continuous stream of autocorrelated binary observations treating each observation as a sample of size n=1. The MBGLR chart with a large upper bound has good overall performance over a wide range of shifts. The MBGLR chart is optimized using the extra number of defectives (END) over a range of upper bounds for the MLE of p. The numerical results show that the optimized MBGLR chart has a smaller END than the optimized Markov binary CUSUM. The second part of this research develops a CUSUM-pp chart and a GLR-pp chart to monitor p and p simultaneously. The CUSUM-pp with two tuning parameters is designed to detect shifts in p and p when the shifted values are known. We apply two CUSUM-pp charts as a chart combination to detect increases in p and increases or decreases in p. The GLR-pp chart with an upper bound on the estimate of p, and an upper bound and a lower bound on the estimate of p works well when the shifts are unknown. We find that the GLR-pp chart has better overall performance. The last part of this research investigates the problem of monitoring p with p remains at the target value when the correlated binary observations are aggregated into samples with n>1. We assume that samples are independent and there is correlation between the observations in a sample. We proposed some GLR and CUSUM charts to monitor p and the performance of the charts are compared. The simulation results show MBNGLR has overall better performance than the other charts. / Ph. D.

Statistical quality control is the application of statistical methods to problems for which it is of interest to evaluate, establish, or verify the quality of a product. The two basic areas of statistical quality control that have received both the greatest attention in the literature and the widest acceptance in industry are acceptance sampling and statistical process control. In the majority of such techniques, a single characteristic of an item is used to describe its quality. In such cases, one of two basic types of product quality measures is typically used: attributes product quality measures and variables product quality measures. Variables product quality measures evaluate an item’s quality by measuring its quality characteristic on a continuous scale. Attributes product quality measures assign a 0 to an item if its characteristic is conforming to some specification, and 1 if its characteristic is nonconforming. Although attributes and variables product quality measures have many appropriate applications, there are many situations m which product quality is best described by classifying a single characteristic of the item using three or more discrete levels. A multilevel discrete product quality measure is a function that assigns a numerical value to such an item corresponding to the level in which it is classified. Several acceptance sampling plans and control charts that incorporate the use of multilevel discrete product quality measures are defined here. In addition to the multilevel discrete product quality measure, each of the defined methods utilizes a quality value function. A quality value function assigns a numerical value to an item based on the classification it receives from the multilevel discrete product quality measure. Each of the defined multilevel acceptance sampling plans and multilevel control charts is evaluated with respect to its probabilistic behavior. In addition, the problem of parameter selection and quality value function specification is addressed for each of the defined techniques. The cases considered are the 3-level case, the 4-level case, and the general j-level case. / Ph. D.

Complexity of production processes, high computing capabilities, and massive datasets characterize today’s manufacturing environments, such as those of continuous andbatch production industries. Continuous production has spread gradually acrossdifferent industries, covering a significant part of today’s production. Commonconsumer goods such as food, drugs, and cosmetics, and industrial goods such as iron,chemicals, oil, and ore come from continuous processes. To stay competitive intoday’s market requires constant process improvements in terms of both effectivenessand efficiency. Statistical process control (SPC) and design of experiments (DoE)techniques can play an important role in this improvement strategy. SPC attempts toreduce process variation by eliminating assignable causes, while DoE is used toimprove products and processes by systematic experimentation and analysis. However,special issues emerge when applying these methods in continuous process settings.Highly automated and computerized processes provide an exorbitant amount ofserially dependent and cross-correlated data, which may be difficult to analyzesimultaneously. Time series data, transition times, and closed-loop operation areexamples of additional challenges that the analyst faces.The overall objective of this thesis is to contribute to using of statisticalmethods, namely SPC and DoE methods, to improve continuous production.Specifically, this research serves two aims: [1] to explore, identify, and outlinepotential challenges when applying SPC and DoE in continuous processes, and [2] topropose simulation tools and new or adapted methods to overcome the identifiedchallenges.The results are summarized in three appended papers. Through a literaturereview, Paper A outlines SPC and DoE implementation challenges for managers,researchers, and practitioners. For example, problems due to process transitions, themultivariate nature of data, serial correlation, and the presence of engineering processcontrol (EPC) are discussed. Paper B further explores one of the DoE challengesidentified in Paper A. Specifically, Paper B describes issues and potential strategieswhen designing and analyzing experiments in processes operating under closed-loopcontrol. Two simulated examples in the Tennessee Eastman (TE) process simulatorshow the benefits of using DoE techniques to improve and optimize such industrialprocesses. Finally, Paper C provides guidelines, using flow charts, on how to use thecontinuous process simulator, “The revised TE process simulator,” run with adecentralized control strategy as a test bed for developing SPC and DoE methods incontinuous processes. Simulated SPC and DoE examples are also discussed.

