Determining reliability parameters for a commodity transfer system with non-independent components

Malinowski, Jacek

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Title: Determining reliability parameters for a commodity transfer system with non-independent components

Abstract:

In this paper, a transmission network composed of n linearly arranged components e_0, ...,e_n is considered. For each i=1 , ... ,n- 1 the component e_i is directly connected to e_i-1 and e_i+1, while e_n is directly connected to e_n-1 alone; e_0 is the source component from which certain commodity (electric power, radio signal, electronic data, water, gas, etc.) is transferred, via e_1, ... ,e_n-1, to e_n. Each component can be in one of two states: 1 - operating, 0 - failed; e_0 is always in operating state. The order in which failed components are chosen for repair depends on the repair policy applied - two of such policies will be considered. A commodity can be transferred from e_0 to e_i, i=1, ... ,n, if and only if e_i is functional and connected to e_0, i.e. e_1, ... ,e_i are in the operating state. As failures of components occur, the periods during which functional e_i is connected to e_0 are interleaved by the periods during which e_i is failed or disconnected from e_0. The main goal of this paper is to determine the mean durations of these time intervals, i.e. the mean time from the moment when the connection between e_0 and e_i is interrupted to the moment when it is restored, and the mean time of uninterrupted connection between e_0 and e_i. It is assumed that the functioning of e_i depends on the states of e_1, ... ,e_i-1 in the following way: e_i can only fail if e_1, ... ,e_i-1 are in the operating state.