Abstract
在可靠度分析的文獻中，大都是建立在二種狀態 (好或壞，失敗或成功)元件所構成的二階狀態系統上。但是由多階狀態元件所構成的多階狀態系統，遠較二階狀態系統來得實際與合理，因此，多階狀態系統愈來愈受到重視。 在多階狀態系統中，離散、整數型態的流量網路就是其中一個例子。在這種流量網路系統中，系統效率 (System Performance) 的評估主要是專注在此流量網路系統能夠從起點 (Source Node ) 傳送一給定單位的流量到終點 (Sink Node) 的可靠度 (Reliability)。 本論文擬針對此流量網路提出一個有效率的蒙地卡羅模擬法來估計系統可靠度，並且提出另一個模擬方法來評估系統元件重要性的指標 (ComponentImportance Index )，以便提供決策者在做系統最佳化研究時充份的訊息，來增進系統效率的參考。Most literatures study system reliability by using binary-state models, i.e. the system and it's components flucturatebetween ``functioning'' and ``failed''.Recently, basic theoryfor the multi-state models or multi-state systems ofmultistate components has been being developed. Flow networkswith discrete, integer-valued capacities for each components(arcs) are one typical class of such multi-state model. How tomeasure the reliability that the flow network system cantransimit at least a given units of flow from the source nodeto the sink node successfully and how to measure theimportance of each component to the system thus attract recentattention.Another question of considerable interest is how tofind out which components are most crucial to the properfunctioning of the system by using the notation of componentimportance measure. This paper first presents a Monte Carlomethod which uses the stratified sampling method to estimtethe reliability of such a flow network. This method isefficient whenever compared to the crude Monte Carlo method.Also, it proposes the CRN method to estimate one of thecomponent importance measures. This method is efficientwhenever compared to the crude Monte Carlo method.