[pt] Este trabalho mostra a implantação de técnicas de Controle Estatístico de Processo (CEP) em uma indústria de cosméticos, em uma situação em que as técnicas convencionais não são aplicáveis. O processo a ser controlado é constituído de oito canais, que produzem em um mesmo instante de tempo oito unidades de um mesmo produto. Tal processo possui a peculiaridade de ter médias variáveis no tempo, mesmo em estado de controle estatístico. Como os métodos de controle propostos na literatura para processos com múltiplos canais têm como premissa médias constantes ao longo do tempo e os canais terem médias e variâncias semelhantes, tais métodos não são aplicáveis ao processo em questão. Para o CEP do processo, então, foi desenvolvida uma metodologia adaptada à realidade da empresa, que conjuga os princípios de group charts e de gráficos de controle de aceitação. Foi ainda realizada uma revisão bibliográfica de algumas técnicas de controle estatístico de processos com múltiplos canais, contemplando métodos tradicionais e não tradicionais. / [en] This study shows the implantation of techniques of Statistical Process Control (SPC) in a cosmetics industry, in a situation in which conventional techniques are not applicable. The process to be controlled is composed of eight streams, which produce eight units of the product at a time. The process has the peculiarity that the means of the streams change in time, even in a condition of statistical control. The control schemes proposed in the literature hitherto for multiple-stream processes assume constant means, and streams with similar means and variance, and are therefore not applicable to this process. A new scheme was then developed for the statistical control of the process, which blends the principles of the group charts and of acceptance control charts. A review was also presented of some techniques of statistical control of multiple-stream processes, including traditional and more recent methods.

The purpose of this thesis is to develop a method of systematic visualization for coordinate measurements at Saab Aerostructures. The thesis begins with mapping the coordinate measuring process. After that, it is proposed to define key measurement points through quality standards as this will simplify the visualization of the measurements with a control chart through a Visual Management-system.  To stay in the forefront of the market and keep the relations with current customers, Saab wants to increase the quality of their products by reducing the amount of measurement deviations. The measurements are currently scarcely visualized to the employees. This is because of the complicated method which currently is being used to reflect which measurements that are deviating. The process of visualization should be definite and simple to use as this will lead to less deviations. Furthermore, it will contribute to continuous improvement for the process of measuring.  The methods used in this thesis include semi structured interviews, observations and studies of internal documents. These methods are then triangulated to be able to map the process in detail. However, no employees knew either the coordinate measuring process or the visualizing process by heart. This led to the author having to proceed with a Process Walk. The method helped map both the processes and through this, problems were identified in the process which would otherwise hinder the visualization of measurements. Moreover, a literature study was conducted of Quality Management Systems as these outline criteria for Saabs products. Visual Management-system was also studied with the likes of information boards as this fit Saab with their previous prerequisites of information boards.  