The safety of the food supply in the United States has become an issue of prominence in the minds of ordinary Americans. Several government agencies, including the United States Department of Agriculture and the Food and Drug Administration, are charged with the responsibility of preserving the safety of the food supply. Food is withdrawn from the market in a product recall when tainted or mislabeled and has the potential to harm the consumer in some manner. This research examines recall events issued by firms over the period of January, 2000 through October, 2009 in the United States. Utilizing economic and management theory to establish predictions, this study employs the Cox proportional hazard regression model to analyze the effects of firm size and branding on the risk of recall recurrence. The size of the firm was measured in both billions of dollars of sales and in thousands of employees. Branding by the firm was measured as a binary variable that expressed if a firm had a brand and as a count of the number of brands within a firm. This study also provides a descriptive statistical analysis and several findings based on the recall data specifically relating to annual occurrences, geographical locations of the firms involved, types of products recalled, and reasons for recall. We hypothesized that the increasing firm size would be associated with increased relative risk of a recall event while branding and an increasing portfolio of brands would be associated with decreased relative risk of a recall event. However, it was found that increased firm size and branding by the firm are associated with an increased risk of recall occurrence. The results of this research can have implications on food safety standards in both the public and private sectors.

Introdução: As técnicas mais comumente empregadas em análise de sobrevida que utilizam dados censurados são o estimador produto limite de Kaplan-Meier (KM) e o modelo de riscos proporcionais de Cox. Estas técnicas têm como suposição que a causa da perda de seguimento seja independente do tempo de sobrevida. Objetivo: O presente estudo visa a analisar o efeito das perdas de seguimento nestas duas técnicas. Material e Métodos: O estudo foi realizado utilizando-se o banco de dados dos pacientes cadastrados no Registro Hospitalar do Hospital do Câncer de São Paulo em 1994. Foram elaborados 28 bancos de dados simulando perdas informativas e não informativas. A perda informativa foi simulada transformando os óbitos em vivos, na proporção de 5 a 50%. A perda não informativa foi simulada através do sorteio de 5 a 50% do total do banco. O estimador de Kaplan-Meier (KM) foi utilizado para estimar a sobrevida acumulada no primeiro, terceiro e quinto ano de seguimento, e o modelo de riscos proporcionais de Cox para estimar as hazard ratio (HR). Todas as estimativas obtidas no KM e as HR's foram comparadas com os resultados do banco de dados original. Resultados: Houve maior proporção de perda nos pacientes com maior escolaridade, admitidos por convênio e particular e os menos graves (estádio I ou II). Quanto maior a proporção de perda informativa, maior a diferença alcançada nas estimativas realizadas pelo KM, verificando-se que a perda de seguimento superior a 15% acarretou diferenças superiores a 20% nas estimativas da probabilidade de sobrevida. As HR's foram menos afetadas, e proporções superiores a 20% de perda de seguimento acarretaram variações de cerca de 10% nas estimativas. Quando as perdas foram não informativas não houve diferenças significativas nas estimativas pelo KM e nas HR's em relação ao banco original. Conclusões: É importante avaliar se as perdas ocorridas em estudos de coorte são informativas ou não, pois se forem podem acarretar distorções principalmente nas estimativas feitas pelo método de KM. / Introduction: The Kaplan Meier product limit estimator (KM) and the Cox proportional hazard (HR) model are the most used tools in survival analysis. These two methods have the key assumption that censoring must be independent from the survival time. Objective: To analyze the consequences of loss to follow up in these two methods. Methods: The study has utilized the data of the Cancer Registry of the patients of Hospital do Cancer in São Paulo of 1994. The informative censure was simulated transforming the death by 5 to 50% into alive. Besides 5 to 50% was spared at random simulating the non-informative censoring. The survival probability and was calculated to the first, third and fifth year of follow –up. All the estimated probabilities and HR’s were compared with the results of the original data. Results: Patients with greater scholars, lower stages and admitted by health plans or private had more losses to follow up. The maximum proportion of accepted loss to follow –up is 10% to 15% when using the KM estimator, and the HR are less affected by the loss to follow-up and one can afford having 20% of it. When the losses were non informative there were no differences between the original probabilities. Conclusions: The possibility of over or under estimated probability must be analyzed in the presence of the losses to follow- up when using the KM and HR in survival analyses.

