Analysis of the Optimal Sharing of Construction Risk in Public Procurement Contracts

This paper discusses a model based on the agency theory to analyze the optimal transfer of construction risk in public works contracts. The base assumption is that of a contract between a principal (public authority) and an agent (firm), where the payment mechanism is linear and contains an incentive mechanism to enhance the effort of the agent to reduce construction costs. A theoretical model is proposed starting from a cost function with a random component and assuming that both the public authority and the firm are risk averse. The main outcome of the paper is that the optimal transfer of construction risk will be lower when the variance of errors in cost forecast, the risk aversion of the firm and the marginal cost of public funds are larger, while the optimal transfer of construction risk will grow when the variance of errors in cost monitoring and the risk aversion of the public authority are larger

Application of the agency theory for the analysis of performance-based mechanisms in road management

El WCTR es un congreso de reconocido prestigio internacional en el ámbito de la investigación del transporte, y aunque las actas publicadas están en formato digital y sin ISSN ni ISBN, lo consideramos lo suficientemente importante como para que se considere en los indicadores. This paper develops a model based on agency theory to analyze road management systems (under the different contract forms available today) that employ a mechanism of performance indicators to establish the payment of the agent. The base assumption is that of asymmetric information between the principal (Public Authorities) and the agent (contractor) and the risk aversion of this latter. It is assumed that the principal may only measure the agent?s performance indirectly and by means of certain performance indicators that may be verified by the authorities. In this model there is presumed to be a relation between the efforts made by the agent and the performance level measured by the corresponding indicators, though it is also considered that there may be dispersion between both variables that gives rise to a certain degree of randomness in the contract. An analysis of the optimal contract has been made on the basis of this model and in accordance with a series of parameters that characterize the economic environment and the particular conditions of road infrastructure. As a result of the analysis made, it is considered that an optimal contract should generally combine a fixed component and a payment in accordance with the performance level obtained. The higher the risk aversion of the agent and the greater the marginal cost of public funds, the lower the impact of this performance-based payment. By way of conclusion, the system of performance indicators should be as broad as possible but should not overweight those indicators that encompass greater randomness in their results.

Evolution and treatment of vitamin B12 deficiency as a risk factor for (cognitive and functional) neurodegenerative diseases in institutionalized elderly = Evolución y tratamiento de la deficiencia de vitamina B12 como factor de riesgo de enfermedades neurodegenerativas (cognitivas y funcionales) en las personas mayores institucionalizadas.