From the mapping of today’s process, problems were identified that would hinder them from systematically visualize their coordinate measuring process. From the problems that were outlined, improvement suggestions were proposed. Firstly, it was conducted that too much data is hindering the transparency of the process. From Quality Standards it is proposed to clearly define key measurements points and document these. This is done through the means of a SIPOC and a FMEA. Furthermore, it is proposed to analyze which measurement data is to be saved as a major part of the data consists of irrelevant information. As the process of visualizing the coordinate measuring process was timed to 90 hours it was also proposed to clarify templates which systematically exports and sorts data in an Excel-format with the use of Saabs ERP-system, instead of converting from XML which is done today. These templates can then immediately be used by Excel to visualize the outcome of the coordinate measurements with the help of a Visual Management-system. The system makes use of bar diagrams to highlight which processes that are producing most deviations. The processes outcome is visualized in a control chart which enhances how the variation of the process is affecting the measurement outcome. The last improvement suggestion states that Saab should use the control chart as a way of stabilizing their processes as this will lead to qualitative processes where capability can be proven to their customers. / Syftet med detta arbete är att utveckla ett arbetssätt för systematisk visualisering av mätutfallet vid koordinatmätning på Saab Aerostructures. Arbetet lägger sin grund i en kartläggning av koordinat-mätningsprocessen för att sedan föreslå att utefter rådande kvalitetsstandarder tydligt definiera nyckelmått som skall förenkla visualisering av mätutfallet med styrdiagram i ett Visual Management-system.  För att Saab ska ligga i framkant av marknaden och behålla de kundrelationer man har ska man öka kvaliteten på produkter genom att minska antalet anmärkningar. Mätutfallet och dess anmärkningar är föga visualiserade för anställda då en komplicerad process krävs för att återspegla vilka mätpositioner som skapar problem. Om processen för visualisering blir konkret och enkel att använda kommer det att bidra till färre anmärkningar och kontinuerlig förbättring av kontrollmätningsprocessen.  Metoder som användes för arbetet inkluderar halvstrukturerade intervjuer, observationer och studier av interna dokument. Dessa metoder trianguleras sedan för att detaljerat kartlägga processen men på grund av att inte tillräckligt många kunde beskriva kontrollmätnings- eller visualiseringsprocessen genomfördes en ytterligare metod, en Process walk. Metoden hjälpte att detaljerat kartlägga kontrollmätnings-processen och dess nuvarande visualiseringsmetod. Från kartläggningen identifierades problem och barriärer för visualisering av data vilka annars skulle hindra visualiseringen av mätutfallet. Utöver dessa metoder genomfördes även en litteraturstudie av Kvalitetsledningssystem då dessa svarar för kriterier för Saabs produkter. Även Visual Management-system studerades med inriktning på informationstavlor då detta passade Saabs förutsättningar med tidigare informationstavlor.   Från kartläggningen av dagens process identifierades problem och barriärer vilka hindrar Saab från att systematiskt visualisera deras kontrollmätningsprocess. Från dessa problem och barriärer utvecklades förbättringsförslag. För det första förbättringsförslaget insågs att alldeles för mycket data hindrar överblickbarheten för processen varpå förslag gavs om att utefter kvalitetsstandarder, definiera nyckelmått och dokumentera dessa för alla produkter som kontrollmäts. Definieringen genomförs med en SIPOC och en FMEA. Vidare föreslås även att se över all lagring av mätdata då data till större del innehåller oviktig information som ändå förkastas. Då processen för visualisering av kontrollmätningsprocessen visade sig ta upp mot 90 timmar föreslogs även att förtydliga mallar som systematiskt exporterar och sorterar data i xlsx-format mot Saabs ERP-system, istället för att först konvertera från XML-format. Dessa mallar används sedan av Excel för att framställa mätutfallet av koordinatmätningarna med hjälp av ett Visual Management-system. Systemet använder sig av stapeldiagram för att förtydliga vilka processer som påvisar flest anmärkningar. Processernas mätutfall visualiseras i ett styrdiagram vilket förtydligar hur variationen i processer påverkar mätutfallet. Det sista förbättringsförslaget är att Saab ska börja använda sig av styrdiagram för att stabilisera deras processer för att få kvalitativa processer där man kan påvisa duglighet för sina kunder.

