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Components of variance estimation for the split-plot designLi, Shou-hua, January 1900 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.
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Otimização de misturas quimicas com flexibilidade na ordem de execução dos experimentos / Chemical mixture optimization with flexibility in the execution order of experimentsBorges, Cleber Nogueira 10 May 2007 (has links)
Orientador: Roy Edward Bruns / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-09T12:52:19Z (GMT). No. of bitstreams: 1
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Previous issue date: 2007 / esumo: Neste trabalho é apresentado o planejamento estatístico split-plot onde as unidades main-plots e sub-plots são planejamentos de misturas químicas. Main-plots e sub-plots são definidos de acordo com a estrutura simplex-centróide. O planejamento foi aplicado para a otimização simultânea de solventes extratores e fases móveis utilizados na separação cromatográfica de compostos químicos de plantas. O interesse foi determinar os melhores valores das respostas (maiores números de picos) em função dos extratores e fases móveis. A vantagem da blocagem dos experimentos segundo a estrutura split-plot é a conveniência por minimizar (ou facilitar) o trabalho experimental ou reduzir resíduos químicos ou ambos. A desvantagem é que o tratamento estatístico de tal sistema se torna mais complexo que os planejamentos com esquemas aleatórios. Gráficos normais foram utilizados para a escolha de modelos e assim, evitando a realização de replicatas dos experimentos / Abstract: A split-plot statistical design is proposed for which the main-plots and sub-plots are both chemical mixture designs. Main-plots and sub-plots are investigated using the simplex-centroid design. The composite mixture-mixture design was applied to the simultaneous optimization of extractor solvents and mobile phases used in the chromatographic separation of chemical compounds from plant materials. The main goal was to determine the best response values, largest number of peaks, as a function of the extractor and mobiles phase components. The advantages of using blocked experiments following the split-plot structure is to minimize (or facilitate) the experimental work as well as reduce the chemical residuals that must be discarded or both. The drawback is that the statistical treatment of the system becomes more complex than designs with random schemes. Normals graphs were utilized for choosing models so, the realization of replicate experiments could be avoided. / Doutorado / Quimica Analitica / Doutor em Ciências
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Otimização de processos contendo variaveis de mistura pelo metodo "split-plot" / Split-plot process optimization containing mixture variablesBortoloti, João Alexandre 22 June 2006 (has links)
Orientador: Roy Edward Bruns / Tese (doutorado) - Universidade Estadual de Campinas. Instituto de Quimica / Made available in DSpace on 2018-08-07T10:15:07Z (GMT). No. of bitstreams: 1
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Previous issue date: 2006 / Doutorado / Físico-Química / Doutor em Quimica
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A study of covariance structure selection for split-plot designs analyzed using mixed modelsQiu, Chen January 1900 (has links)
Master of Science / Department of Statistics / Christopher I. Vahl / In the classic split-plot design where whole plots have a completely randomized design, the conventional analysis approach assumes a compound symmetry (CS) covariance structure for the errors of observation. However, often this assumption may not be true. In this report, we examine using different covariance models in PROC MIXED in the SAS system, which are widely used in the repeated measures analysis, to model the covariance structure in the split-plot data in which the simple compound symmetry assumption does not hold. The comparison of the covariance structure models in PROC MIXED and the conventional split-plot model is illustrated through a simulation study. In the example analyzed, the heterogeneous compound symmetry (CSH) covariance model has the smallest values for the Akaike and Schwarz’s Bayesian information criteria fit statistics and is therefore the best model to fit our example data.
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Design Issues in Nonregular and Follow-Up Split-Plot DesignsTichon, Jenna Gaylene 10 September 2010 (has links)
In industrial experimentation, time and material costs are often at a premium. In designing an experiment, one needs to balance the desire for sufficient experimental runs to provide adequate data analysis, with the need to conduct a cost-effective experiment. A common compromise is the use of fractional factorial (FF) designs, in which only a fraction of the total possible runs is utilized.
After discussing the basic concepts of FF designs, we introduce the fractional factorial split-plot (FFSP) design. Such designs occur frequently, because certain factors are often harder to vary than others, thus imposing randomization restric- tions.
This thesis examines two techniques aimed at reducing run size that have not been greatly explored in the FFSP setting — nonregular designs and semifoldover designs. We show that these designs offer competitive alternatives to the more standard regular and full foldover designs and we produce tables of optimal designs in both scenarios.