Prevalence of vitamin B12 deficiency is very common in elderly people and can reach values as high as 40.5% of the population. It can be the result of the interaction among several factors. Vitamin B12 deficiencies have been associated with neurological, cognitive deterioration, haematological abnormalities and cardiovascular diseases that have an important influence on the health of the elderly and their quality of life. It is necessary to approach the problems arisen from the lack of data relative to them. The main objective of this thesis was to analyse the evolution of vitamin B12 status and related parameters, lipid and haematological profiles and their relationship to health risk factors, and to functional and cognitive status over one year and to determine the effect of an oral supplementation of 500 μg of cyanocobalamin for a short period of 28 days. An additional objective was to analyze the possible effects of medicine intakes on vitamin B status. Three studies were performed: a) a one year longitudinal follow-up with four measure points; b) an intervention study providing an oral liquid supplement of 500 μg of cyanocobalamin for a 28 days period; and c) analysis of the possible effect of medication intake on vitamin B status using the ATC classification of medicines. The participants for these studies were recruited from nursing homes for the elderly in the Region of Madrid. Sixty elders (mean age 84 _ 7y, 19 men and 41 women) were recruited for Study I and 64 elders (mean age 82 _ 7y, 24 men and 40 women) for Study II. For Study III, baseline data from the initially recruited participants of the first two studies were used. An informed consent was obtained from all participants or their mentors. The studies were approved by the Ethical Committee of the University of Granada. Blood samples were obtained at each examination date and were analyzed for serum cobalamin, holoTC, serum and RBC folate and total homocysteine according to laboratory standard procedures. The haematological parameters analyzed were haematocrit, haemoglobin and MCV. For the lipid profile TG, total cholesterol, LDL- and HDLcholesterol were analyzed. Anthropometric measures (BMI, skinfolds [triceps and subscapular], waist girth and waist to hip ratio), functional tests (hand grip, arm and leg strength tests, static balance) and MMSE were obtained or administered by trained personal. The vitamin B12 supplement of Study II was administered with breakfast and the medication intake was taken from the residents’ anamnesis. Data were analyzed by parametric and non-parametric statistics depending on the obtained data. Comparisons were done using the appropriate ANOVAs or non-parametric tests. Pearsons’ partial correlations with the variable “time” as control were used to define the association of the analyzed parameters. XIII The results showed that: A) Over one year, in relationship to vitamin B status, serum cobalamin decreased, serum folate and mean corpuscular volumen increased significantly and total homocysteine concentrations were stable. Regarding blood lipid profile, triglycerides increased and HDL-cholesterol decreased significantly. Regarding selected anthropometric measurements, waist circumference increased significantly. No significant changes were observed for the rest of parameters. B) Prevalence of hyperhomocysteinemia was high in the elderly studied, ranging from 60% to 90 % over the year depending on the cut-off used for the classification. LDL-cholesterol values were high, especially among women, and showed a tendency to increase over the year. Results of the balance test showed a deficiency and a tendency to decrease; this indicates that the population studied is at high risk for falls. Lower extremity muscular function was deficient and showed a tendency to decrease. A highly significant relationship was observed between the skinfold of the triceps and blood lipid profile. C) Low cobalamin concentrations correlated significantly with low MMSE scores in the elderly studied. No correlations were observed between vitamin B12 status and functional parameters. D) Regarding vitamin B12 status, holo-transcobalamin seems to be more sensitive for diagnosis; 5-10% of the elderly had a deficiency using serum cobalamin as a criterion, and 45-52% had a deficiency when using serum holotranscobalamin as a criterion. E) 500 μg of cyanocobalamin administered orally during 28 days significantly improved vitamin B12 status and significantly decreased total homocysteine concentrations in institutionalized elderly. No effect of the intervention was observed on functional and cognitive parameters. F) The relative change (%) of improvement of vitamin B12 status was higher when using serum holo-transcobalamin as a criterion than serum cobalamin. G) Antiaenemic drug intake normalized cobalamin, urologic drugs and corticosteroids serum folate, and psychoanaleptics holo-transcobalamin levels. Drugs treating pulmonary obstruction increased total homocysteine concentration significantly. H) The daily mean drug intake was 5.1. Fiftynine percent of the elderly took medication belonging to 5 or more different ATC groups. The most prevalent were psycholeptic (53%), antiacid (53%) and antithrombotic (47%) drugs.

Implementation of a module for risk of ozone impacts assessment to vegetation in the integrated assessment modelling system for the Iberian peninsula. Evaluation for wheat and holm oak

A module to estimate risks of ozone damage to vegetation has been implemented in the Integrated Assessment Modelling system for the Iberian Peninsula. It was applied to compute three different indexes for wheat and Holm oak; daylight AOT40 (cumulative ozone concentration over 40 ppb), cumulative ozone exposure index according to the Directive 2008/50/EC (AOT40-D) and PODY (Phytotoxic Ozone Dose over a given threshold of Y nmol m−2 s−1). The use of these indexes led to remarkable differences in spatial patterns of relative ozone risks on vegetation. Ozone critical levels were exceeded in most of the modelling domain and soil moisture content was found to have a significant impact on the results. According to the outputs of the model, daylight AOT40 constitutes a more conservative index than the AOT40-D. Additionally, flux-based estimations indicate high risk areas in Portugal for both wheat and Holm oak that are not identified by AOT-based methods.

Seismic Risk Scenarios in Puerto Principe (Haiti). A Tool for Reconstruction and Emergency Planning

The 12 January 2010, an earthquake hit the city of Port-au-Prince, capital of Haiti. The earthquake reached a magnitude Mw 7.0 and the epicenter was located near the town of Léogâne, approximately 25 km west of the capital. The earthquake occurred in the boundary region separating the Caribbean plate and the North American plate. This plate boundary is dominated by left-lateral strike slip motion and compression, and accommodates about 20 mm/y slip, with the Caribbean plate moving eastward with respect to the North American plate (DeMets et al., 2000). Initially the location and focal mechanism of the earthquake seemed to involve straightforward accommodation of oblique relative motion between the Caribbean and North American plates along the Enriquillo-Plantain Garden fault system (EPGFZ), however Hayes et al., (2010) combined seismological observations, geologic field data and space geodetic measurements to show that, instead, the rupture process involved slip on multiple faults. Besides, the authors showed that remaining shallow shear strain will be released in future surface-rupturing earthquakes on the EPGFZ. In December 2010, a Spanish cooperation project financed by the Politechnical University of Madrid started with a clear objective: Evaluation of seismic hazard and risk in Haiti and its application to the seismic design, urban planning, emergency and resource management. One of the tasks of the project was devoted to vulnerability assessment of the current building stock and the estimation of seismic risk scenarios. The study was carried out by following the capacity spectrum method as implemented in the software SELENA (Molina et al., 2010). The method requires a detailed classification of the building stock in predominant building typologies (according to the materials in the structure and walls, number of stories and age of construction) and the use of the building (residential, commercial, etc.). Later, the knowledge of the soil characteristics of the city and the simulation of a scenario earthquake will provide the seismic risk scenarios (damaged buildings). The initial results of the study show that one of the highest sources of uncertainties comes from the difficulty of achieving a precise building typologies classification due to the craft construction without any regulations. Also it is observed that although the occurrence of big earthquakes usually helps to decrease the vulnerability of the cities due to the collapse of low quality buildings and the reconstruction of seismically designed buildings, in the case of Port-au-Prince the seismic risk in most of the districts remains high, showing very vulnerable areas. Therefore the local authorities have to drive their efforts towards the quality control of the new buildings, the reinforcement of the existing building stock, the establishment of seismic normatives and the development of emergency planning also through the education of the population.