A competitividade é um fator de extrema importância para o sucesso das organizações. Os expressivos resultados alcançados pela Motorola e General Electric (GE), por meio do programa Seis Sigma, tem sido uma fonte de inspiração para muitas empresas seguirem o seu exemplo e conseguir maior competitividade. O programa Seis Sigma foi criado e evoluiu em ambiente de manufatura, mas também pode ser aplicado em processos de serviços. Entretanto a aplicação em serviços tem sido feita de forma mais modesta, com menor participação de empresas, e conseqüentemente menor número de casos e relatos divulgados. A literatura menciona que de forma geral o desempenho dos processos de serviços é inferior aos processos de manufatura, e isso pode ser um indicativo de boa oportunidade para a aplicação do programa Seis Sigma. Este trabalho tem como objetivo a análise comparativa da aplicação do programa Seis Sigma em processos de manufatura e serviços, por meio de revisão da literatura e pesquisa com empresas que aplicam o programa, visando entender as diferenças da aplicação em benefício da aplicação em serviços. Os resultados obtidos sugerem indícios de similaridades e diferenças significativas, tais como \"no perfil do Black Belt, nas equipes de projeto, no tempo de execução de um projeto, no uso da CTQ, na disponibilidade e natureza dos dados e na aplicação de técnicas e ferramentas\" que podem ajudar na expansão do programa em serviços, e assim, espera-se que possa motivar mais pesquisas com esse tema de trabalho. / Competitiveness is an important factor for any organization success. The Six Sigma program, which has been used by companies like Motorola and GE since the 1980\'s, has proved to be a successful way to make any company improve all areas of business and therefore, become more competitive. Although it was created and has been growing in manufacturing successfully, its implementation can reach a much wider field of application. In the last few years, some service corporations also been benefited by the use of this program. However, different from manufacturing, its application is less popular and still restricted to few companies that have already implemented it, which explains limited case studies and projects published in the literature. This paper has the goal to perform a comparative analysis of Six Sigma program implementation in manufacturing as well as in services process and consequently, comprehend the differences and advantages of its application in these different fields. The results of this study, which are based on literature review and also a survey with service companies, have led to some significant similarities and differences like the profile of the Black Belt, project time execution, CTQ use, the nature and availability of the data and application of techniques and tools. Further research, can certainly contribute to the expansion of the Six Sigma methodology improvement in service quality.

[pt] Esta dissertação trata do controle estatístico de processos (CEP) multi-canal, assunto pouco tratado na literatura especializada. As técnicas encontradas na literatura pressupõem condições de validade nem sempre verificadas na prática, a saber: medidas sucessivas efetuadas em cada canal independentes e identicamente distribuídas; todos os canais ajustados, com mesma média e desvio-padrão; e (na maioria dos trabalhos) canais independentes, sem correlação cruzada. O estudo foi motivado por um caso real, em que nenhuma dessas condições se verifica. Este trabalho propõe adaptações e extensões de técnicas existentes para lidar com processos nessa situação; detalha como aplicá-las; ilustra sua aplicação no caso prático analisado; discute limitações e propõe alternativas, e inicia uma discussão sobre as diferentes condições (características das situações práticas) em que cada uma das alternativas é mais apropriada. O trabalho iniciou- se com uma análise exploratória dos processos da empresa, de modo a permitir um diagnóstico do CEP que vinha sendo realizado, e fundamentar a proposta de um novo esquema de controle, mais adequado. O esquema proposto, aplicado aos dados, sinalizou problemas com os processos que as técnicas empregadas não sinalizavam. Embora, em virtude dos prazos para finalização da dissertação e da programação da produção da empresa, que teve interrupções, não tenha sido possível incluir nesta análise a investigação de causas especiais, com revisão dos limites de controle e utilização dos gráficos assim revistos no monitoramento on line, para fins de acompanhamento do desempenho do esquema proposto, mesmo assim a aplicação desse esquema aos dados disponíveis demonstrou ser ele mais sensível a causas especiais que os gráficos que vinham sendo utilizados, e levantou algumas questões, não abordadas na literatura, que são indicadas para pesquisa futura. / [en] This dissertation tackles the problem of statistical control of multi-channel processes, which has been scarcely dealt with in the specialized literature. The techniques found in the literature assume validity conditions which are not always verified in practice, namely: successive measurements taken in each channel should be independent an identically distributed; all the channels should be adjusted, with same mean and standard deviation; and most works assume the channels to be independent, with no cross correlation. The study was motivated by a real case, in which no one of these conditions holds. This work proposes adaptations and extensions of existing techniques in order to deal with this and similar real situations; details the application of the adapted/extended techniques; illustrates their application in the case under analysis; discusses limitations and proposes alternatives, and initiates a discussion about the different conditions (practical situations´ characteristics) in which each alternative is most appropriate. The work began with an exploratory data analysis of the enterprise´s production processes, so as to enable a diagnosis of the statistical process control procedures that were in use, and serve as a basis for the proposal of a new, more adequate, control scheme. The proposed scheme, when applied to the data, signalled problems with the processes which the techniques in use did not signal. Due to the deadlines for ending this dissertation and to programmed interruptions in the production, it has not been possible to include in the analysis the search for special causes with corresponding revisions of the charts´ control limits and the use of the revised charts in on-line monitoring, for the purposes of feedback on the proposed scheme´s performance. Its application to the available data has nevertheless shown it more sensitive to special causes than the charts that were in use, and raised some issues not approached in the literature, which are left as indications for future research.

