In multivariate statistical process control it is generally assumed that the process variables follow a multivariate normal distribution with mean vector " and covariance matrix •, but this is rarely satisfied in practice. Some robust control charts have been developed to monitor the mean and variance of univariate processes, or the mean vector " of multivariate processes, but the development of robust multivariate charts for monitoring • has not been adequately addressed. The control charts that are most affected by departures from normality are actually the charts for • not the charts for ". In this article, the robust design of several MEWMA-type control charts for monitoring • is investigated. In particular, the robustness and efficiency of different MEWMA-type control charts are compared for the in-control and out-of-control cases over a variety of multivariate distributions. Additionally, the total extra quadratic loss is proposed to evaluate the overall performance of control charts for multivariate processes. / Ph. D.

A performance analysis of three different Minimax control charts is performed with respect to their Chi-Square control chart counterparts under several different conditions. A unique control chart must be constructed for each process described by a unique combination of quality characteristic mean vector and associated covariance matrix. The three different charts under consideration differ in the number of quality characteristic variables of concern. In each case, without loss of generality the in-control quality characteristic mean vector is assumed to have zero entries and the associated covariance matrix is assumed to have non-negative entries. The performance of the Chi-Square and Minimax charts are compared under different values of the sample size, the probability of a Type I error, and selected shifts in the quality characteristic mean vector. Minimax and Chi-Square charts that are compared share identical in-control average run lengths (ARL) making the out-of-control ARL the appropriate performance measure. A combined Tausworthe pseudorandom number generator is used to generate the out-of-control mean vectors. Issues regarding multivariate uniform pseudorandom number generation are addressed. / Master of Science

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.