Bioaccessibility of heavy metals and risk assessment in urban gardens of Madrid

Human health problems and solutions. Urban gardening has spread worldwide in recent years as it enhances food security and selfsupply and promotes community integration. However urban soils are significantly enriched in trace elements relative to background levels. Exposure to the soil in urban gardens may therefore result in adverse health effects depending on the degree of contact during gardening, infant recreational activities and ingestion of vegetables grown in them. In order to evaluate this potential risk, 36 composite samples were collected from the top 20 cm of the soil of 6 urban gardens in Madrid. The aqua regia (pseudototal) and glycine-extractable (bioaccessible) concentrations of Co, Cr, Cu, Ni, Pb and Zn were determined by atomic absorption spectrophotometry. Additionally, pH, texture, Fe, Ca, and Mn concentrations, and organic matter and calcium carbonate contents were determined in all urban gardens and their influence on trace element bioaccessibility was analyzed.

Probabilistic assessment of risk from the exposure to mercury in artisanal gold mining communities in Colombia

Colombia is one the largest per capita mercury polluters as a consequence of its artisanal gold mining operations, which are steadily increasing following the rising price of this metal. Compared to gravimetric separation methods and cyanidation, the concentration of gold using Hg amalgams presents several advantages: the process is less time-consuming and minimizes gold losses, and Hg is easily transported and inexpensive relative to the selling price of gold. Very often, mercury amalgamation is carried out on site by unprotected workers. During this operation large amounts of mercury are discharged to the environment and eventually reach the fresh water bodies in the vicinity where it is subjected to methylation. Additionally, as gold is released from the amalgam by heating on open charcoal furnaces in small workshops, mercury vapors are emitted and inhaled by the artisanal smelters and the general population

Methodologies for Collision Risk Computation = Metodologías para Cálculo de Riesgo de Colisión