A cana-de-açúcar é uma das culturas mais importantes economicamente no Brasil e concede ao país a posição de maior produtor e exportador mundial. A perspectiva para os próximos anos é de expansão da área cultivada para atender a demanda, principalmente, do mercado internacional. Além do aumento de produção obtido pela expansão da área cultivada é de fundamental importância a manutenção e o incremento da produtividade da cultura, otimizando assim os recursos já disponibilizados. Uma das alternativas para o aumento da produtividade é o aprimoramento dos processos produtivos de implantação, condução e colheita. As operações envolvidas com esses processos tem influência direta sobre a produtividade e qualidade da matéria prima produzida. Embora todas as operações tenham a sua importância é necessário, por questões operacionais e custos envolvidos, identificar aquelas de maior importância para o processo de produção e estabelecer os padrões a serem atendidas pelas mesmas. Para tanto o objetivo deste trabalho foi identificar e avaliar as variáveis críticas do processo de produção da cana-de-açúcar. O trabalho foi desenvolvido em duas etapas. A primeira constou da identificação das variáveis críticas referentes às diversas etapas de produção da cana-de-açúcar através da utilização da FMEA - Failure Mode and Effects Analysis. A segunda constou da avaliação no campo da variável de maior criticidade para determinar a capacidade do processo através do índice Cpk. Os resultados permitiram identificar dezessete variáveis e a cana crua e o espaçamento irregular entre foram consideradas as mais críticas. Com relação ao espaçamento entre sulcos os atuais sistemas de orientação para abertura dos sulcos, manual e automático, não são capazes de atender aos limites de tolerância adotados pela Usina. É necessário rever esses limites e/ou analisar alternativas para melhorar os sistemas e dessa forma atender aos padrões desejados. / Sugar cane is one of the cultures more important economically in Brazil, which is at the same time the leading producer and exporter in the word. The perspectives for the next few years are expansion of cultivated area in order to attend the demand, mainly the international market. Besides the increasing of production, giving the expansion of cultivated area, it is of the great importance the maintenance and the increasing of the crop productivity optimizing in this way the resources already available. One of the alternatives for the increasing the productivity is the improving of the productivity process. Among them the plant, cultivation and harvest should be enhanced. Due to the operational issues and the involved costs it is necessary to determine the most important operations for the production process and set the patterns to be applied by them. The aim of this work was to identify and evaluate the critical variables in the sugar cane production process. The work was carried out in two ways. The first one consisted of the identification of the critical variables that were present along the several stages of sugar cane production and the FMEA - Failure Mode and Effects Analysis- was the technique used for the evaluation. The second stage consisted of the evaluation in the field to find the most critical variables and the capacity of the process. The results made possible to identify seventeen variables. The most critical of them were space among furrows and the harvesting of raw sugar cane. Concerning the space among furows the current guide systems, automatic and manual, are not able to attend the limits of tolerance adopted by the mill. It is necessary to have this limits reviewed and/or analyse some new alternatives for the improvements in the systems, in order to attend the wanted patterns.