The objective of the present study is to investigate various problems associate with breast cancer and lung cancer patients. In this study, we compare the effectiveness of breast cancer treatments using decision tree analysis and come to the conclusion that although certain treatment shows overall effectiveness over the others, physicians or doctors should discretionally give different treatment to breast cancer patients based on their characteristics. Reoccurrence time of breast caner patients who receive different treatments are compared in an overall sense, histology type is also taken into consideration. To further understand the relation between relapse time and other variables, statistical models are applied to identify the attribute variables and predict the relapse time. Of equal importance, the transition between different breast cancer stages are analyzed through Markov Chain which not only gives the transition probability between stages for specific treatment but also provide guidance on breast cancer treatment based on stating information. Sensitivity analysis is conducted on breast cancer doubling time which involves two commonly used assumptions: spherical tumor and exponential growth of tumor and the analysis reveals that variation from those assumptions could cause very different statistical behavior of breast cancer doubling time. In lung cancer study, we investigate the mortality time of lung cancer patients from several different perspectives: gender, cigarettes per day and duration of smoking. Statistical model is also used to predict the mortality time of lung cancer patients.

Introdução: As técnicas mais comumente empregadas em análise de sobrevida que utilizam dados censurados são o estimador produto limite de Kaplan-Meier (KM) e o modelo de riscos proporcionais de Cox. Estas técnicas têm como suposição que a causa da perda de seguimento seja independente do tempo de sobrevida. Objetivo: O presente estudo visa a analisar o efeito das perdas de seguimento nestas duas técnicas. Material e Métodos: O estudo foi realizado utilizando-se o banco de dados dos pacientes cadastrados no Registro Hospitalar do Hospital do Câncer de São Paulo em 1994. Foram elaborados 28 bancos de dados simulando perdas informativas e não informativas. A perda informativa foi simulada transformando os óbitos em vivos, na proporção de 5 a 50%. A perda não informativa foi simulada através do sorteio de 5 a 50% do total do banco. O estimador de Kaplan-Meier (KM) foi utilizado para estimar a sobrevida acumulada no primeiro, terceiro e quinto ano de seguimento, e o modelo de riscos proporcionais de Cox para estimar as hazard ratio (HR). Todas as estimativas obtidas no KM e as HR's foram comparadas com os resultados do banco de dados original. Resultados: Houve maior proporção de perda nos pacientes com maior escolaridade, admitidos por convênio e particular e os menos graves (estádio I ou II). Quanto maior a proporção de perda informativa, maior a diferença alcançada nas estimativas realizadas pelo KM, verificando-se que a perda de seguimento superior a 15% acarretou diferenças superiores a 20% nas estimativas da probabilidade de sobrevida. As HR's foram menos afetadas, e proporções superiores a 20% de perda de seguimento acarretaram variações de cerca de 10% nas estimativas. Quando as perdas foram não informativas não houve diferenças significativas nas estimativas pelo KM e nas HR's em relação ao banco original. Conclusões: É importante avaliar se as perdas ocorridas em estudos de coorte são informativas ou não, pois se forem podem acarretar distorções principalmente nas estimativas feitas pelo método de KM. / Introduction: The Kaplan Meier product limit estimator (KM) and the Cox proportional hazard (HR) model are the most used tools in survival analysis. These two methods have the key assumption that censoring must be independent from the survival time. Objective: To analyze the consequences of loss to follow up in these two methods. Methods: The study has utilized the data of the Cancer Registry of the patients of Hospital do Cancer in São Paulo of 1994. The informative censure was simulated transforming the death by 5 to 50% into alive. Besides 5 to 50% was spared at random simulating the non-informative censoring. The survival probability and was calculated to the first, third and fifth year of follow –up. All the estimated probabilities and HR’s were compared with the results of the original data. Results: Patients with greater scholars, lower stages and admitted by health plans or private had more losses to follow up. The maximum proportion of accepted loss to follow –up is 10% to 15% when using the KM estimator, and the HR are less affected by the loss to follow-up and one can afford having 20% of it. When the losses were non informative there were no differences between the original probabilities. Conclusions: The possibility of over or under estimated probability must be analyzed in the presence of the losses to follow- up when using the KM and HR in survival analyses.

