<p>The use of process capability indices in the industry is traditionally based on the assumptions that a sample from a process are observations on independently, identically and normally distributed random variables<i>, IIN</i>. However, all three assumptions are open to discussion and in this thesis, the estimation of the indices is studied when the assumption of independence is not fulfilled.</p><p>In five reports, the indices <i>C</i><i>pk</i> and <i>C</i><i>pm </i>are studied, and instead of random samples, samples are regarded as observations on a time series.</p><p>In the first four reports, each index is studied for either an <i>AR(1)</i> or an <i>MA(1)</i> process and the fifth report, both indices are studied for a general <i>ARMA(p,q</i>) process.</p><p>In all reports, alternatives to <i>C</i><i>pk</i><i> </i>and <i>C</i><i>pm</i><i> </i>are suggested as well as point and interval estimators for the suggested indices. The accuracy of interval estimators are evaluated through large Monte Carlo simulations and the difference between empirical coverage rates and nominal confidence limits are calculated.</p><p>It was found in all reports that a dependency among observations has a great impact on the coverage rates. The coverage rate difference depends on both the size of the autocorrelation and the type of time series model and for the original <i>C</i><i>pk</i> and <i>C</i><i>pm</i> the difference can be large. With the suggested alternative indices, however, the differences are always reduced and unless the autocorrelations are close to ±1, the sizes of differences are of little consequence.</p>

The use of process capability indices in the industry is traditionally based on the assumptions that a sample from a process are observations on independently, identically and normally distributed random variables, IIN. However, all three assumptions are open to discussion and in this thesis, the estimation of the indices is studied when the assumption of independence is not fulfilled. In five reports, the indices Cpk and Cpm are studied, and instead of random samples, samples are regarded as observations on a time series. In the first four reports, each index is studied for either an AR(1) or an MA(1) process and the fifth report, both indices are studied for a general ARMA(p,q) process. In all reports, alternatives to Cpk and Cpm are suggested as well as point and interval estimators for the suggested indices. The accuracy of interval estimators are evaluated through large Monte Carlo simulations and the difference between empirical coverage rates and nominal confidence limits are calculated. It was found in all reports that a dependency among observations has a great impact on the coverage rates. The coverage rate difference depends on both the size of the autocorrelation and the type of time series model and for the original Cpk and Cpm the difference can be large. With the suggested alternative indices, however, the differences are always reduced and unless the autocorrelations are close to ±1, the sizes of differences are of little consequence.

Índices de capacidade mal empregados geram conclusões errôneas, comprometendo o estudo e análise do processo, prejudicando o atendimento de exigências gerenciais ou de clientes externos. Assim, o objetivo do presente trabalho é propor índices de capacidade para processos monitorados com gráficos de controle baseado em modelos de regressão conteplando limites simétricos e assimétricos. Realizou-se um mapeamento dos artigos publicados em nove periódicos no período de 2000 a 2009, visando identificar as abordagens pesquisadas sobre capacidade de processos. Um fluxograma orientativo é apresentado, com a finalidade de direcionar a escolha do tipo de gráfico de controle e índices de capacidade para processos com variáveis de resposta: (i) não correlacionadas, (ii) correlacionadas dependentes da variável de controle e (iii) autocorrelacionadas. O uso do fluxograma foi ilustrado através da aplicação do mesmo em um processo de torneamento de uma empresa de máquinas agrícolas. / Capability indices wrongly appointed generate erroneous conclusions, compromising the study and analysis of the process, jeopardizing the fulfillment of the requirements management or external customers. Therefore, the objective of this study is to propose capability indices for processes monitored with control charts based on regression models considering symmetric and asymmetric limits. A mapping of the articles published in nine journals, during the period of 2000 to 2009, was conducted to identify the different approaches surveyed on process capability. A flowchart is presented to direct the choice of control chart and capability indices for processes with response variables: (i) noncorrelated, (ii) correlated dependent control variables and (iii) autocorrelated. The use of the flowchart was illustrated by applying it to the hard turning process of an agricultural machinery company.

