The load-sharing model has been studied since the early 1940s to account for the stochastic dependence of components in a parallel system. It assumes that, as components fail one by one, the total workload applied to the system is shared by the remaining components and thus affects their performance. Such dependent systems have been studied in many engineering applications which include but are not limited to fiber composites, manufacturing, power plants, workload analysis of computing, software and hardware reliability, etc. Many statistical models have been proposed to analyze the impact of each redistribution of the workload; i.e., the changes on the hazard rate of each remaining component. However, they do not consider how long a surviving component has worked for prior to the redistribution. We name such load-sharing models as memoryless. To remedy this potential limitation, we propose a general framework for load-sharing models that account for the work history. Through simulation studies, we show that an inappropriate use of the memoryless assumption could lead to inaccurate inference on the impact of redistribution. Further, a real-data example of plasma display devices is analyzed to illustrate our methods.
A comprehensive reliability allocation method, which is applicable to the cases of lack of data in design stage, as well as the complexity of the influence factors and uncertainty of expert evaluation, is presented based on the gray system theory. The key of this method is to modify the weights of influence factors which are associated with expert scoring data by gray correlation analysis before reliability indices are assigned linearly to each subsystem. Based on gray evaluation with 4 levels, the application of this method is illustrated with the reliability allocation of a rotary machine under the consideration that complexity, technical level, importance and environment condition are chosen as influence factors. Compared with the actual faults statistics results, the validity and feasibility of the method is verified.
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