Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/124869


Title: 以階段型機率分佈表示異質生成衝擊系統
A System Subject to Non-Homogeneous Pure Birth Shocks with Phase-Type Distributions
Authors: 劉宏展
Liu, Hong-Zhan
Contributors: 陸行
Luh, Hsing
劉宏展
Liu, Hong-Zhan
Keywords: 衝擊模型
階段型分佈
異質生成過程
再生過程
馬可夫過程
年齡置換策略
穩定機率
Shock model
Phase-type distribution
Non-homogeneous pure birth process
Renewal process
Markov process
Age replacement policy
Stationary probability
Date: 2019
Issue Date: 2019-08-07 16:35:33 (UTC+8)
Abstract: 考慮一個衝擊系統,它的衝擊依據異質生成過程而產生。這個系統有兩
種類型的損壞。類型一的損壞可以被修理消除。類型二的損壞可以被不定
期置換消除。假設兩個連續衝擊之間的時間間隔服從階段型分佈。例如,
在一個特殊的階段型分佈—亞指數分佈—之下,我們發現穩定機率存在的
條件。在這個模型下探討年齡置換策略,我們導出置換週期內的期望成本
率。為了找到最小化期望成本率的最佳定期置換年齡,我們提供一個有效
率的演算法並開發一個 MATLAB 工具來實現。一系列數值範例促使我們發
現新的定理,它比以前的定理更簡單,更實際,更直觀。該定理表明最佳定期置換年齡的存在性。
We consider a system subject to shocks which occur according to a non-homogeneous pure birth process. The system has two types of failures. Type-I failure can be removed by a repair. Type-II failure can be removed by an unplanned replacement. We assume that the inter-arrival time between consecutive shocks follows phase-type distributions. For example, under a special PH-distribution that is a hypo-exponential distribution, we find the conditions of the existence of stationary probability. Under this model we investigate the age replacement policy. We derive the expected cost rate of a replacement cycle. To find the optimal planned replacement age that minimizes the expected cost rate, we give an efficient algorithm and develop a MALAB tool for implementation. A series of numerical examples motivate us to write a new theorem. That is simpler, more practical, and more intuitive than a previous theorem. This theorem shows the existence of the optimal planned replacement age.
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Description: 碩士
國立政治大學
應用數學系
105751004
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0105751004
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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