Índices de capacidade mal empregados geram conclusões errôneas, comprometendo o estudo e análise do processo, prejudicando o atendimento de exigências gerenciais ou de clientes externos. Assim, o objetivo do presente trabalho é propor índices de capacidade para processos monitorados com gráficos de controle baseado em modelos de regressão conteplando limites simétricos e assimétricos. Realizou-se um mapeamento dos artigos publicados em nove periódicos no período de 2000 a 2009, visando identificar as abordagens pesquisadas sobre capacidade de processos. Um fluxograma orientativo é apresentado, com a finalidade de direcionar a escolha do tipo de gráfico de controle e índices de capacidade para processos com variáveis de resposta: (i) não correlacionadas, (ii) correlacionadas dependentes da variável de controle e (iii) autocorrelacionadas. O uso do fluxograma foi ilustrado através da aplicação do mesmo em um processo de torneamento de uma empresa de máquinas agrícolas. / Capability indices wrongly appointed generate erroneous conclusions, compromising the study and analysis of the process, jeopardizing the fulfillment of the requirements management or external customers. Therefore, the objective of this study is to propose capability indices for processes monitored with control charts based on regression models considering symmetric and asymmetric limits. A mapping of the articles published in nine journals, during the period of 2000 to 2009, was conducted to identify the different approaches surveyed on process capability. A flowchart is presented to direct the choice of control chart and capability indices for processes with response variables: (i) noncorrelated, (ii) correlated dependent control variables and (iii) autocorrelated. The use of the flowchart was illustrated by applying it to the hard turning process of an agricultural machinery company.

Índices de capacidade mal empregados geram conclusões errôneas, comprometendo o estudo e análise do processo, prejudicando o atendimento de exigências gerenciais ou de clientes externos. Assim, o objetivo do presente trabalho é propor índices de capacidade para processos monitorados com gráficos de controle baseado em modelos de regressão conteplando limites simétricos e assimétricos. Realizou-se um mapeamento dos artigos publicados em nove periódicos no período de 2000 a 2009, visando identificar as abordagens pesquisadas sobre capacidade de processos. Um fluxograma orientativo é apresentado, com a finalidade de direcionar a escolha do tipo de gráfico de controle e índices de capacidade para processos com variáveis de resposta: (i) não correlacionadas, (ii) correlacionadas dependentes da variável de controle e (iii) autocorrelacionadas. O uso do fluxograma foi ilustrado através da aplicação do mesmo em um processo de torneamento de uma empresa de máquinas agrícolas. / Capability indices wrongly appointed generate erroneous conclusions, compromising the study and analysis of the process, jeopardizing the fulfillment of the requirements management or external customers. Therefore, the objective of this study is to propose capability indices for processes monitored with control charts based on regression models considering symmetric and asymmetric limits. A mapping of the articles published in nine journals, during the period of 2000 to 2009, was conducted to identify the different approaches surveyed on process capability. A flowchart is presented to direct the choice of control chart and capability indices for processes with response variables: (i) noncorrelated, (ii) correlated dependent control variables and (iii) autocorrelated. The use of the flowchart was illustrated by applying it to the hard turning process of an agricultural machinery company.

Materials have traditionally been selected for the design of a product; however, advances in the understanding of material processing along with simulation and computation techniques are now making it possible to systematically design materials by tailoring the properties of the material to achieve the desired product performance. Material design offers the potential to increase design freedom and enable improved product performance; however, this increase in design freedom brings with it significant complexity in predictive models used for design, as well as many new design variables to consider. Material selection, on the other hand, is a well-established method for identifying the best materials for a product and does not require the complex models needed for material design. But material selection inherently limits the design of products by only considering existing materials. To balance increasing design costs with potentially improved product performance, designers must have a method for assessing the value of material design in the context of product design. In this thesis, the Design Space Expansion Strategy (DSES) and the Value of Design Space Expansion (VDSE) metric are proposed for supporting a designer s decision between material selection and material design in the context of product design. The strategy consists of formulating and solving two compromise Decision Support Problems (cDSP). The first cDSP is formulated and solved using a selected baseline material. The second cDSP is formulated and solved in an expanded material design space defined by material property variables in addition to other system variables. The two design solutions are then compared using the VDSE metric to quantify the value of expanding the material design space. This strategy is demonstrated in this thesis with an example of blast resistant panel design and is validated by application of the validation square, a framework for the validating design methods.