Esta tesis aborda metodologías para el cálculo de riesgo de colisión de satélites. La minimización del riesgo de colisión se debe abordar desde dos puntos de vista distintos. Desde el punto de vista operacional, es necesario filtrar los objetos que pueden presentar un encuentro entre todos los objetos que comparten el espacio con un satélite operacional. Puesto que las órbitas, del objeto operacional y del objeto envuelto en la colisión, no se conocen perfectamente, la geometría del encuentro y el riesgo de colisión deben ser evaluados. De acuerdo con dicha geometría o riesgo, una maniobra evasiva puede ser necesaria para evitar la colisión. Dichas maniobras implican un consumo de combustible que impacta en la capacidad de mantenimiento orbital y por tanto de la visa útil del satélite. Por tanto, el combustible necesario a lo largo de la vida útil de un satélite debe ser estimado en fase de diseño de la misión para una correcta definición de su vida útil, especialmente para satélites orbitando en regímenes orbitales muy poblados. Los dos aspectos, diseño de misión y aspectos operacionales en relación con el riesgo de colisión están abordados en esta tesis y se resumen en la Figura 3. En relación con los aspectos relacionados con el diseño de misión (parte inferior de la figura), es necesario evaluar estadísticamente las características de de la población espacial y las teorías que permiten calcular el número medio de eventos encontrados por una misión y su capacidad de reducir riesgo de colisión. Estos dos aspectos definen los procedimientos más apropiados para reducir el riesgo de colisión en fase operacional. Este aspecto es abordado, comenzando por la teoría descrita en [Sánchez-Ortiz, 2006]T.14 e implementada por el autor de esta tesis en la herramienta ARES [Sánchez-Ortiz, 2004b]T.15 proporcionada por ESA para la evaluación de estrategias de evitación de colisión. Esta teoría es extendida en esta tesis para considerar las características de los datos orbitales disponibles en las fases operacionales de un satélite (sección 4.3.3). Además, esta teoría se ha extendido para considerar riesgo máximo de colisión cuando la incertidumbre de las órbitas de objetos catalogados no es conocida (como se da el caso para los TLE), y en el caso de querer sólo considerar riesgo de colisión catastrófico (sección 4.3.2.3). Dichas mejoras se han incluido en la nueva versión de ARES [Domínguez-González and Sánchez-Ortiz, 2012b]T.12 puesta a disposición a través de [SDUP,2014]R.60. En fase operacional, los catálogos que proporcionan datos orbitales de los objetos espaciales, son procesados rutinariamente, para identificar posibles encuentros que se analizan en base a algoritmos de cálculo de riesgo de colisión para proponer maniobras de evasión. Actualmente existe una única fuente de datos públicos, el catálogo TLE (de sus siglas en inglés, Two Line Elements). Además, el Joint Space Operation Center (JSpOC) Americano proporciona mensajes con alertas de colisión (CSM) cuando el sistema de vigilancia americano identifica un posible encuentro. En función de los datos usados en fase operacional (TLE o CSM), la estrategia de evitación puede ser diferente debido a las características de dicha información. Es preciso conocer las principales características de los datos disponibles (respecto a la precisión de los datos orbitales) para estimar los posibles eventos de colisión encontrados por un satélite a lo largo de su vida útil. En caso de los TLE, cuya precisión orbital no es proporcionada, la información de precisión orbital derivada de un análisis estadístico se puede usar también en el proceso operacional así como en el diseño de la misión. En caso de utilizar CSM como base de las operaciones de evitación de colisiones, se conoce la precisión orbital de los dos objetos involucrados. Estas características se han analizado en detalle, evaluando estadísticamente las características de ambos tipos de datos. Una vez concluido dicho análisis, se ha analizado el impacto de utilizar TLE o CSM en las operaciones del satélite (sección 5.1). Este análisis se ha publicado en una revista especializada [Sánchez-Ortiz, 2015b]T.3. En dicho análisis, se proporcionan recomendaciones para distintas misiones (tamaño del satélite y régimen orbital) en relación con las estrategias de evitación de colisión para reducir el riesgo de colisión de manera significativa. Por ejemplo, en el caso de un satélite en órbita heliosíncrona en régimen orbital LEO, el valor típico del ACPL que se usa de manera extendida es 10-4. Este valor no es adecuado cuando los esquemas de evitación de colisión se realizan sobre datos TLE. En este caso, la capacidad de reducción de riesgo es prácticamente nula (debido a las grandes incertidumbres de los datos TLE) incluso para tiempos cortos de predicción. Para conseguir una reducción significativa del riesgo, sería necesario usar un ACPL en torno a 10-6 o inferior, produciendo unas 10 alarmas al año por satélite (considerando predicciones a un día) o 100 alarmas al año (con predicciones a tres días). Por tanto, la principal conclusión es la falta de idoneidad de los datos TLE para el cálculo de eventos de colisión. Al contrario, usando los datos CSM, debido a su mejor precisión orbital, se puede obtener una reducción significativa del riesgo con ACPL en torno a 10-4 (considerando 3 días de predicción). Incluso 5 días de predicción pueden ser considerados con ACPL en torno a 10-5. Incluso tiempos de predicción más largos se pueden usar (7 días) con reducción del 90% del riesgo y unas 5 alarmas al año (en caso de predicciones de 5 días, el número de maniobras se mantiene en unas 2 al año). La dinámica en GEO es diferente al caso LEO y hace que