A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty

In this paper, the effects of uncertainty and expected costs of failure on optimum structural design are investigated, by comparing three distinct formulations of structural optimization problems. Deterministic Design Optimization (DDO) allows one the find the shape or configuration of a structure that is optimum in terms of mechanics, but the formulation grossly neglects parameter uncertainty and its effects on structural safety. Reliability-based Design Optimization (RBDO) has emerged as an alternative to properly model the safety-under-uncertainty part of the problem. With RBDO, one can ensure that a minimum (and measurable) level of safety is achieved by the optimum structure. However, results are dependent on the failure probabilities used as constraints in the analysis. Risk optimization (RO) increases the scope of the problem by addressing the compromising goals of economy and safety. This is accomplished by quantifying the monetary consequences of failure, as well as the costs associated with construction, operation and maintenance. RO yields the optimum topology and the optimum point of balance between economy and safety. Results are compared for some example problems. The broader RO solution is found first, and optimum results are used as constraints in DDO and RBDO. Results show that even when optimum safety coefficients are used as constraints in DDO, the formulation leads to configurations which respect these design constraints, reduce manufacturing costs but increase total expected costs (including expected costs of failure). When (optimum) system failure probability is used as a constraint in RBDO, this solution also reduces manufacturing costs but by increasing total expected costs. This happens when the costs associated with different failure modes are distinct. Hence, a general equivalence between the formulations cannot be established. Optimum structural design considering expected costs of failure cannot be controlled solely by safety factors nor by failure probability constraints, but will depend on actual structural configuration. (c) 2011 Elsevier Ltd. All rights reserved.

An economic evaluation of antihypertensive therapies based on clinical trials

OBJECTIVE: Hypertension is a major issue in public health, and the financial costs associated with hypertension continue to increase. Cost-effectiveness studies focusing on antihypertensive drug combinations, however, have been scarce. The cost-effectiveness ratios of the traditional treatment (hydrochlorothiazide and atenolol) and the current treatment (losartan and amlodipine) were evaluated in patients with grade 1 or 2 hypertension (HT1-2). For patients with grade 3 hypertension (HT3), a third drug was added to the treatment combinations: enalapril was added to the traditional treatment, and hydrochlorothiazide was added to the current treatment. METHODS: Hypertension treatment costs were estimated on the basis of the purchase prices of the antihypertensive medications, and effectiveness was measured as the reduction in systolic blood pressure and diastolic blood pressure (in mm Hg) at the end of a 12-month study period. RESULTS: When the purchase price of the brand-name medication was used to calculate the cost, the traditional treatment presented a lower cost-effectiveness ratio [US$/mm Hg] than the current treatment in the HT1-2 group. In the HT3 group, however, there was no difference in cost-effectiveness ratio between the traditional treatment and the current treatment. The cost-effectiveness ratio differences between the treatment regimens maintained the same pattern when the purchase price of the lower-cost medication was used. CONCLUSIONS: We conclude that the traditional treatment is more cost-effective (US$/mm Hg) than the current treatment in the HT1-2 group. There was no difference in cost-effectiveness between the traditional treatment and the current treatment for the HT3 group.