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Design Issues in Nonregular and Follow-Up Split-Plot DesignsTichon, Jenna Gaylene 10 September 2010 (has links)
In industrial experimentation, time and material costs are often at a premium. In designing an experiment, one needs to balance the desire for sufficient experimental runs to provide adequate data analysis, with the need to conduct a cost-effective experiment. A common compromise is the use of fractional factorial (FF) designs, in which only a fraction of the total possible runs is utilized.
After discussing the basic concepts of FF designs, we introduce the fractional factorial split-plot (FFSP) design. Such designs occur frequently, because certain factors are often harder to vary than others, thus imposing randomization restric- tions.
This thesis examines two techniques aimed at reducing run size that have not been greatly explored in the FFSP setting — nonregular designs and semifoldover designs. We show that these designs offer competitive alternatives to the more standard regular and full foldover designs and we produce tables of optimal designs in both scenarios.
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Hålrumsvariationer vid asfalttillverkning : En fallstudie vid Skanska enligt DMAIC avseende förbättringsmöjligheter vid kalltillsatt asfaltåtervinning / Void volume variations in asphalt manufacturing : A case study at Skanska based on DMAIC regarding opportunities for improvement when using cold RAPJohansson, Paulina January 2018 (has links)
Att optimera hålrumshalten i färdig beläggning är essentiellt bland annat för att en vägkonstruktion inte ska få sprickor, spårbildning eller andra deformationer vid temperaturväxlingar (Monismith, 1992). Eftersom både återvunnen och jungfrulig asfaltmassa består av stenmaterial, bitumen och tillsatsmedel är återvunnen asfalt värd den jungfruliga massans vikt ton för ton vid utbyte i ett arbetsrecept (Brock & Richmonds, 2007). I takt med att asfaltåtervinning blivit vanligare ökar dock komplexiteten, då återvunnet material är betydligt svårare än jungfruligt att karaktärisera (Karlsson & Isacsson, 2006). Eftersom användningen av återvunnet material förväntas öka samtidigt som lite forskning gjorts i ämnet är det därför av vikt att undersöka hålrumshalter vid kalltillsatt asfaltåtervinning. För studien undersöktes asfaltmassan ABT11 160/220 vid kalltillsättning av upp till 25 % asfaltåtervinning. Sex Sigmas problemlösningsmetodik DMAIC, vilket står för ett projektbaserat förhållningssätt i de fem faserna define, measure, analyze, improve och control, användes för att få en djupgående förståelse för hålrumsproblematiken. I metodiken användes i sin tur statistisk processtyrning och försöksplanering för att svara på studiens syfte, vilket var att granska och utvärdera orsakerna till varför hålrumshalter under asfalttillverkning varierar vid tillsättning av kallt asfaltgranulat samt ge rekommendationer för en förbättrad produktion med avseende på hålrumshalt. Efter granskning av historiska data, beräkningar, intervjuer och observationer ansågs de viktigaste orsakerna till hålrumsvariationer uppkomma från de fem källorna datahantering, kommunikation, resurshantering, materialkunskap och organisationskultur, där de två sistnämnda ansågs vara rotorsaker. På grund av examensarbetets avgränsning granskades endast materialkunskapen mer djupgående. För att fördjupa materialkunskapen valdes faktorerna asfaltåtervinning, jungfruligt bitumen, jungfruligt filler samt tillverknings- och instampningstemperatur ut för fortsatta studier genom två experiment. I det första experimentet granskades hur hålrumshalten påverkades av olika instampningstemperaturer genom en OFAT-studie och i det andra experimentet ansattes ett 24-1 faktorförsök enligt Splitplot där hålrummet mättes vid vanlig instampningstemperatur (135 ˚C) samt genom en vägsimulering. Resultatet från det första experimentet uppvisade ett förhållande enligt ett tredjegradspolynom mellan hålrum och instampningstemperatur med stora hålrumsförändringar under 125 ˚C och över 145 ˚C. Detta medför att det är av än större vikt att kontrollera temperaturen för lågtempererad massa och massa med mycket återvinning för att uppnå godkända hålrum vid utläggning. Det andra experimentet visade att även bitumen och återvinning är signifikanta effekter för hålrummet, där minskade bitumenhalter och ökade återvinningshalter medför högre hålrumshalter samt att återvinningshalter över 15 % medför oönskad ökning av hålrumshalter vid utläggning på väg. För att avhjälpa orsakerna till hålrumsvariationerna rekommenderas att data samlas, utvärderas, kommuniceras och följs upp i större utsträckning genom användning av statistisk processtyrning, värdeflödesanalyser och fortsatta materialstudier. Organisationskulturen bör förändras för att skapa en förståelse för vikten av rekommenderade metoder. Kan rekommendationerna följas innebär det en uppskattad ekonomisk besparing på 11 520 000kr/år, samtidigt som det skulle innebära miljömässiga fördelar i form av bland annat ett minskat uttag av ändliga resurser och minskade CO2-utsläpp. / Optimizing void volumes are essential for the serviceability of asphalt concrete pavements, as fatigue cracking, rutting and other permanent deformations can be caused by e.g. temperature changes (Monismith, 1992). Since both reclaimed asphalt pavement (RAP) and virgin asphalt concrete consist of mineral aggregate, bitumen and additives, RAP is worth the virgin material it replaces ton for ton (Brock & Richmonds, 2007). As the use of RAP