[EN] The global objective of the present thesis was to study the functional longevity defined as length of productive life (LPL) in five Spanish specialized lines of rabbit (A, V, H and LP). Chapter 3, aimed to check the genetic heterogeneity for longevity between the five lines estimating the additive variance and the corresponding effective heritabilities. As well as to test the genetic importance of time-dependent factors such as positive palpation order (OPP), physiological status (PS) and number of kits born alive (NBA) on the genetics of longevity. This point has been assessed using four different Cox proportional hazard models; the first one (Model 1) included all the previous factors in addition to the year-season effect, the inbreeding coefficient effect and finally the animal effect as random factor. The remaining three models were the same as Model 1 but excluding OPP (Model 2), or PS (Model 3), or NBA (Model 4). The complete data set comprised 15,670 does with records 35.6 % having censoring data, and the full pedigree file involved 19,405 animals. The heritability estimates for longevity in the five lines were low and ranged from 0.02±0.01 to 0.14±0.09, and consequently, it is not recommended to include this trait as selection criteria in rabbit breeding programs. Despite of the large variation of the heritability estimates, the corresponding HPD95% always overlapped and consequently the hypothesis of all lines having the same heritability cannot be discarded. Comparing the additive variance estimates of the four models, it was observed that by correcting for PS 51, 39, 38, 83 and 75% of the additive variance in lines A, V, H, LP and R, respectively, was removed. The risk of death or culling decreases as OPP advanced. Non-pregnant-non-lactating females are those under the higher risk. The does which had zero NBA had the highest risk, apart for this special figure (zero NBA) the risk decreased as NBA increased. Chapter 4 intended to estimate the genetic and environmental correlations between longevity and two prolificacy traits (number of kits born alive (NBA) and number of kits alive at weaning (NW)). Furthermore, to estimate the genetic and environmental correlations between longevity and the percentage of days that the doe spent in the different physiological statuses with respect to its entire productive life. The complete pedigree file comprised 19,405 animals. The datasets included records on 15,670 does which had 58,329 kindlings and 57,927 weanings. In general the genetic correlations between NBA and NW, and the hazard were low to very low, and the only line for which it can be said these genetic correlation to be different from zero was the LP line. Regarding the correlations between longevity and the percentage of days the doe spent in each physiological status, there were evidences of non-negligible genetic correlations between the two traits. Chapter 5 purposed to compare the five lines at their foundation and at fixed time periods during their selection programs. The first comparison was done at the origin of the lines, involving the complete data set, and using a genetic model (CM) including the additive values of the animals, so the effect of selection was considered. For the second comparison the same model as the first comparison was used, but excluding the additive effects from the model of analysis (IM), and involving only the data corresponding to each period, so the differences between the lines included the additive values of the animals. The lines V, H and LP showed at foundation a substantial superiority over line A. The line R had higher risk of death or culling with relevant differences when compared to V, H and LP lines. The maximum relative risks were observed between the lines LP and R (0.239), and between LP and A (0.317). For the comparisons at fixed times, the pattern of the differences between the A line and the others was similar to those observed at foundation. / [ES] El objetivo global de la presente tesis fue estudiar la longevidad funcional en cinco líneas españolas de conejos (A, V, H y LP), el carácter se definió como la longitud de la vida productiva. En el Capítulo 3, dirigido a comprobar la heterogeneidad genética de la longevidad entre las 5 líneas, se estimaron las varianzas aditivas y sus correspondientes heredabilidades efectivas. Y además se evaluó la importancia