Abstract
In the present paper, a three-component, stationary, multistate flow network system is studied. Detailed costs and incomes are specified. The aim is to minimize the expected total net loss with respect to the expected times the components spend in each state. This represents a novelty in that we connect the expected component times spent in each state to the minimal total net loss of the system, without first finding the component importance. This is of interest in the design phase where one may tune the components to minimize the expected total net loss. Due to the complex nature of the problem, we first study a simplified version. There the expected times spent in each state are assumed equal for each component. Then a modified version of the full model is presented. The optimization in this model is completed in two steps. First the optimization is carried out for a set of pre-chosen fixed expected life cycle lengths. Then the overall minimum is identified by varying these expectations. Both the simplified and the modified optimization problems are nonlinear. The setup used in this article is such that it can easily be modified to represent other flow network systems and cost functions. The challenge lies in the optimization of real life systems.
Highlights
A series of challenges concerning reliability engineering is presented in [1]
We will define incomes and cost functions for the purpose of minimizing the expected total net loss over a time period with respect to the expected component times in the different states. This represents a novelty in that we connect the expected component times spent in each state to the minimal total net loss of the system, without first finding the component importances
For instance one of the functioning states is redundant for two of the three cost function types when the cost function parameter is increasing. For both problems we see that the minimum expected total net loss is increasing with increasing component cost per repair
Summary
A series of challenges concerning reliability engineering is presented in [1]. Some of these challenges are connected to the representation and modeling of complex systems, such as multistate systems, and their. We will define incomes and cost functions for the purpose of minimizing the expected total net loss over a time period with respect to the expected component times in the different states. In the simplified version we see that the optimal expected time spent in each state increases with increasing operational time for all three cost function types considered. For instance one of the functioning states is redundant for two of the three cost function types when the cost function parameter is increasing For both problems we see that the minimum expected total net loss is increasing with increasing component cost per repair.
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