馬可夫過程可修復系統加入更新隨機干擾之模型的穩定狀態機率

Abstract

本篇論文主要是想探討，當馬可夫過程中加入更新隨機干擾，變成非馬可夫過程之後，此非馬可夫過程的模型之穩定狀態機率。此外，因為模型的穩定狀態機率計算較為繁複，我們提出另ㄧ個計算比較容易的馬可夫過程穩定狀態機率，來近似此非馬可夫過程的模型之穩定狀態機率。在論文中，我們是將模型套用在可修復系統上，並且會舉數個例子來比較兩者的結果。

This thesis is focused on deriving the steady state probabilities of a non-Markov process obtained from a Markov process subject to renewal random interventions. In addition, we propose the steady state probabilities from a different but related Markov process which can be computed easily and with high precision to the steady state probabilities from a non-Markov process. In this thesis, a non-Markov process is applied in a repairable system, and several examples are presented.