del orden de la palpación positiva (OPP), el estado fisiológico (PS) y el número de gazapos nacidos vivos (NBA) sobre el determinismo genético de la longevidad. Para ello se utilizaron 4 modelos de Cox de riesgos proporcionales; el primer modelo (Modelo 1) incluyó todos los factores anteriores, además del efecto del año-estación, el efecto de la consanguinidad y, finalmente, el valor aditivo de los animales como efecto aleatorio. Los otros tres modelos fueron igual que el Modelo 1 pero excluyendo OPP (Modelo 2), o PS (Modelo 3), o NBA (Modelo 4). Los datos de longevidad estaban referidos a 15,670 conejas y tuvieron una tasa de censura de 35.6%. La genealogía completa involucró a 19,405 animales. Las estimas de heredabilidad efectiva para la longevidad en las 5 líneas fueron bajas y variaron de 0.02±0.01 a 0.14±0.09. A pesar de la gran variación de las estimas puntuales de heredabilidad, los correspondientes intervalos HPD95% siempre se solaparon y por lo tanto la hipótesis de que todas las líneas tengan la misma heredabilidad no pudo descartase. Se observó que la exclusión de PS incrementó la varianza aditiva aproximadamente, en un 51, 39, 38, 83 y 75% en las líneas A, V, H, LP y R, respectivamente. El riesgo de muerte o eliminación disminuía a medida que avanzaba el OPP, observándose el riesgo más alto durante los primeros dos partos, partos en los que las conejas todavía están creciendo lo que sería un factor de riesgo importante. El nivel No-Gestante-No-Lactante de PS tuvo el mayor riesgo. Este nivel se interpreta como indicador de baja fertilidad y/o problemas de salud de la coneja. Las conejas que tenían cero NBA tuvieron el mayor riesgo de muerte o eliminación, aunque para el resto de niveles de NBA se apreció una disminución del riesgo a medida que aumenta la prolificidad. En el capítulo 4, se estimaron las correlaciones genéticas y ambientales entre la longevidad y dos caracteres de prolificidad [número de gazapos nacidos vivos (NBA) y el número de destetados (NW)]. El fichero de datos incluyó 58,329 partos y 57,927 destetes. También se estimaron las correlaciones entre longevidad y el porcentaje de días que la coneja pasó en los diferentes estados fisiológicos con respecto a la totalidad de su vida productiva. La única línea para la que se puede decir que la correlación genética entre NBA o NW y el riesgo fue significativamente diferente de cero fue la línea LP. Hubo evidencias de correlaciones genéticas no despreciables entre la longevidad y el porcentaje de días que la hembra pasó en cada estado fisiológico los dos caracteres. En el capítulo 5 se compararon las longevidades medias de las 5 líneas en su fundación y en períodos de tiempo determinados. La comparación de las líneas en el origen, utilizó todos los datos y un modelo genético (CM) que incluía los valores aditivos de los animales. Para la comparación en tiempos fijos se utilizó el mismo modelo, pero excluyendo los efectos aditivos del modelo de análisis (IM), utilizando sólo los datos correspondientes a cada período, por lo que las diferencias entre las líneas incluían los cambios debidos a la selección. Las líneas V, H y LP mostraron una superioridad sustancial sobre las líneas A y R. Los riesgos relativos máximos se observaron entre las líneas LP y R (0.239), y entre LP y A (0.317). Con respecto a las comparaciones en tiempos fijos, el patrón de las diferencias entre la línea de A y las otras líneas fue similar a los observados en la fundación. / [CAT] L'objectiu global de la present tesi va ser estudiar la longevitat funcional en cinc línies espanyoles de conills (A, V, H i LP), el caràcter es va definir com la longitud de la vida productiva. Al Capítol 3, dirigit a comprovar l'heterogeneïtat genètica de la longevitat entre les 5 línies, es van estimar les variàncies additives i les seues corresponents heretabilitats efectives. A més a més, es va avaluar la importància de factors dependents del temps, com l'orde de la palpació positiva (OPP) , l'estat fisiològic (PS) i el nombre de llorigons nascuts vius (NBA) sobre el determinisme genètic de la longevitat. Per a això es van utilitzar 4 models de Cox de riscos proporcionals; el primer model (Model 1) va incloure tots els factors anteriorment assenyalats, a més de l'efecte de l'any-estació, l'efecte de la consanguinitat i, finalment, el valor additiu dels animals com a efecte aleatori. Els altres