el crecimiento de las incertidumbres orbitales con el tiempo de propagación sea menor. Por el contrario, las incertidumbres derivadas de la determinación orbital son peores que en LEO por las diferencias en las capacidades de observación de uno y otro régimen orbital. Además, se debe considerar que los tiempos de predicción considerados para LEO pueden no ser apropiados para el caso de un satélite GEO (puesto que tiene un periodo orbital mayor). En este caso usando datos TLE, una reducción significativa del riesgo sólo se consigue con valores pequeños de ACPL, produciendo una alarma por año cuando los eventos de colisión se predicen a un día vista (tiempo muy corto para implementar maniobras de evitación de colisión).Valores más adecuados de ACPL se encuentran entre 5•10-8 y 10-7, muy por debajo de los valores usados en las operaciones actuales de la mayoría de las misiones GEO (de nuevo, no se recomienda en este régimen orbital basar las estrategias de evitación de colisión en TLE). Los datos CSM permiten una reducción de riesgo apropiada con ACPL entre 10-5 y 10-4 con tiempos de predicción cortos y medios (10-5 se recomienda para predicciones a 5 o 7 días). El número de maniobras realizadas sería una en 10 años de misión. Se debe notar que estos cálculos están realizados para un satélite de unos 2 metros de radio. En el futuro, otros sistemas de vigilancia espacial (como el programa SSA de la ESA), proporcionarán catálogos adicionales de objetos espaciales con el objetivo de reducir el riesgo de colisión de los satélites. Para definir dichos sistemas de vigilancia, es necesario identificar las prestaciones del catalogo en función de la reducción de riesgo que se pretende conseguir. Las características del catálogo que afectan principalmente a dicha capacidad son la cobertura (número de objetos incluidos en el catalogo, limitado principalmente por el tamaño mínimo de los objetos en función de las limitaciones de los sensores utilizados) y la precisión de los datos orbitales (derivada de las prestaciones de los sensores en relación con la precisión de las medidas y la capacidad de re-observación de los objetos). El resultado de dicho análisis (sección 5.2) se ha publicado en una revista especializada [Sánchez-Ortiz, 2015a]T.2. Este análisis no estaba inicialmente previsto durante la tesis, y permite mostrar como la teoría descrita en esta tesis, inicialmente definida para facilitar el diseño de misiones (parte superior de la figura 1) se ha extendido y se puede aplicar para otros propósitos como el dimensionado de un sistema de vigilancia espacial (parte inferior de la figura 1). La principal diferencia de los dos análisis se basa en considerar las capacidades de catalogación (precisión y tamaño de objetos observados) como una variable a modificar en el caso de un diseño de un sistema de vigilancia), siendo fijas en el caso de un diseño de misión. En el caso de las salidas generadas en el análisis, todos los aspectos calculados en un análisis estadístico de riesgo de colisión son importantes para diseño de misión (con el objetivo de calcular la estrategia de evitación y la cantidad de combustible a utilizar), mientras que en el caso de un diseño de un sistema de vigilancia, los aspectos más importantes son el número de maniobras y falsas alarmas (fiabilidad del sistema) y la capacidad de reducción de riesgo (efectividad del sistema). Adicionalmente, un sistema de vigilancia espacial debe ser caracterizado por su capacidad de evitar colisiones catastróficas (evitando así in incremento dramático de la población de basura espacial), mientras que el diseño de una misión debe considerar todo tipo de encuentros, puesto que un operador está interesado en evitar tanto las colisiones catastróficas como las letales. Del análisis de las prestaciones (tamaño de objetos a catalogar y precisión orbital) requeridas a un sistema de vigilancia espacial se concluye que ambos aspectos han de ser fijados de manera diferente para los distintos regímenes orbitales. En el caso de LEO se hace necesario observar objetos de hasta 5cm de radio, mientras que en GEO se rebaja este requisito hasta los 100 cm para cubrir las colisiones catastróficas. La razón principal para esta diferencia viene de las diferentes velocidades relativas entre los objetos en ambos regímenes orbitales. En relación con la precisión orbital, ésta ha de ser muy buena en LEO para poder reducir el número de falsas alarmas, mientras que en regímenes orbitales más altos se pueden considerar precisiones medias. En relación con los aspectos operaciones de la determinación de riesgo de colisión, existen varios algoritmos de cálculo de riesgo entre dos objetos espaciales. La Figura 2 proporciona un resumen de los casos en cuanto a algoritmos de cálculo de riesgo de colisión y como se abordan en esta tesis. Normalmente se consideran objetos esféricos para simplificar el cálculo de riesgo (caso A). Este caso está ampliamente abordado en la literatura y no se analiza en detalle en esta tesis. Un caso de ejemplo se proporciona en la sección 4.2. Considerar la forma real de los objetos (caso B) permite calcular el riesgo de una manera más precisa. Un nuevo algoritmo es definido en esta tesis para calcular el riesgo de colisión cuando al menos uno de los objetos se considera complejo (sección 4.4.2). Dicho algoritmo permite calcular el riesgo de colisión para objetos formados por un conjunto de cajas, y se ha presentado en varias conferencias internacionales. Para evaluar las prestaciones de dicho algoritmo, sus resultados se han comparado con un análisis de Monte Carlo que se ha definido para considerar colisiones entre cajas de manera adecuada (sección 4.1.2.3), pues la búsqueda de colisiones