As Boas Práticas de Fabricação de Medicamentos (BPFM) enfatizam que a indústria farmacêutica deve dirigir seus esforços no sentido de compreender a variação do processo, incluindo as fontes, o grau de variação e o impacto dessa variação nas características de qualidade do produto. O processo de fabricação de medicamentos tem apresentado significativas mudanças, em especial no que se refere à introdução de tecnologias analíticas que permitem o controle do processo em tempo real. A abordagem baseada na análise de risco e no novo Sistema de Qualidade Farmacêutica constitui ponto central das BPFM para o século XXI. Os órgãos regulatórios têm exigido da indústria farmacêutica sua adesão na melhoria contínua relativa ao desempenho de seus processos e, por consequência, na qualidade do produto. O objetivo do presente trabalho foi o desenvolvimento e validação de método analítico empregando espectroscopia no infravermelho próximo, assim como a avaliação do processo de fabricação de comprimidos de Captopril 25 mg, empregando abordagem racional-científica. Com referência à avaliação do processo, foram adotadas as seguintes ferramentas: análise de modos e efeitos de falhas (FMEA); gráficos de controle; índices de capacidade e análise de variância (ANOVA). A espectroscopia por infravermelho próximo (NIR) foi selecionada por apresentar maior rapidez na obtenção dos resultados, maior simplicidade na preparação das amostras, multiplicidade das análises a partir de uma única leitura e por apresentar característica não invasiva. Os resultados comprovaram a adequação dessa tecnologia na avaliação quantitativa do Captopril nas etapas de mistura de pós e de compressão. Os desvios padrão relativos na determinação da uniformidade de Captopril na mistura de pós e nos comprimidos empregando método no NIR foram, respectivamente 3,15 e 0,18%. No que se refere à avaliação da estabilidade e da capacidade do processo, as ferramentas adotadas permitiram a compreensão das fontes de variabilidade, assim como a determinação de seu grau, nas diferentes etapas do processo. Os índices de capacidade (CpK) relativos à uniformidade de Captopril (% p/v) na mistura de pós, ao peso médio do comprimido, à uniformidade de conteúdo e à % (p/v) dissolvida de Captopril, no ensaio de dissolução, foram 0,70, 1,94, 1,80 e 2,19, respectivamente. / The Good Manufacturing Practices (GMP) for Medicinal Products point out that the pharmaceutical industry must direct efforts to understand the variation of the processes, including the sources, the level of variation and the variation impact on the process in characteristics of the product. The manufacturing process has shown meaningful changes, especially in the introduction of new analytical technologies that allow the process control in real time. The approach based on risk analyses and on the new Pharmaceutical Quality System is a central key for the GMP for the XXI century. The Regulatory Agencies have demanded the pharmaceutical industry to adhere the continuous improvement related to the performance of its processes and, consequently, the product quality. Thus, the present paper aimed the development and validation of the analytical method employing NIR spectroscopy as the assessment of manufacturing process of Captopril 25 mg tablets, using rational scientific approach. Regarding the process assessment, the following tools were adopted: analysis of failure modes and effects analysis (FMEA), control charts, capability indexes, as well as analysis of variance (ANOVA). The near-infrared spectroscopy was selected due to its greater speed in getting the results, simplicity in sample preparation, and multiplicity of analysis from a single reading and provide non-invasive feature. The results confirmed the suitability of this technology in quantitative assessment of Captopril on the steps of mixing powders and compression. The relative standard deviations for the determination of Captopril uniformity in the post mixtures and in the tablets employing NIR were 3,15 e 0,18%, respectively. In reference to the stability assessment and process capacity, the tools adopted permitted the understanding of the sources of variability, as well as the determination of their level in different phases of the process. The capacity indexes relating to Captopril uniformity (% p/v) in the powder mixture, the average weight of the tablet, the content uniformity and the % (p/v) dissolved Captopril, in the dissolution assay were 0,70, 1,94, 1,80 and 2,19, respectively.