tres models van ser igual que el Model 1 però excloent l'OPP (Model 2) , o PS (Model 3) , o NBA (Model 4) . Les dades de longevitat estaven referides a 15,670 conilles i van tindre una taxa de censura de 35.6%. La genealogia completa va involucrar a 19,405 animals. Les estimes d'heretabilitat efectiva (Model 1) per a la longevitat en les 5 línies van ser baixes i van variar de 0.02±0.01 a 0.14±0.09. A pesar de la gran variació de les estimes puntuals d'heretabilitat, els corresponents intervals HPD95% sempre es van solapar i per tant la hipòtesi que totes les línies tinguen la mateixa heretabilitat no va poder descartar-se. Es va observar que l'exclusió de PS va incrementar la variància additiva, aproximadament, en un 51, 39, 38, 83 i 75% en les línies A, V, H, LP i R, respectivament. El risc de mort o eliminació disminuïa a mesura que avançava l'OPP, observant-se el risc més alt durant els primers dos parts, en què les conilles encara estan creixent el que seria un factor de risc important. El nivell No-Gestant-No-Lactant de PS va tindre el major risc en comparació amb els altres nivells. Les conilles que tenien zero NBA van tindre el major risc de mort o eliminació, encara que per a la resta de nivells de NBA es va apreciar una disminució del risc a mesura que augmentà la prolificitat. Al Capítol 4, es van estimar les correlacions genètiques i ambientals entre la longevitat i dos caràcters de prolificitat [nombre de llorigons nascuts vius (NBA) i el nombre de deslletats (NW)]. El fitxer de dades va incloure 58,329 parts i 57,927 deslletaments. L'única línia per a la que es pot dir que la correlació genètica entre NBA o NW i el risc va ser significativament diferent de zero va ser la línia LP. Evidències de correlacions genètiques no menyspreables entre longevitat i els percentatge de dies que la femella va passar en cada estat fisiològic. Al Capítol 5 es compararen les longevitats mitges de les 5 línies en la seua fundació i en períodes de temps determinats. Per a la comparació de les línies a l'origen, es van utilitzar totes les dades i un model genètic (CM) que incloïa els valors additius dels animals, per la qual cosa es va considerar l'efecte de la selecció a partir de la fundació. En la comparació en temps fixos se va utilitzar el mateix model que en l'anterior, però excloent els efectes additius del model d'anàlisi (IM), utilitzant només les dades corresponents a cada període, per la qual cosa les diferències entre les línies incloïen els canvis deguts a la selecció. Les línies V, H i LP van mostrar una superioritat substancial sobre les línies A i R. Els riscos relatius màxims es van observar entre les línies LP i R (0.239), i entre LP i A (0.317). Respecte a les comparacions en temps fixos, el patró de les diferències entre la línia de A i les altres línies va ser semblant als observats en la fundació. / El Nagar, AGF. (2015). Genetic analysis of longevity in specialized lines of rabbits [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/52390 / TESIS

Acute respiratory infections (ARI) caused by influenza and other respiratory viruses affect millions of people annually. Although usually self-limiting a more complicated or severe course may occur in previously healthy people but are more likely in individuals with underlying illnesses. The most common viral agent is rhinovirus whereas influenza is less frequent but is well known to cause winter epidemics. In primary care, rapid diagnosis of influenza virus infections is essential in order to provide treatment. Clinical presentations vary among the different pathogens but may overlap and may also depend on host factors. Predictive models have been developed for influenza but study results may be biased because only individuals presenting with fever were included. Most of these models have not been adequately validated and their predictive power, therefore, is likely overestimated. The main objective of this thesis was to compare different mathematical models for the derivation of clinical prediction rules in individuals presenting with symptoms of ARI to better distinguish between influenza, influenza A subtypes and entero-/rhinovirus-related illness in children and adults and to evaluate model performance by using data-splitting for internal validation. Data from a completed prospective cluster-randomized trial for the indirect effect of influenza vaccination