The reliability of structures subjected to time-invariant or time-variant random loads is considered herein. This is an important field of engineering, as it provides the framework for assessing whether newly designed or existing structural systems meet their design requirements in a given lifetime, or whether they experience what is termed “structural failure”. An important aspect of reliability analysis is the study of structures subjected to multiple time-varying loads. For this class of systems, it is well-known that by modelling the loads as (time-variant) random processes, the reliability may be evaluated by considering the outcrossing of a vector process out of a safe domain. However, due to the possibility that the loads may not be fully-dependent, all loads may not necessarily contribute to structural failure. To account for this the treatment of vector-outcrossings may need to allow for the possibility of outcrossings being caused by individual loads, as distinct from combinations of all loads. The procedure used to analyse combinations of loads depends on the stochastic process model used to represent the loads. Two well-known load models have been presented in the literature—they are referred to herein as the ‘on-off’ model and the ‘standard’ model. The ‘on-off’ model typically assumes loads are non-negative, and are either ‘on’ (eg their value is non-zero) or ‘off’ (eg their value is strictly zero). They can contribute to failure only when they are ‘on’. This model is represented by a somewhat artificial ‘composite’ probability distribution, obtained by modifying the original load probability density function (pdf) so that a ‘finite’ non-zero probability represents explicitly the possibility that the load is ‘off’. To implement this model in time-variant analysis, it is necessary to consider all possible combinations of loads being ‘on’ and ‘off’. In contrast, the ‘standard’ model (which is the more commonly used) typically allows loads to be negative; it is also typically represented solely by the original load pdf, and therefore effectively assumes each load is always ‘on’. To allow for the possibility of one or more loads not to cause failure, herein the value of such loads is held ‘constant’ at the time of failure, when the value of all loads actually causing failure is allowed to change. Use of the ‘standard’ model is examined herein. The “Directional Simulation in the Load Space (DS-LS)” approach is a tool used to perform reliability analysis. It is particularly suitable for time-variant analysis, as it allows loads to be represented as random processes, and to be modelled properly. DS-LS has so far been shown to work well for relatively simple structures subjected to one or more time-invariant random loads, and has been used to examine vector outcrossings in systems comprising either discrete or continuous loads. To enable the proper consideration of load combinations, and to provide some improvements in the formulation of the technique, a generalisation of the DS-LS approach is proposed herein. The generalisation is achieved in two stages. The first involves modifying the time-invariant and time-variant DS-LS formulation to allow for the possibility of positioning the origin of DS-LS not only in the ‘safe’ region of the load space (which the formulation currently requires) but in the ‘failure’ region, or even ‘exactly’ on the boundary separating the safe and failure regions. The modifications are necessary because for even simple structures, the ‘exact’ location of the safe and failure region is not always known explicitly ‘a priori’. The second involves developing the time-variant DS-LS formulation to consider explicitly outcrossings caused by combinations of one or more loads, during analysis of systems comprising stationary continuous gaussian loads. To do this, the direction of the load process vector is ‘fixed’ at each point of outcrossing, to physically represent the particular combination of loads causing the outcrossing. By considering each possible load combination, all loads not causing an outcrossing are then held constant during radial integration, thereby modelling those that do not contribute to each outcrossing. The proposed formulation differs from most load combination analysis techniques (which, evidently, simplify the analysis) as it is analytically ‘exact’, and it considers explicitly all possible combinations of loads. The concepts and formulations proposed herein may provide further understanding of reliability analysis performed by DS-LS (or other techniques) and may aid their future development. / PhD Doctorate