政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/124869

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/124869

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | 全文筆數/總筆數 : 112704/143671 (78%)
造訪人次 : 49786458 線上人數 : 682

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

搜尋範圍

查詢小技巧：

您可在西文檢索詞彙前後加上"雙引號"，以獲取較精準的檢索結果

若欲以作者姓名搜尋，建議至進階搜尋限定作者欄位，可獲得較完整資料

進階搜尋

主頁 ‧ 登入 ‧ 上傳 ‧ 說明 ‧ 關於政大典藏 ‧ 管理

到手機版

政大機構典藏 > 理學院 > 應用數學系 > 學位論文 > Item 140.119/124869

請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/124869

題名:	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
作者:	劉宏展 Liu, Hong-Zhan
貢獻者:	陸行 Luh, Hsing 劉宏展 Liu, Hong-Zhan
關鍵詞:	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
日期:	2019
上傳時間:	2019-08-07 16:35:33 (UTC+8)
摘要:	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.
參考文獻:	[1] M. S. A-Hameed and F. Proschan. Nonstationary shock models. Stochastic Processes and their Applications, 1(4):383–404, 1973. [2] M. S. A-Hameed and F. Proschan. Shock Models with Underlying Birth Process. Journal of Applied Probability, 12(1):18–28, 1975. [3] S. Asmussen, O. Nerman, and M. Olsson. Fitting phase-type distributions via the em algorithm. Scandinavian Journal of Statistics, 23(4):419–441, 1996. [4] R. Barlow and L. Hunter. Optimum preventive maintenance policies. Operations Research, 8(1):90–100, 1960. [5] P. Buchholz, J. Kriege, and I. Felko. Input Modeling with Phase-Type Distributions and Markov Models: Theory and Applications. Springer, New York, 2014. [6] D. R. Cox. Renewal Theory. Methuen, London, 1962. [7] J. D. Esary, A. W. Marshall, and F. Proschan. Shock Models and Wear Processes. The Annals of Probability, 1(4):627–649, 1973. [8] F. S. Hillier and G. J. Lieberman. Introduction To Operations Research. McGraw-Hill, New York, 10th edition, 2015. [9] R. S. Maier and C. A. O’Cinneide. A Closure Characterisation of Phase-Type Distributions. Journal of Applied Probability, 29(1):92–103, 1992. [10] D. Montoro-Cazorla, R. PérezOcón, and M. C. Segovia. Shock and wear models under policy N using phase-type distributions. Applied Mathematical Modelling, 33:543–554, 2009. [11] M. F. Neuts. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore, 1981. [12] B. F. Nielsen. Lecture notes on phase–type distributions for 02407 Stochastic Processes, 2017. [13] S.H. Sheu, C.C. Chang, Z. G. Zhang, and Y.H. Chien. A note on replacement policy for a system subject to non-homogeneous pure birth shocks. European Journal of Operational Research, 216:503–508, 2012. [14] H. M. Taylor and S. Karlin. An Introduction to Stochastic Modeling. Academic Press, Cambridge, Massachusetts, 3rd edition, 1998.
描述:	碩士國立政治大學應用數學系 105751004
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0105751004
資料類型:	thesis
DOI:	10.6814/NCCU201900384
顯示於類別:	[應用數學系] 學位論文

文件中的檔案:

檔案	大小	格式	瀏覽次數
100401.pdf	762Kb	Adobe PDF2	0	檢視/開啟

在政大典藏中所有的資料項目都受到原著作權保護.

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

DSpace Software Copyright © 2002-2004 MIT & Hewlett-Packard / Enhanced by NTU Library IR team Copyright © - 回饋