Submitted by JOSIANE SANTOS DE OLIVEIRA (josianeso) on 2017-05-19T12:43:37Z No. of bitstreams: 1 Davenilcio Luiz de. Souza_.pdf: 539499 bytes, checksum: cf86851f0b7523f3b7d78589539fdbcb (MD5) / Made available in DSpace on 2017-05-19T12:43:37Z (GMT). No. of bitstreams: 1 Davenilcio Luiz de. Souza_.pdf: 539499 bytes, checksum: cf86851f0b7523f3b7d78589539fdbcb (MD5) Previous issue date: 2017-03-13 / Nenhuma / Os crimes de lavagem de dinheiro têm provocado grandes perdas aos países e a seus sistemas financeiros, o volume de dados em transações digitais representa dificuldade para a detecção deste tipo de ilícito. As auditorias em dados financeiros mostram-se limitadas na identificação de fraudes, pois em grande parte, ainda são realizadas com dados coletados por amostragem e incapazes de identificar as situações de delito em tempo real. Este trabalho, visando auxiliar no atendimento a esta lacuna, tem por objetivo propor um método estatístico de monitoramento por Cartas de Controle multivariadas, com base na Lei de Benford, para a detecção de suspeitas de fraude em lançamentos financeiros, entre eles os devidos à lavagem de dinheiro. Foi definido um modelo conceitual com distribuição de probabilidades representando dados oriundos de lançamentos financeiros, e adotada a suposição de que aderem a distribuição da Lei de Benford. Posteriormente foi considerada a distribuição empírica, estimada a partir dos próprios dados e dois procedimentos foram testados para verificar as suspeitas de fraude por lavagem de dinheiro utilizando a avaliação dos primeiros dígitos significativos: A Carta de Controle multivariada _2 e a Carta de Controle multivariada T2 de Hotelling. Foram simulados dados com auxílio do software R-Project até a ocorrência do 50.000o sinal. Foram avaliados casos simulados e reais, com o fim de exemplificar a operação do método. A partir da simulação, as duas Cartas de Controle testadas foram avaliadas quanto ao ARL, isto é, o número médio de observações até sinalizar que a série passou a operar em um estado fora de controle, o que significa a suspeita de lançamentos fraudulentos. Após aplicação do método de análise retrospectiva, com base nas proporções dos primeiros dígitos de Benford em lançamentos financeiros da campanha para Prefeito em 2016, não foram evidenciadas suspeitas de fraude nos dados obtidos junto ao sítio do Tribunal Superior Eleitoral (TSE). Em um conjunto de dados de uma instituição financeira, foram observados sinais de divergência entre as frequências dos primeiros dígitos nos lançamentos e nos valores esperados, porém os pontos além dos limites de controleidentificados encontram-se em um período próximo nas três análises realizadas, concentrando os dados de investigação para a auditoria financeira. A contribuição acadêmica deu-se pelo desenvolvimento de um modelo de aplicação de Cartas de Controle multivariadas e da Lei de Benford, com uma abordagem inovadora do controle estatístico de processos voltado à área financeira, utilizando recurso computacional acessível, de fácil processamento, confiável e preciso, que permite aprimoramento por novas abordagens acadêmicas. No que tange à contribuição à sociedade, se dá pelo uso do modelo por entidades que atuam com movimentações financeiras e pela comunidade, em dados de organizações civis e estatais divulgados nos canais de informação, de modo a proporcionar a prática cidadã pelo acesso à análise e a constatação da idoneidade dos fatos e dos dados. / Large losses are generated in the countryes financial systems, by money laundering. The volume of financial data is big issue to identify digital crime and money laundering. Audits in financial data have limitations in detecting fraud, in large part it is still performed in a traditional way, data are collected by sampling and often unable to identify a real-time crime situation. This research is aiming to serve in addressing this gap, to propose an monitoring statistical method, from multivariate control chart based on Benford’s law for detecting suspicious of fraud in financial data, including those due to money laundering. It was initially defined as a conceptual model in order to determine the type of probability distribution that represents data from financial launches. It was adopted an assumption that this type of data adheres to the Benford’s Law distribution. Subsequently, an empirical distribution was obtained, estimated from the own data. Two procedures were tested to verify a suspected money laundering fraud through the significant first-digit assessment: The Multivariate 2 Control Chart and the Multivariate Hotelling’s T2 Control Chart. Data were simulated using the R-Project software until the occurrence of the 50.000o signal. Finally, the simulation procedures were applied to real data in order to exemplify the method operationally. From the simulation, the two Control Charts tested were evaluated for ARL, that is, average number of observations until the signaling that the series started to operate in an out-of-control state, which it means suspicious of fraudulent launches. The application of the retrospective analysis method in the financial launchings of county’s campaign from 2016 Elections in five capitals of Brazil, based on the expected proportions from the first digit given by Benford’s Law, no suspicions fraud were evidenced in the data obtained from the site of Tribunal Superior Eleitoral (TSE). Considering the application in a set of data from a financial institution, signs of divergence between the frequencies of the first digits of the entries and the expected values were observed, but these points beyond the identified limits are close in all three analyzes. Indicating the period of the data which ones the audit will focus in a further investigation. Academic contribution is identified by developing a multivariate Control Chart together the Benford’s law in an application model with an innovative approach to the statistical process control aimed at the financial area,using accessible, easy to process, reliable and accurate computational resources that allow improvement through new academic approaches. As regard to the contribution to society, it is given the opportunity of applying the model by financial entities and the community in the data of civil and state organizations, disclosed in the information channels in order to provide access to analysis and verification of the suitability of facts and data by citizen practice.