becomes more and more popular, the complexity of asphalt manufacturing increases (Karlsson & Isacsson, 2006). This, because the recycled material is harder to characterize than virgin material. Since the usage of RAP is expected to increase in hot-mix asphalt (HMA), while little research has been made in the field of cold feed RAP, it is of great importance to investigate the void volumes with this method. During this study, ABT11 160/220 with the addition of up to 25% cold feed RAP was therefore investigated. Six Sigma’s project improvement methodology DMAIC, acronym for the five phases define, measure, analyze, improve and control, were used to get an in depth understanding for the variations in void volumes. In this method, Statistical Process Control and Design of Experiments were used to answer the research purpose, which was to investigate and evaluate the reasons to why void volumes during asphalt manufacturing varies when adding cold RAP and give recommendations for an improved production regarding void volumes. After an investigation of historic data, calculations, interviews and observations, the most important causes for variations in void volumes came from data collection, communication, resource management, material knowledge and organizational culture, where the last two are seen as root causes. Because of the research delimitations, only the material knowledge was looked into further. To extend the knowledge of the material, the factors RAP, virgin bitumen, virgin filler, manufacturing temperature and temperature for Marshall testing were analyzed through two experiments. In the first experiment, the relationship between void volumes and the temperature for Marshall testing were investigated through an OFAT study, and the second experiment was made through a 24-1 factorial design according to Split plot, in which the void volumes were measured through the normal Marshall testing temperature (135 ˚C) and through a road simulation. The OFAT result showed that a third degree linear relationship is present between the void volumes and the Marshall testing temperature, with large changes for temperatures lower than 125 ˚C and greater than 145 ˚C. This entails an increased importance of controlling the temperature for warm-mix asphalt (WMA) and asphalt with increased volumes of RAP. The Split plot experiment showed that also bitumen and RAP are significant effects for the void volume, where decreased volumes of bitumen and increased volumes of RAP entails higher void volumes in the pavement. Over 15 % RAP also entails greater void volumes. To decrease the causes for variations in void volumes, the recommendation is to collect, evaluate, communicate and follow up data at a higher extent through implementation of statistical process control, value flow analysis and continued material studies. The organizational culture ought to be changed to create an understanding of the recommended methods. If the recommendations are followed, estimated economic savings of 11 520 000kr/year can be a reality, as well as environmental benefits of e.g. a decreased use of finite resources and reduced CO2 emissions.
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Otimização simultanea de variaveis de processo e mistura em cromatografia liquida de alta eficiencia / Optimization of process and mixture variables in high performance liquid chromatographyBreitkreitz, Márcia Cristina, 1979- 07 June 2007 (has links)
Orientadores: Roy Edward Bruns, Isabel Cristina S. F. Jardim / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-09T16:30:39Z (GMT). No. of bitstreams: 1
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Previous issue date: 2007 / Resumo: Este trabalho teve como objetivo o desenvolvimento de modelos combinados considerando simultaneamente o tipo de Fase Estacionária (FE) como variável de processo e diferentes composições de Fase Móvel (FM) como variáveis de mistura para descrever a influência de cada uma destas variáveis, bem como a interação entre elas, na separação de diversos compostos presentes em duas amostras: uma mistura de compostos neutros e uma mistura de agrotóxicos. Os experimentos necessários para a determinação dos coeficientes dos modelos foram realizados de acordo com um planejamento split-plot, no qual os tipos de FE, C 8 e C 18 foram considerados main-plots e as composições de FM, sub-plots. Os resultados foram tratados de duas maneiras: de acordo com a estrutura split-plot do planejamento e supondo completa aleatorização na realização dos experimentos. Para descrever a qualidade da separação, foi utilizada uma função objetiva e o procedimento de otimização simultânea de várias respostas, descrito por Derringer e Suich, empregando, neste caso, critérios elementares como fator de retenção, resolução e fator de separação como respostas. Os modelos foram avaliados empregando-se Análise da Variância quanto à significância dos tratamentos e falta de ajuste. Na descrição da qualidade da separação dos compostos nas duas misturas, o procedimento de Derringer e Suich se mostrou superior às funções objetivas, pois permitiu a construção de modelos tendo como respostas parâmetros cromatográficos, os quais são, de fato, funções da composição da FM e da FE. Estes modelos, quando combinados através da desejabilidade global, permitiram que as condições para a melhor separação de todos os compostos em cada mistura fossem alcançadas, sem perda de informações sobre a separação individual dos pares de picos. Todos os modelos apresentaram capacidade preditiva para as respostas avaliadas ¿ fatores