simples aplicables para objetos esféricos no es aplicable a este caso. Este análisis de Monte Carlo se considera la verdad a la hora de calcular los resultados del algoritmos, dicha comparativa se presenta en la sección 4.4.4. En el caso de satélites que no se pueden considerar esféricos, el uso de un modelo de la geometría del satélite permite descartar eventos que no son colisiones reales o estimar con mayor precisión el riesgo asociado a un evento. El uso de estos algoritmos con geometrías complejas es más relevante para objetos de dimensiones grandes debido a las prestaciones de precisión orbital actuales. En el futuro, si los sistemas de vigilancia mejoran y las órbitas son conocidas con mayor precisión, la importancia de considerar la geometría real de los satélites será cada vez más relevante. La sección 5.4 presenta un ejemplo para un sistema de grandes dimensiones (satélite con un tether). Adicionalmente, si los dos objetos involucrados en la colisión tienen velocidad relativa baja (y geometría simple, Caso C en la Figura 2), la mayor parte de los algoritmos no son aplicables requiriendo implementaciones dedicadas para este caso particular. En esta tesis, uno de estos algoritmos presentado en la literatura [Patera, 2001]R.26 se ha analizado para determinar su idoneidad en distintos tipos de eventos (sección 4.5). La evaluación frete a un análisis de Monte Carlo se proporciona en la sección 4.5.2. Tras este análisis, se ha considerado adecuado para abordar las colisiones de baja velocidad. En particular, se ha concluido que el uso de algoritmos dedicados para baja velocidad son necesarios en función del tamaño del volumen de colisión proyectado en el plano de encuentro (B-plane) y del tamaño de la incertidumbre asociada al vector posición entre los dos objetos. Para incertidumbres grandes, estos algoritmos se hacen más necesarios pues la duración del intervalo en que los elipsoides de error de los dos objetos pueden intersecar es mayor. Dicho algoritmo se ha probado integrando el algoritmo de colisión para objetos con geometrías complejas. El resultado de dicho análisis muestra que este algoritmo puede ser extendido fácilmente para considerar diferentes tipos de algoritmos de cálculo de riesgo de colisión (sección 4.5.3). Ambos algoritmos, junto con el método Monte Carlo para geometrías complejas, se han implementado en la herramienta operacional de la ESA CORAM, que es utilizada para evaluar el riesgo de colisión en las actividades rutinarias de los satélites operados por ESA [Sánchez-Ortiz, 2013a]T.11. Este hecho muestra el interés y relevancia de los algoritmos desarrollados para la mejora de las operaciones de los satélites. Dichos algoritmos han sido presentados en varias conferencias internacionales [Sánchez-Ortiz, 2013b]T.9, [Pulido, 2014]T.7,[Grande-Olalla, 2013]T.10, [Pulido, 2014]T.5, [Sánchez-Ortiz, 2015c]T.1. ABSTRACT This document addresses methodologies for computation of the collision risk of a satellite. Two different approaches need to be considered for collision risk minimisation. On an operational basis, it is needed to perform a sieve of possible objects approaching the satellite, among all objects sharing the space with an operational satellite. As the orbits of both, satellite and the eventual collider, are not perfectly known but only estimated, the miss-encounter geometry and the actual risk of collision shall be evaluated. In the basis of the encounter geometry or the risk, an eventual manoeuvre may be required to avoid the conjunction. Those manoeuvres will be associated to a reduction in the fuel for the mission orbit maintenance, and thus, may reduce the satellite operational lifetime. Thus, avoidance manoeuvre fuel budget shall be estimated, at mission design phase, for a better estimation of mission lifetime, especially for those satellites orbiting in very populated orbital regimes. These two aspects, mission design and operational collision risk aspects, are summarised in Figure 3, and covered along this thesis. Bottom part of the figure identifies the aspects to be consider for the mission design phase (statistical characterisation of the space object population data and theory computing the mean number of events and risk reduction capability) which will define the most appropriate collision avoidance approach at mission operational phase. This part is covered in this work by starting from the theory described in [Sánchez-Ortiz, 2006]T.14 and implemented by this author in ARES tool [Sánchez-Ortiz, 2004b]T.15 provided by ESA for evaluation of collision avoidance approaches. This methodology has been now extended to account for the particular features of the available data sets in operational environment (section 4.3.3). Additionally, the formulation has been extended to allow evaluating risk computation approached when orbital uncertainty is not available (like the TLE case) and when only catastrophic collisions are subject to study (section 4.3.2.3). These improvements to the theory have been included in the new version of ESA ARES tool [Domínguez-González and Sánchez-Ortiz, 2012b]T.12 and available through [SDUP,2014]R.60. At the operation phase, the real catalogue data will be processed on a routine basis, with adequate collision risk computation algorithms to propose conjunction avoidance manoeuvre optimised for every event. The optimisation of manoeuvres in an operational basis is not approached along this document. Currently, American Two Line Element (TLE) catalogue is the only public source of data providing orbits of objects in space to identify eventual conjunction events. Additionally, Conjunction Summary Message (CSM) is provided by Joint Space Operation Center (JSpOC) when the American system identifies a possible collision among satellites and debris. Depending on the data used for collision avoidance evaluation, the conjunction avoidance approach may be different. The main features of currently available data need to be analysed (in regards to accuracy) in order to perform estimation of eventual encounters to be found along the mission lifetime. In the case of TLE, as these data is not provided with accuracy information, operational collision avoidance may be also based on statistical accuracy information as the one used in the mission design approach. This is not the case for CSM data, which includes the state vector and orbital accuracy of the two involved objects. This aspect has been analysed in detail and is depicted in the document, evaluating in statistical way the characteristics of both data sets in regards to the main aspects related to collision avoidance. Once the analysis of data set was completed, investigations on the impact of those features in the most convenient avoidance approaches have been addressed (section 5.1). This analysis is published in a peer-reviewed journal [Sánchez-Ortiz, 2015b]T.3. The analysis provides recommendations for different mission types (satellite size and orbital regime) in regards to the most appropriate collision avoidance approach for relevant risk reduction. The risk reduction capability is very much dependent on the accuracy of the catalogue utilized to identify eventual collisions. Approaches based on CSM data are recommended against the TLE based approach. Some approaches based on the maximum risk associated to envisaged encounters are demonstrated to report a very large number of events, which makes the approach not suitable for operational activities. Accepted Collision Probability Levels are recommended for the definition of the avoidance strategies for different mission types. For example for the case of a LEO satellite in the Sun-synchronous regime, the typically used ACPL value of 10-4 is not a suitable value for collision avoidance schemes based on TLE data. In this case the risk reduction capacity is almost null (due to the large uncertainties associated to TLE data sets, even for short time-to-event values). For significant reduction of risk when using TLE data, ACPL on the order of 10-6 (or lower) seems to be required, producing about 10 warnings per year and mission (if one-day ahead events are considered) or 100 warnings per year (for three-days ahead estimations). Thus, the main conclusion from these results is the lack of feasibility of TLE for a proper collision avoidance approach. On the contrary, for CSM data, and due to the better accuracy of the orbital information when compared with TLE, ACPL on the order of 10-4 allows to significantly reduce the risk. This is true for events estimated up to 3 days ahead. Even 5 days ahead events can be considered, but ACPL values down to 10-5 should be considered in such case. Even larger prediction times can be considered (7 days) for risk reduction about 90%, at the cost of larger number of warnings up to 5 events per year, when 5 days prediction allows to keep the manoeuvre rate in 2 manoeuvres per year. Dynamics of the GEO orbits is different to that in LEO, impacting on a lower increase of orbits uncertainty along time. On the contrary, uncertainties at short prediction times at this orbital regime are larger than those at LEO due to the differences in observation capabilities. Additionally, it has to be accounted that short prediction times feasible at LEO may not be appropriate for a GEO mission due to the orbital period being much larger at this regime. In the case of TLE data sets, significant reduction of risk is only achieved for small ACPL values, producing about a warning event per year if warnings are raised one day in advance to the event (too short for any reaction to be considered). Suitable ACPL values would lay in between 5•10-8 and 10-7, well below the normal values used in current operations for most of the GEO missions (TLE-based strategies for collision avoidance at this regime are not recommended). On the contrary, CSM data allows a good reduction of risk with ACPL in between 10-5 and 10-4 for short and medium prediction times. 10-5 is recommended for prediction times of five or seven days. The number of events raised for a suitable warning time of seven days would be about one in a 10-year mission. It must be noted, that these results are associated to a 2 m radius spacecraft, impact of the satellite size are also analysed within the thesis. In the future, other Space Situational Awareness Systems (SSA, ESA program) may provide additional catalogues of objects in space with the aim of reducing the risk. It is needed to investigate which are the required performances of those catalogues for allowing such risk reduction. The main performance aspects are coverage (objects included in the catalogue, mainly limited by a minimum object size derived from sensor performances) and the accuracy of the orbital data to accurately evaluate the conjunctions (derived from sensor performance in regards to object observation frequency and accuracy). The results of these investigations (section 5.2) are published in a peer-reviewed journal [Sánchez-Ortiz, 2015a]T.2. This aspect was not initially foreseen as objective of the thesis, but it shows how the theory described in the thesis, initially defined for mission design in regards to avoidance manoeuvre fuel allocation (upper part of figure 1), is extended and serves for additional purposes as dimensioning a Space Surveillance and Tracking (SST) system (bottom part of figure below). The main difference between the two