in children of Hutterite communities served as a basis of my thesis. There were a total of 3288 first episodes per season of ARI in 2202 individuals and 321 (9.8%) influenza positive events over three influenza seasons (2008-2011). The data set was divided into children under 18 years and adults. Both data sets were randomly split by subjects into a derivation (2/3 of the dataset) and a validation population (1/3 of the dataset). All predictive models were developed in the derivation sets. Demographic factors and the classical symptoms of ARI were evaluated with logistic regression and Cox proportional hazard models using forward stepwise selection applying robust estimators to account for non-independent data and by means of recursive partitioning. The beta coefficients of the independent predictors were used to develop different point scores. These scores were then tested in the validation groups and performance between validation and derivation set was compared using receiver operating characteristics (ROC) curves. We determined sensitivities and specificities, positive and negative predictive values, and likelihood ratios at different cut-points which could reflect test and treatment thresholds. Fever, chills, and cough were the most important predictors in children whereas chills and cough but not fever were most predictive of influenza virus infection in adults. Performance of the individual models was moderate with areas under the receiver operating characteristic curves between 0.75 and 0.80 for the main outcome influenza A or B virus infection. There was no statistically significant difference in performance between the derivation and validation sets for the main outcome. The results have shown, that various mathematical models have similar discriminative ability to distinguish influenza from other respiratory viruses. The scores could assist clinicians in their decision-making. However, performance of the models was slightly overestimated due to potential clustering of data and the results would first needed to be validated in a different population before application in clinical practice. / Thesis / Master of Science (MSc) / Every year, millions of people are attacked by "the flu" or the common cold. Certain signs and symptoms apparently are more discriminative between the common cold and the flu. However, the decision between starting a simple symptom orientated treatment, treating empirically for influenza or ordering a rapid diagnostic test that has only moderate sensitivity and specificity can be challenging. This thesis, therefore, aims to help physicians in their decision-making process by developing simple scores and decision trees for the diagnosis of influenza versus non-influenza respiratory infections. Data from a completed trial for the indirect effect of influenza vaccination in children of Hutterite communities served as a basis of my thesis. There were a total of 3288 first seasonal episodes of ARI in 2202 individuals and 321 (9.8%) influenza positive events over three influenza seasons (2008-2011). The data set was divided into children under 18 years and adults. Both data sets were split into a derivation and a validation set (=holdout group). Different mathematical models were applied to the derivation set and demographic factors as well as the classical symptoms of ARI were evaluated. The scores generated from the most important factors that remained in the model were then tested in the validation group and performance between validation and derivation set was compared. Accuracy was determined at different cut-points which could reflect test and treatment thresholds. Fever, chills, and cough were the most important predictors in children whereas chills and cough but not fever were most predictive of influenza virus infection in adults. Performance of the individual models was moderate for the main outcome influenza A or B virus infection. There was no statistically significant difference in performance between the derivation and validation sets for the main outcome. The results have shown, that various mathematical models have similar discriminative ability to distinguish influenza from other respiratory viruses. The scores could assist clinicians in their decision-making. However, the results would first needed to be validated in a different population before application in clinical practice.

