Splitting and importance sampling are the two primary techniques to make important rare events happen more frequently in a simulation, and obtain an unbiased estimator with much smaller variance than the standard Monte Carlo estimator. Importance sampling has been discussed and studied in several articles presented at the Winter Simulation Conference in the past. A smaller number of WSC articles have examined splitting. In this paper, we review the splitting technique and discuss some of its strengths and limitations from the practical viewpoint. We also introduce improvements in the implementation of the multilevel splitting technique. This is done in a setting where we want to estimate the probability of reaching B before reaching (or returning to) A when starting from a fixed state x 0 ∈ B, where A and B are two disjoint subsets of the state space and B is very rarely attained. This problem has several practical applications.

Objectives Shift work has been categorised as a probable human carcinogen by the International Agency for Research on Cancer. This is an exposure assessment for a study of shift work and cancer in a cohort created by linkage of the Canadian national cancer registry and the 1991 long form census, which recorded occupation and industry of employment for 2.1 million Canadians, but did not query specific exposures. We used a contemporary (1993) survey to characterise shift work exposures by occupation, industry, and sex. Methods Analyses were conducted on the 1993 Survey of Labour and Income Dynamics (SLID) to determine the prevalence of night shift work in the contemporary population, highly exposed industries and occupations and sex differences in shift work prevalence within industries. All analyses were restricted to the employed population and weighted to account for sampling methodology. Results 17% of employed 1993 SLID respondents were exposed to night shift work, with 5% of reporting a regular evening work schedule, 2% a regular night shift and 10% a rotating shift. Night shift work was most common (>65%) in pulping control operators in the pulp and paper industry; food service helpers, servers and bartenders in hotels and motels; uncommissioned police officers; and light duty cleaners. Exposure to shift work was similar in men and women (18% vs 16%), but sex differences were apparent in certain industries. Within protective services (includes police) shift work prevalence was 11% in women and 20% in men while within hospitals prevalence was 37% in women and 29% in men. Conclusions This exposure assessment for a census cohort has the advantage of drawing from a contemporary population based sample, demonstrating that occupation, industry and sex are important dimensions for a shift work exposure matrix designed for application to a census cohort or other general population sample.

In this research work, new modifications for the microplane constitutive law are first presented to precisely simulate concrete behaviour under various levels of lateral confinement pressure. A key feature of the suggested formula is to make the microplane theory valid to represent concrete behaviour under both low and high lateral confining pressures. An analysis is then carried out using two different numerical procedures. The first procedure is the use of a three-dimensional finite element analysis with the modified microplane formulations as a user-supplied subroutine into the FE commercial software ADINA to model the concrete behaviour under various stress and strain histories. Here, the sub-objective is to validate the formulated microplane approach that is proposed in the first phase of the research program. In the second analysis; the confinement behaviour is simulated using an in-house code. The code uses the proposed formulations for the microplane theory to represent the concrete characteristics to predict the stress-strain relationships of FRP-wrapped concrete columns up to failure. An accurate equation correlating the axial stiffness of the FRP laminates and the lateral strain of the concrete columns to the confining pressure is incorporated in the in-house code. The two analyses give almost the same predictions, with minor discrepancies due to some numerical aspects. An experimental program consisting of testing thirty eight concrete cylinders under various lateral confinement pressures is carried out to assess the accuracy of the numerical predictions. In the experimental program, the lateral pressure is designed to give almost the same lateral confinement behaviour as that resulting from applying FRP sheets. The numerical predictions are finally compared to experimental results for FRP-wrapped and un-wrapped concrete columns under various levels of lateral pressure. This paper gives an overview for the whole research program with a special emphasis on the theoretical part.