Safety risk assessment forms an integral part of the design and development of Safety Critical Systems. Conventionally in these systems, standards and policies have been developed to prescribe processes for safety risk assessment. These standards provide guidelines, references and structure to personnel involved in the risk assessment process. However, in some of these standards, the prescribed methods for safety decision making were found to be deficient in some respects. Two such deficiencies have been addressed in this thesis. First, when different safety metrics are required to be combined for a safety related decision, the current practices of using safety risk matrices were found to be inconsistent with the axioms of decision theory. Second, in the safety risk assessment process, when multiple experts are consulted to provide their judgment on the severity and/or likelihood of hazards, the standards were lacking detailed guidelines for aggregating experts' judgements. Such deficiencies could lead to misconceptions pertaining to the safety risk level of critical hazards. These misconceptions potentially give rise to inconsistent safety decisions that might ultimately result in catastrophic outcomes. This thesis addresses both these concerns present in SRM processes. For the problem of combining safety metrics, three potential approaches have been proposed. Normative Decision Analysis tools such as Utility Theory and Multi-attribute Utility Theory were proposed in the first and second approaches. The third approach proposes the use of a Multi-Objective Optimization technique - Pareto Analysis. For problems in Expert Aggregation, behavioral and mathematical solutions have been explored and the implications of using these methods for Safety Risk Assessment have been discussed. Two standard documents that contain the Safety Risk Management Processes of the Federal Aviation Agency (FAA) and the U.S. Navy were used to structure the case studies. This thesis has two main contributions. First, it evaluates the use of decision analysis in safety decision process of Safety Critical Systems. It provides guidelines to decision makers on how to meaningfully use and/or combine different safety metrics in the decision process. Second, it identifies the best practices and methods of aggregating expert assessments pertaining to safety decision making. / Master of Science / Safety risk assessment forms an important part of the design and development of Safety Critical Systems. Safety Critical Systems are those systems whose failure could potentially result in the loss of human life. Commonly in these systems, standards and policies have been developed to prescribe processes for safety risk assessment. These standards provide guidelines, references and structure to personnel involved in the risk assessment process. However, in some of these standards, the prescribed methods for safety decision making were found to be deficient in some respects. Two such deficiencies have been addressed in this thesis. First, when different safety metrics are required to be combined to provide information for a safety related decision, the current practices of the safety risk assessment do not yield consistent recommendations. Second, in the safety risk assessment process, often multiple experts are consulted to provide their judgment on the criticality of a potential safety risk of the system. The standards and policies that are currently being used, do not provide clear instructions on how to synthesize the judgements of multiple experts. This lack of clear guidelines could potentially lead to an incorrect final judgement on the criticality of the risk and ultimately result in choosing an improper method to reduce the safety risk. This thesis addresses both these concerns present in safety risk assessment process of Safety Critical Systems. For the problem of combining safety metrics, three approaches have been proposed. Two of the proposed approaches make use of normative decision analysis practices and therefore the recommendations reached using these methods will be consistent with the safety objective of the decision maker. The third approach makes use of a traditional concept called -Pareto Analysis which provides a visual method to analyze the advantages and drawbacks of a given safety concern for a system. For problems in combining the judgements of multiple experts a variety of methods was studied. The methods include group consensus and mathematical techniques and the implications of using these methods in safety risk assessment was discussed. The FAA and the U.S. Navy's standard documents and policies were used to frame the discussions. This thesis has two main contributions. First, it evaluates the use of Normative Decision Analysis methods in safety decision process of Safety Critical Systems. It provides guidelines to decision makers on how to meaningfully use and/or combine different safety metrics in the decision process. Second, it identifies the best practices and methods of aggregating expert assessments pertaining to safety decision making.

Nous nous intéressons à prévoir séquentiellement une suite arbitraire d'observations. À chaque instant, des experts nous proposent des prévisions de la prochaine observation. Nous formons alors notre prévision en mélangeant celles des experts. C'est le cadre de l'agrégation séquentielle d'experts. L'objectif est d'assurer un faible regret cumulé. En d'autres mots, nous souhaitons que notre perte cumulée ne dépasse pas trop celle du meilleur expert sur le long terme. Nous cherchons des garanties très robustes~: aucune hypothèse stochastique sur la suite d'observations à prévoir n'est faite. Celle-ci est supposée arbitraire et nous souhaitons des garanties qui soient vérifiées quoi qu'il arrive. Un premier objectif de ce travail est l'amélioration de la performance des prévisions. Plusieurs possibilités sont proposées. Un exemple est la création d'algorithmes adaptatifs qui cherchent à s'adapter automatiquement à la difficulté de la suite à prévoir. Un autre repose sur la création de nouveaux experts à inclure au mélange pour apporter de la diversité dans l'ensemble d'experts. Un deuxième objectif de la thèse est d'assortir les prévisions d'une mesure d'incertitude, voire de prévoir des lois. Les applications pratiques sont nombreuses. En effet, très peu d'hypothèses sont faites sur les données. Le côté séquentiel permet entre autres de traiter de grands ensembles de données. Nous considérons dans cette thèse divers jeux de données du monde de l'énergie (consommation électrique, prix de l'électricité,...) pour montrer l'universalité de l'approche. / We are interested in online forecasting of an arbitrary sequence of observations. At each time step, some experts provide predictions of the next observation. Then, we form our prediction by combining the expert forecasts. This is the setting of online robust aggregation of experts. The goal is to ensure a small cumulative regret. In other words, we want that our cumulative loss does not exceed too much the one of the best expert. We are looking for worst-case guarantees: no stochastic assumption on the data to be predicted is made. The sequence of observations is arbitrary. A first objective of this work is to improve the prediction accuracy. We investigate several possibilities. An example is to design fully automatic procedures that can exploit simplicity of the data whenever it is present. Another example relies on working on the expert set so as to improve its diversity. A second objective of this work is to produce probabilistic predictions. We are interested in coupling the point prediction with a measure of uncertainty (i.e., interval forecasts,…). The real world applications of the above setting are multiple. Indeed, very few assumptions are made on the data. Besides, online learning that deals with data sequentially is crucial to process big data sets in real time. In this thesis, we carry out for EDF several empirical studies of energy data sets and we achieve good forecasting performance.