The mechanisms that control growth processes in biology tissues have attracted continuous research interest despite their complexity. With the emergence of big data experimental approaches there is an urgent need to develop statistical and computational models to fit the experimental data and that can be used to make predictions to guide future research. In this work we apply statistical methods on growth process of different biological tissues, focusing on development of neuron dendrites and tumor cells. We first examine the neuron cell growth process, which has implications in neural tissue regenerations, by using a computational model with uniform branching probability and a maximum overall length constraint. One crucial outcome is that we can relate the parameter fits from our model to real data from our experimental collaborators, in order to examine the usefulness of our model under different biological conditions. Our methods can now directly compare branching probabilities of different experimental conditions and provide confidence intervals for these population-level measures. In addition, we have obtained analytical results that show that the underlying probability distribution for this process follows a geometrical progression increase at nearby distances and an approximately geometrical series decrease for far away regions, which can be used to estimate the spatial location of the maximum of the probability distribution. This result is important, since we would expect maximum number of dendrites in this region; this estimate is related to the probability of success for finding a neural target at that distance during a blind search. We then examined tumor growth processes which have similar evolutional evolution in the sense that they have an initial rapid growth that eventually becomes limited by the resource constraint. For the tumor cells evolution, we found an exponential growth model best describes the experimental data, based on the accuracy and robustness of models. Furthermore, we incorporated this growth rate model into logistic regression models that predict the growth rate of each patient with biomarkers; this formulation can be very useful for clinical trials. Overall, this study aimed to assess the molecular and clinic pathological determinants of breast cancer (BC) growth rate in vivo.

The input collected from warranty claims data links customer feedback with product quality. Results from warranty claim analysis can potentially improve product quality, customer relationships and positively affect business. However working on warranty claims data holds many challenges that requires a significant share of time devoted to data cleaning and data processing. The purpose of warranty claims analysis is to get the comprehensive overview of the reliability, costs and quality of household appliances produced by ASKO. While there are different ways to approach this problem, we will focus on non-parametric and semi-parametric methods, by using Kaplan-Meier estimators and Cox proportional hazard model respectively. These kinds of models are time dependent and therefore used for prediction of household appliance reliability. Even though non-parametric models are quite informative they cannot handle additional characteristics about observable product hence the semi-parametric Cox proportional hazard model was proposed. Apart from the reliability analysis, we will also predict warranty costs with probit model and observe inequality in household appliances part failures as a part of quality control analysis. Described methods were selected due to the fact that the warranty claims analysis will be practiced in future by ASKO’s quality department and therefore straight forward methods with very informative results are needed.

Cox proportional hazard model is often used to estimate the effect of covariates on hazard for censored event times. In this thesis we study the semiparametric models of additive risk for censored data. In this model the hazard is given as a sum of unknown baseline hazard function and a product of covariates and coefficients. Further the general additive-multiplicative model is assumed. In this model the effect of a covariate can be either multiplicative, additive or both at the same time. We focuse on determining the effect of a covariate in the general model. This model can be used to test for the multiplicative or addtive effect of a covariate on the hazard.

<p>  </p> <p>During the construction of a bridge, more specifically a concrete bridge deck, there are sometimes defects in materials or workmanship, resulting in what is called a construction defect. These defects can have a large impact on the lifecycle performance of the bridge deck, potentially leading to more preventative and reactive maintenance actions over time and thus a larger monetary investment by the bridge owner. Bridge asset managers utilize prediction software to inform their annual budgetary needs, however this prediction software traditionally relies only on historical condition rating data for its predictions. When attempting to understand how deterioration of a bridge deck changes with the influence of construction defects, utilizing the current prediction software is not appropriate as there is not enough historical data available to ensure accuracy of the prediction. There are numerical modeling approaches available that capture the internal physical and chemical deterioration processes, and these models can account for the change in deterioration when construction defects are present. There are also numerical models available that capture the effect of external factors that may be affecting the deterioration patterns of the bridge deck, in parallel to the internal processes. The goal of this study is to combine a mechanistic model capturing the internal physical and chemical processes associated with deterioration of a concrete bridge deck, with a model that is built strictly from historical condition rating data, in order to predict the changes in condition rating prediction of a bridge deck for a standard construction case versus a substandard construction case. Being able to measure the change in prediction of deterioration when construction defects are present then allows for quantifying the additional cost that would be required to maintain the defective bridge deck which is also presented. </p>