A non-intrusive stochastic finite-element method is proposed for uncertainty propagation through mechanical systems with uncertain input described by random variables. A polynomial chaos expansion (PCE) of the random response is used. Each PCE coefficient is cast as a multi-dimensional integral when using a projection scheme. Common simulation schemes, e.g. Monte Carlo Sampling (MCS) or Latin Hypercube Sampling (LHS), may be used to estimate these integrals, at a low convergence rate though. As an alternative, quasi-Monte Carlo (QMC) methods, which make use of quasi-random sequences, are proposed to provide rapidly converging estimates. The Sobol' sequence is more specifically used in this paper. The accuracy of the QMC approach is illustrated by the case study of a truss structure with random member properties (Young's modulus and cross section) and random loading. It is shown that QMC outperforms MCS and LHS techniques for moment, sensitivity and reliability analyses.

This paper investigates the structural reliability of a discrete choice experiment within health technology assessment. Two versions of a discrete choice experiment, in the form of a self-completion questionnaire, were randomly administered to two samples of women who had recently given birth as part of an exercise to determine women's preferences for alternative modes of intrapartum care. In the first questionnaire, two of the attributes had only their highest and lowest levels included, while in the second questionnaire all three levels for these two attributes were included. The levels included for all other attributes remained the same throughout both questionnaires. The evidence relating to the structural reliability of the discrete choice experiment in this context was mixed. The results indicated that the relative importance of the two attributes in which the levels were varied increased as the number of levels for these attributes increased. However, the relative importance of the attributes in which the levels were not varied remained relatively stable throughout. The results provide evidence in support of a psychological effect whereby respondents place more importance upon specific attributes as the number of levels for these attributes increases. It is recommended that further research of both a qualitative and quantitative nature should be undertaken to assess the potential importance (or otherwise) of a psychological effect relating to the number of levels chosen for attributes within discrete choice experiments in health technology assessment.

This paper is devoted to a model which has applications in the study of reliability, extinction of species, inventory depletion, and urn sampling, among others. A series–parallel system consists of (k + 1) subsystems C0, C1, · · ·, Ck, also called cut sets. Cut set Ci contains ni components arranged in parallel, i = 0, 1, · · ·, k. No two cut sets have a component in common. It is assumed that after t components have failed, each of the remaining components is equally likely to fail, t = 0, 1, · · ·. It is also assumed that the components fail one at a time. In Part 1 of this paper we study the probability that the system fails because a specified cut set C0, say, fails first. We obtain several alternative expressions and recurrence relations for this probability. Some of these formulae are useful for computation, while others permit us to derive qualitative features such as monotonicity, Schur-concavity, asymptotic limits, etc. These results are extended to cover the case in which some cut set first drops to level a, where a is a specified positive integer. In Part 2, we compute the probability distribution, frequency function, and failure rate of the lifelengths of series–parallel systems. We also obtain corresponding recurrence relations and finite and asymptotic properties.