Reliability analysis of load-sharing systems with memory

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.

SEMI-MARKOV EMBEDDABLE RELIABILITY STRUCTURES AND APPLICATIONS TO LOAD-SHARING k-OUT-OF-n SYSTEMS

This paper deals with the application of nonhomogeneous semi-Markov processes in reliability modeling. The notion of a semi-Markov embeddable reliability structure is introduced and discussed. As an example, load-sharing k-out-of-n : G systems of equal components with arbitrary life distributions under the equal load-sharing rule are treated in the context of semi-Markov embeddable systems. Besides some discussion about load-life models, the case of repairable components is to some extent treated as well.