As Boas Práticas de Fabricação de Medicamentos (BPFM) enfatizam que a indústria farmacêutica deve dirigir seus esforços no sentido de compreender a variação do processo, incluindo as fontes, o grau de variação e o impacto dessa variação nas características de qualidade do produto. O processo de fabricação de medicamentos tem apresentado significativas mudanças, em especial no que se refere à introdução de tecnologias analíticas que permitem o controle do processo em tempo real. A abordagem baseada na análise de risco e no novo Sistema de Qualidade Farmacêutica constitui ponto central das BPFM para o século XXI. Os órgãos regulatórios têm exigido da indústria farmacêutica sua adesão na melhoria contínua relativa ao desempenho de seus processos e, por consequência, na qualidade do produto. O objetivo do presente trabalho foi o desenvolvimento e validação de método analítico empregando espectroscopia no infravermelho próximo, assim como a avaliação do processo de fabricação de comprimidos de Captopril 25 mg, empregando abordagem racional-científica. Com referência à avaliação do processo, foram adotadas as seguintes ferramentas: análise de modos e efeitos de falhas (FMEA); gráficos de controle; índices de capacidade e análise de variância (ANOVA). A espectroscopia por infravermelho próximo (NIR) foi selecionada por apresentar maior rapidez na obtenção dos resultados, maior simplicidade na preparação das amostras, multiplicidade das análises a partir de uma única leitura e por apresentar característica não invasiva. Os resultados comprovaram a adequação dessa tecnologia na avaliação quantitativa do Captopril nas etapas de mistura de pós e de compressão. Os desvios padrão relativos na determinação da uniformidade de Captopril na mistura de pós e nos comprimidos empregando método no NIR foram, respectivamente 3,15 e 0,18%. No que se refere à avaliação da estabilidade e da capacidade do processo, as ferramentas adotadas permitiram a compreensão das fontes de variabilidade, assim como a determinação de seu grau, nas diferentes etapas do processo. Os índices de capacidade (CpK) relativos à uniformidade de Captopril (% p/v) na mistura de pós, ao peso médio do comprimido, à uniformidade de conteúdo e à % (p/v) dissolvida de Captopril, no ensaio de dissolução, foram 0,70, 1,94, 1,80 e 2,19, respectivamente. / The Good Manufacturing Practices (GMP) for Medicinal Products point out that the pharmaceutical industry must direct efforts to understand the variation of the processes, including the sources, the level of variation and the variation impact on the process in characteristics of the product. The manufacturing process has shown meaningful changes, especially in the introduction of new analytical technologies that allow the process control in real time. The approach based on risk analyses and on the new Pharmaceutical Quality System is a central key for the GMP for the XXI century. The Regulatory Agencies have demanded the pharmaceutical industry to adhere the continuous improvement related to the performance of its processes and, consequently, the product quality. Thus, the present paper aimed the development and validation of the analytical method employing NIR spectroscopy as the assessment of manufacturing process of Captopril 25 mg tablets, using rational scientific approach. Regarding the process assessment, the following tools were adopted: analysis of failure modes and effects analysis (FMEA), control charts, capability indexes, as well as analysis of variance (ANOVA). The near-infrared spectroscopy was selected due to its greater speed in getting the results, simplicity in sample preparation, and multiplicity of analysis from a single reading and provide non-invasive feature. The results confirmed the suitability of this technology in quantitative assessment of Captopril on the steps of mixing powders and compression. The relative standard deviations for the determination of Captopril uniformity in the post mixtures and in the tablets employing NIR were 3,15 e 0,18%, respectively. In reference to the stability assessment and process capacity, the tools adopted permitted the understanding of the sources of variability, as well as the determination of their level in different phases of the process. The capacity indexes relating to Captopril uniformity (% p/v) in the powder mixture, the average weight of the tablet, the content uniformity and the % (p/v) dissolved Captopril, in the dissolution assay were 0,70, 1,94, 1,80 and 2,19, respectively.

Οι δείκτες αποτελεσματικότητας μιας διαδικασίας μετρούν τον βαθμό στον οποίο μια διαδικασία, που βρίσκεται σε στατιστική ισορροπία, παράγει προϊόντα τα οποία ικανοποιούν τις προδιαγραφές του πελάτη. Στη διπλωματική αυτή εργασία δίνονται οι ορισμοί διαφόρων τέτοιων δεικτών που έχουν προταθεί από τη βιβλιογραφία, για μονοδιάστατες και διδιάστατες μεταβλητές, οι οποίες ακολουθούν κανονική κατανομή. Παρουσιάζονται οι ιδιότητες καθώς και οι σχέσεις μεταξύ των δεικτών αυτών και αναλύονται τα μειονεκτήματα και τα πλεονεκτήματα της χρήσης τους. Δίνονται εκτιμητές κάποιων δεικτών και ιδιότητες αυτών όπως αναμενόμενη τιμή, διασπορά, συνάρτηση πυκνότητας. Κατασκευάζονται επίσης διαστήματα εμπιστοσύνης και έλεγχοι υποθέσεων για τους εκτιμητές των δεικτών. Τέλος, παρουσιάζονται αριθμητικά παραδείγματα και εφαρμογές των δεικτών αποτελεσματικότητας στη βιομηχανία. / Process capability indices are intended to provide single-number assessment of the capability, of a process in statistical control, to produce items that meet the customer΄s specifications. We present the definitions of various such indices that have been proposed for univariate and bivariate normal distributions. We refer to their properties, the relations among them and the weaknesses or benefits from their use. Estimators of the indices are considered and their properties such as expected value, variance and probability density function are derived. Confidence intervals and tests of hypothesis are constructed for their estimators. Finally, numerical examples and applications of process capability indices in industry are presented.

This thesis aims to evaluate a new manufacturing process by using statistical methods SPC. In the theoretical part provides the basic methods and rules applied in the assessment of control charts. The next part evaluates the current state of the company Hanhart Morkovice s.r.o. analysis and production of coils. The analytical part deals with control charts for reference and quality characters using statistical software process capability indexes and control charts. Based on information from the analytical part, conclusions are drawn and designed for long-term steps using established methods of SPC for quality characters.