條件式部份期望值在專案進行時，對專案作業平均時間在不同機率分佈下的動態推算

Using Conditional Partial Expected Value towards the Dynamic Estimation of Mean Project Activity Time Under Different Probability Distribution

汪家興(Chia-Hsing Wang)

指導教授 ： 林逾先

國立臺北科技大學/管理學院/商業自動化與管理研究所/碩士(2006年)

https://doi.org/10.6841/NTUT.2006.00400

摘要

在日常生活中，許多大型工程都是由專案的模式進行，在一專案工程中往往包含許多活動與作業，由於專案工程是運用特定的資源、人力、物力在有限的時間內以最有效率的方式達成目標，因此必須利用專案管理的技術，來控管專案中各作業的時間，使得整個專案能如期完成，並有效的分派資源，使之不致有所衝突。由於專案管理最重要的工作在於時間的掌控，因此對於專案作業時程的分析在專案管理中的技術種類相當多，計畫評核術（Program Evaluation and Review Technique, PERT）排程技術主要是以三個估時(悲觀、最可能、樂觀估時)來取代CPM中的單一估時，並採用機率概念以Beta 分佈理論來推算單一作業的作業時間。

由於專案的不確定性和影響因素的不同，對於所有專案的時間排程都是呈現Beta 分佈的假設令人質疑且由PERT推算出來的作業完成平均時間只限定在專案尚未開始行動時對整個專案的作業時間做估計，因此要如何在專案進行中推算出往後專案的作業完成平均時間是一值得研究的課題。本研究以PERT為基礎，對一項專案作業引用”條件式部份期望值”的觀念去推估在專案作業進行至某一階段時，對於往後專案進度的作業完成平均時間的推算，並配合假設專案作業時間排程呈現均勻(uniform)分佈、三角形分佈、Beta分佈、常態分佈等四種分佈的個別情形下作推算，以獲得在專案進行中且作業時間排程呈現在不同分佈下作業平均完成時間的計算公式，協助作為專案資源調派及工期管控的基準。

關鍵字

專案管理 ； PERT ； 專案作業時間

並列摘要

In daily life, there are multitudes of engineering works in project model, in a project schedule often include a lot of activities. Because the project is to use specific resource, manpower, material resources to reach the goal in a most efficient way within limited time so must use the technology of project management to management the activity time in project and make the whole project can be finished as scheduled. Because project management most important work is to control time, so to there are many technological kinds to analysis activity time in project management. Program Evaluation and Review Technique (PERT) is to use three time estimates (least possible time, greatest possible time, modal time) to replace Critical Path Method (CPM) for calculate each activity time under Beta distribution.
The project is usually filled with uncertainties and influence factors. Consequent PERT suppose that the all activity time in project scheduled must obey Beta distribution make people to query and PERT make estimate of the mean project activity time only limiting when the project has not begun to take action. In this research is based on the PERT and use the “Conditional Partial Expected Value” towards the dynamic estimation of mean project activity time. And under the suppose activity time in project is uniform distribution, triangular distribution, Beta distribution, normal distribution for the specific situation to towards the dynamic estimation of mean project activity time so to obtain the general formula. The formula could adjust to resource and scheduled progress that would be beneficial to project schedule management in future.

並列關鍵字

Project Management ； PERT ； Project Activity Time

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