de retenção/resolução/fatores de retenção relativos - nas duas misturas, sem ou com pequena falta de ajuste. Embora todos os planejamentos tenham sido realizados de acordo com um procedimento split-plot, não foram verificadas diferenças nos valores dos erros dos coeficientes dos modelos matemáticos nos cálculos split-plot e supondo completa aleatorização e isto se deveu ao fato do erro main-plot ter sido muito menor que o erro sub-plot / Abstract: The aim of this work was to develop combined statistical models including the stationary phase (SP) as process variables and different compositions of the mobile phase (MP) as mixture variables in order to describe the influence of each type of variable as well as their interactions for the separation of compounds in two samples sets: one containing ten neutral compounds and another containing eleven pesticides. The experiments required to determine the coefficients of the models were carried out according to a split-plot approach, in which the stationary phases, C 8 or C 18 were considered as main-plots and the mobile phase compositions as sub-plots. The results were treated according to the split-plot approach and also supposing a completely random setup. The results provided by an objective function were compared to those obtained by Derringer¿s desirability functions constructed with simple chromatographic criteria such as resolution and relative retention factors as responses. The models were evaluated by means of Analysis of Variance, regarding regression significance and lack of fit. In order to describe the quality of the separation of the compounds in the two mixtures, the desirability procedure was preferred over the objective functions because the responses used in the latter were, in fact, functions of the stationary and mobile phases. The models combined into a global desirability function allowed the best conditions to the separation of all compounds to be found, without loss of information on the individual peak separation. All models presented predictive capabilities for the responses evaluated with none or little lack of fit. Although the experiments were carried out according to a split-plot approach, no significant differences were found in coefficient errors comparing to the complete random approach, which can be explained based on the low main-plot error / Mestrado / Quimica Analitica / Mestre em Química
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Profile Monitoring - Control Chart Schemes for Monitoring Linear and Low Order Polynomial ProfilesJanuary 2010 (has links)
abstract: The emergence of new technologies as well as a fresh look at analyzing existing processes have given rise to a new type of response characteristic, known as a profile. Profiles are useful when a quality variable is functionally dependent on one or more explanatory, or independent, variables. So, instead of observing a single measurement on each unit or product a set of values is obtained over a range which, when plotted, takes the shape of a curve. Traditional multivariate monitoring schemes are inadequate for monitoring profiles due to high dimensionality and poor use of the information stored in functional form leading to very large variance-covariance matrices. Profile monitoring has become an important area of study in statistical process control and is being actively addressed by researchers across the globe. This research explores the understanding of the area in three parts. A comparative analysis is conducted of two linear profile-monitoring techniques based on probability of false alarm rate and average run length (ARL) under shifts in the model parameters. The two techniques studied are control chart based on classical calibration statistic and a control chart based on the parameters of a linear model. The research demonstrates that a profile characterized by a parametric model is more efficient monitoring scheme than one based on monitoring only the individual features of the profile. A likelihood ratio based changepoint control chart is proposed for detecting a sustained step shift in low order polynomial profiles. The test statistic is plotted on a Shewhart like chart with control limits derived from asymptotic distribution theory. The statistic is factored to reflect the variation due to the parameters in to aid in interpreting an out of control signal. The research also looks at the robust parameter design study of profiles, also referred to as signal response systems. Such experiments are often necessary for understanding and reducing the common cause variation in systems. A split-plot approach is proposed to analyze the profiles. It is demonstrated that an explicit modeling of variance components using generalized linear mixed models approach has more precise point estimates and tighter confidence intervals. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010
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Otimização multivariada para determinação direta de Ni utilizando voltametria de redissolução anodica em um sistema homogeneo de solventes / Multivariate optimization for the direct determination of Ni using anodic stripping voltammetry in a homogeneous solvent systemMay, Gyda Marie 28 June 2006 (has links)
Orientador: João Carlos de Andrade / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-08T12:04:09Z (GMT). No. of bitstreams: 1
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Previous issue date: 2006 / Doutorado / Quimica Analitica / Doutor em Ciências
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