In this paper we consider a company including both a forward supply chain producing and supplying products to markets and an after-sales supply chain providing spare parts to fulfill its after-sales commitments. Uncertainty in estimating product demand in the premarkets and spare parts demands in the after-sales markets and qualified outputs of production facilities throughout these two chains are considered in this problem. Stochastic qualified outputs of these facilities are due to their imperfect productions systems. We show that uncertainties propagate and qualified flow depreciates by moving material, components, and products from upstream to the downstream of these supply chains, and these phenomena should be quantified to determine the service levels of this company in the pre- and after-sales markets. At the end, we propose a mathematical model determining the best marketing strategies for this company (i.e., price, warranty length, and service levels) in the markets and their preserving reliable flow dynamics throughout the chains’ networks. Finally, the model is tested on a test problem defined in engine industry and some managerial insights are provided by analyzing the results.

Current limit state surrogate modeling methods for system reliability analysis usually build surrogate models for failure modes individually or build composite limit states. In practical engineering applications, multiple system responses may be obtained from a single setting of inputs. In such cases, building surrogate models individually will ignore the correlation between different system responses and building composite limit states may be computationally expensive because the nonlinearity of composite limit state is usually higher than individual limit states. This paper proposes a new efficient Kriging surrogate modeling approach for system reliability analysis by constructing composite Kriging surrogates through selection of Kriging surrogates constructed individually and Kriging surrogates built based on singular value decomposition. The resulting composite surrogate model will combine the advantages of both types of Kriging surrogate models and thus reduce the number of required training points. A new stopping criterion and a new surrogate model refinement strategy are proposed to further improve the efficiency of this approach. The surrogate models are refined adaptively with high accuracy near the active failure boundary until the proposed new stopping criterion is satisfied. Three numerical examples including a series, a parallel, and a combined system are used to demonstrate the effectiveness of the proposed method.

It is desirable for complex engineered systems to be resilient to various sources of uncertainty throughout their life cycle. Such systems are high in cost and complexity, and often incorporate highly sophisticated materials, components, design, and other technologies. There are many uncertainties such systems will face throughout their life cycles due to changes in internal and external conditions, or states of interest, to the designer, such as technology readiness, market conditions, or system health. These states of interest affect the success of the system design with respect to the main objectives and application of the system, and are generally uncertain over the life cycle of the system. To address such uncertainties, we propose a resilient design approach for engineering systems. We utilize a Kalman filter approach to model the uncertain future states of interest. Then, based upon the modeled states, the optimal change in the design of the system is achieved to respond to the new states. This resilient method is applicable in systems when the ability to change is embedded in the system design. A design framework is proposed encompassing a set of definitions, metrics, and methodologies. A case study of a communication satellite system is presented to illustrate the features of the approach.

The paper discusses a new method for the propagation of risk levels. This discretization takes place by considering the phase space of the state and its subdivision into boxes. In each time step, the method computes the probability of the state being in one box. We start with a variety of technical and physical problems by showing how discrete modeling under uncertainties is technically meaningful and often even problem inherent. Then we select the technical problem of contaminant spread in water grids, to which we apply the method of risk-level propagation in depth. Extensions of the method such as modeling of contaminant mixing at junctions in the discretized phase space and the applicability of conservation laws arise naturally along these lines and are discussed in the context of the general theory.

The presence of aerodynamics loadings makes the design of some classes of elastic structures, as, for instance, marine structures and risers, very challenging. Moreover, capturing the complex physical interaction between the structure and the fluid is challenging for both theoretical and numerical models. One of the most important phenomena that appear in these situations is vortex-induced vibrations. The picture is even more complicated when multiple elastic elements are close enough to interact by modifying the fluid flow pattern. In the present work, we show how the common design practice for these structures, which is entirely based on deterministic simulations, needs to be complemented by the uncertainty quantification analysis. The model problem is a structure constituted by two elastically mounted cylinders exposed to a two-dimensional uniform flow at Reynolds number 200. The presence of a manufacturing tolerance in the relative position of the two cylinders, which we consider to be a source of uncertainty, is addressed. The overall numerical procedure is based on a Navier–Stokes immersed boundary solver that uses a flexible moving least squares approach to compute the aerodynamics loadings on the structure, whereas the uncertainty quantification propagation is obtained by means of a nonintrusive polynomial chaos technique. A range of reduced velocities is considered, and the quantification, in a probabilistic sense, of the difference in the performances of this structure with respect to the case of an isolated cylinder is provided. The numerical investigation is also complemented by a global sensitivity analysis based on the analysis of variance.

The fuzziness of the traditional multiaxial fatigue prediction model is discussed and the fuzzy theory is applied into fatigue reliability analysis. The fuzzy linear regression analysis method is used to determine the fuzzy coefficients in the multiaxial stress–life equation under a small sample condition, and the corresponding multiaxial fatigue probabilistic stress–life curve is calculated with different confidence levels.

Change mode and effects analysis (CMEA) is a powerful technique for measuring product flexibility toward future changes and diminishing the cost of redesign as well as shortening time to market. As a systematic methodology, it provides an in-depth view for the investigation of potential changes, causes, and effects in designs, products, and processes. Traditional CMEA determines the risk priorities of change modes by using change potential number, which requires the risk factors of design flexibility, occurrence, and readiness to be precisely evaluated. However, this is not always possible in real applications due to the uncertainty and subjectivity involved in the early design stages. It has been criticized much for its deficiencies in criteria weighting of the risk factors, change potential number calculation, and risk priorities determination of the change modes. This paper presents a systematic evaluation approach for determining a more rational rank of change modes by combining with the entropy weight method, rough number, and grey relational analysis. In this study, the entropy weight method is adopted to calculate the relative importance of risk factors. Rough number is presented to aggregate individual weights and preferences, and to manipulate the vagueness in the evaluation process. Then a rough number enhanced grey relational analysis is proposed to evaluate the risk ranking of change modes. Finally, a practical example is put forward to validate the performance of the proposed method. The result shows that the proposed change mode evaluation method can effectively overcome the shortcomings of traditional CMEA and strengthen the objectivity of product flexibility measurement.