Abstract
在如安全、生產、電子、電腦、機械、控制及大眾運輸等系統，常能見並聯("Parallel System"可稱為"並聯","平行"或"並行"系統)及k-out-of-n二類系統的存在。本文針對此二系統分別使用由Nakagawa與Barlow提出的二個置換策略。為方便起見，稱此二策略分別稱為策略壹與策略貳(Policy Tow)。其中由Barlow提出的置換策略被稱為 Age ReplacementPolicy。若作業系統採用策略壹，則該系統將在一個距時間原點特定且固定的時間點 T被一個新的且完全相同的系統所取代。若作業系統採用策略貳，則從時間原點起，該系統將在下列狀況發生時，被一個新的且完全相同的系統所取代，1.距時間原點特定且固定的時間點 T，2.系統故障時，視何者先發生。於置換新的系統後，稱該系統被"更新" (Renewal)。 在系統被 "更新"的同時，時間原點也被重新設於此時，此系統則繼續等待上述被置換的時機。如此週而復始的置換過程，稱之為 "更新過程"(Renewal Process)。 本文目標乃是利用隨機過程的方法，在假設追求長期平均成本最小的前提下，求出上述所言 "最佳距時間原點特定且固定的時間點"Consider a system of n components. It is called a parallesystem if it fails whenever all units fails; a k-out-of-nsystem if it functions whenever at least k components function.In this thesis, two policies which were originally presented byNakagawa and Barlow are implemented to each of such two kindsof systems respectively. The later policy is called the AgeReplacemet. For convenience, such two policies are calledpolicy one and policy two respectively. Under policy one, theoperating system will be replaced by a new one only at kT forspecified T for k=1,2,... Under policy two, the system will bereplaced whenever it fails and at time kT for k=1,2,... whichoccurs first. The target of our paper is to find the specifiedT such we have the minimal long run average cost.