The objective of this paper is to provide an improved reorder decision policy for general multi-echelon distribution systems utilizing the shared stock information. It has been known that traditional reorder policies sometimes show poor performance in distribution systems. Thus, in our previous research we introduced the order risk policy which utilizes the shared stock information more accurately for the 2- echelon distribution system and proved the optimality. However, since the real world supply chain is generally composed with more than 2 echelons, we extend the order risk policy for the general multi-echelon systems. Since the calculation of the exact order risk value for general multi-echelon systems is very complex, we provide two approximation methods for the real-time calculation. Through the computational experiment comparing the order risk policy with the existing policies under various conditions, we show the performance of the order risk policy and analyze the value of the shared stock information varying with the characteristics of the supply chain.