approaches is the consideration of the catalogue features as part of the theory which are not modified (for the satellite mission design case) instead of being an input for the analysis (in the case of the SST design). In regards to the outputs, all the features computed by the statistical conjunction analysis are of importance for mission design (with the objective of proper global avoidance strategy definition and fuel allocation), whereas for the case of SST design, the most relevant aspects are the manoeuvre and false alarm rates (defining a reliable system) and the Risk Reduction capability (driving the effectiveness of the system). In regards to the methodology for computing the risk, the SST system shall be driven by the capacity of providing the means to avoid catastrophic conjunction events (avoiding the dramatic increase of the population), whereas the satellite mission design should consider all type of encounters, as the operator is interested on avoiding both lethal and catastrophic collisions. From the analysis of the SST features (object coverage and orbital uncertainty) for a reliable system, it is concluded that those two characteristics are to be imposed differently for the different orbital regimes, as the population level is different depending on the orbit type. Coverage values range from 5 cm for very populated LEO regime up to 100 cm in the case of GEO region. The difference on this requirement derives mainly from the relative velocity of the encounters at those regimes. Regarding the orbital knowledge of the catalogues, very accurate information is required for objects in the LEO region in order to limit the number of false alarms, whereas intermediate orbital accuracy can be considered for higher orbital regimes. In regards to the operational collision avoidance approaches, several collision risk algorithms are used for evaluation of collision risk of two pair of objects. Figure 2 provides a summary of the different collision risk algorithm cases and indicates how they are covered along this document. The typical case with high relative velocity is well covered in literature for the case of spherical objects (case A), with a large number of available algorithms, that are not analysed in detailed in this work. Only a sample case is provided in section 4.2. If complex geometries are considered (Case B), a more realistic risk evaluation can be computed. New approach for the evaluation of risk in the case of complex geometries is presented in this thesis (section 4.4.2), and it has been presented in several international conferences. The developed algorithm allows evaluating the risk for complex objects formed by a set of boxes. A dedicated Monte Carlo method has also been described (section 4.1.2.3) and implemented to allow the evaluation of the actual collisions among a large number of simulation shots. This Monte Carlo runs are considered the truth for comparison of the algorithm results (section 4.4.4). For spacecrafts that cannot be considered as spheres, the consideration of the real geometry of the objects may allow to discard events which are not real conjunctions, or estimate with larger reliability the risk associated to the event. This is of particular importance for the case of large spacecrafts as the uncertainty in positions of actual catalogues does not reach small values to make a difference for the case of objects below meter size. As the tracking systems improve and the orbits of catalogued objects are known more precisely, the importance of considering actual shapes of the objects will become more relevant. The particular case of a very large system (as a tethered satellite) is analysed in section 5.4. Additionally, if the two colliding objects have low relative velocity (and simple geometries, case C in figure above), the most common collision risk algorithms fail and adequate theories need to be applied. In this document, a low relative velocity algorithm presented in the literature [Patera, 2001]R.26 is described and evaluated (section 4.5). Evaluation through comparison with Monte Carlo approach is provided in section 4.5.2. The main conclusion of this analysis is the suitability of this algorithm for the most common encounter characteristics, and thus it is selected as adequate for collision risk estimation. Its performances are evaluated in order to characterise when it can be safely used for a large variety of encounter characteristics. In particular, it is found that the need of using dedicated algorithms depend on both the size of collision volume in the B-plane and the miss-distance uncertainty. For large uncertainties, the need of such algorithms is more relevant since for small uncertainties the encounter duration where the covariance ellipsoids intersect is smaller. Additionally, its application for the case of complex satellite geometries is assessed (case D in figure above) by integrating the developed algorithm in this thesis with Patera’s formulation for low relative velocity encounters. The results of this analysis show that the algorithm can be easily extended for collision risk estimation process suitable for complex geometry objects (section 4.5.3). The two algorithms, together with the Monte Carlo method, have been implemented in the operational tool CORAM for ESA which is used for the evaluation of collision risk of ESA operated missions, [Sánchez-Ortiz, 2013a]T.11. This fact shows the interest and relevance of the developed algorithms for improvement of satellite operations. The algorithms have been presented in several international conferences, [Sánchez-Ortiz, 2013b]T.9, [Pulido, 2014]T.7,[Grande-Olalla, 2013]T.10, [Pulido, 2014]T.5, [Sánchez-Ortiz, 2015c]T.1.