Submitted by JOSIANE SANTOS DE OLIVEIRA (josianeso) on 2017-05-22T13:46:14Z No. of bitstreams: 1 Rossano Santos Noronha_.pdf: 585085 bytes, checksum: 88117b318c3e9c30134fce5bf0bdc22e (MD5) / Made available in DSpace on 2017-05-22T13:46:14Z (GMT). No. of bitstreams: 1 Rossano Santos Noronha_.pdf: 585085 bytes, checksum: 88117b318c3e9c30134fce5bf0bdc22e (MD5) Previous issue date: 2017-03-07 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Devido à dificuldade em se estimar os custos de operação associados ao monitoramento estatístico do processo nos trabalhos identificados na literatura, este trabalho tem por objetivo propor um modelo de otimização econômico para a carta de controle _X que considere as incertezas em relação aos custos variáveis e dependentes do desvio em relação à média do processo. O levantamento bibliográfico efetuado auxiliou no entendimento de como a incerteza em relação aos custos na utilização das cartas de controle são tratados. Percebeu-se o tratamento dos custos bem como do parâmetro de desvio do processo em relação a média _ como variáveis discretas e que impactavam na carta. A proposta aqui apresentada consiste em tratar não apenas o desvio em relação a média mas também dois dos custos associados à operação da carta de controle _X como variáveis aleatórias de distribuição contínua, inserindo assim um componente de incerteza na sua estimação. Desenvolveu-se assim uma nova formulação para o problema de otimização. Foram escolhidas instâncias para a otimização e comparados os resultados com os obtidos por autores da literatura. Os resultados foram obtidos por meio da metaheurística simulated annealing. Como resultados, o método mostrou-se eficiente, mostrando que o nível de dependência entre o parâmetro de mudança de processo e o custo e, da incerteza que se tem quanto aos valores definidos de custo de operação impactam nos custos totais de operação do CEP. A principal contribuição deste trabalho de pesquisa está na apresentação de uma formulação matemática de otimização da carta de controle _X que trata não somente o desvio em relação à média do processo mas também os custos de operação do CEP como variáveis aleatórias. A originalidade da formulação está em considerar os custos linearmente dependentes do tamanho do desvio do processo em relação a sua média. / Due to the difficulty in estimating the operating costs associated to the statistical monitoring of the process described in the literature, this paper aims to propose a model of economic optimization for the _X control chart that considers the uncertainties in relation to the variable costs and dependent on the deviation in relation to the average of the process. The literature review performed supported the understanding of how the uncertainty in relation to costs in the use of control charts is treated. The treatment of the costs as well as the parameter of deviation of the process in relation to the _ average were indicated as discrete variables and that impacted on the chart. The proposal presented here consists of treating not only the deviation from the mean but also two costs associated with the operation of the _X control chart as random variables of continuous distribution, thus inserting a component of uncertainty in its estimation. A new formulation for the optimization problem was developed. Instances for optimization were chosen and the results were compared with those obtained by authors described in the literature. The results were obtained through simulated annealing metaheuristics. As a result, the method proved to be efficient, showing that the level of dependence between the process change parameter and the cost, as well as the uncertainty regarding the defined operating cost values impact on the total cost of operation of the SPC. The main contribution of this research work is the presentation of a mathematical formulation of optimization of the _X control chart that treats not only the deviation in relation to the average of the process but also the operating costs of the SPC as random variables. The originality of the formulation is to consider costs linearly dependent on the size of the process deviation in relation to its mean.