Reliability allocation problem in a series-parallel system

In order to improve system reliability, designers may introduce in a system different technologies in parallel. When each technology is composed of components in series, the configuration belongs to the series-parallel systems. This type of system has not been studied as much as the parallel-series architecture. There exist no methods dedicated to the reliability allocation in series-parallel systems with different technologies. We propose in this paper theoretical and practical results for the allocation problem in a series-parallel system. Two resolution approaches are developed. Firstly, a one stage problem is studied and the results are exploited for the multi-stages problem. A theoretical condition for obtaining the optimal allocation is developed. Since this condition is too restrictive, we secondly propose an alternative approach based on an approximated function and the results of the one-stage study. This second approach is applied to numerical examples.