Abstract
錯誤樹是現今機率安全分析的一項技術,然而由於許多事件從未發生，或發生的次數不多以致於缺乏合理的統計資料．為了解決這個問題，對各種不同基礎事件失敗機率我們可以用模糊數來表達其不確定的情形，以便計算頂端事件的失敗機率． 以往有關模糊錯誤樹量化分析的文獻都是假設所有的基礎事件都是同一型的模糊屬性函數．如梯形．三角形．鐘形等．本論文主張錯誤樹中所有的基礎事件的模糊屬性函數形狀可以不全相同，或可以是其他不規則的形狀． 另外對於證據理論在錯誤樹的應用方面， Guth把基礎事件的失敗機率區間轉換成三值邏輯形式，用三值邏輯AND, OR 閘運算求得頂端事件的三值邏輯形式，最後再把頂端事件的三值邏輯形式轉換成失敗機率區間． 事實上我們可以把基礎事件的上下限區間直接代入運算，以求得頂端事件失敗的區間．若以模糊集合的觀念來看，上下限區間可以看成是一個矩形屬性函數的模糊數．即對於這區間上的數值，專家沒有主觀的權重表示何處較為可信．一旦這區間各部份被判定了不同的權重，屬性函數便可以用來描述專家主觀的意見，進行錯誤樹量化分析．Fault tree analysis is one of the probabilistic safetyanalysis. However due to the fact that many failure eventswhich have never occured so far or have occured but soinfrequently and so their reasonable data are not available. Tosolve this problem, we may use fuzzy probability to describethe uncertainty of the failure probability for each basicevent, and then perform mathematical operation to evaluatesystem reliability. A number of papers have been presented topropose using fuzzy sets to describe the imprecise or vaguenessof events in fault tree analysis. They all assume the basicevent in a same fault tree are of the same type, liketrapezoidal, trangular, and bell shape. The main idea of thisthesis is supposed that all the basic events in a fault treemay have different shapes, or any other irregular shape. Andfor evidence theory in fault tree analysis, Guth rewrote thefailure probability interval of each basic event into 3-valueform and constructed AND/OR gate truth table to implement thefault tree quantitive evaluation. In fact, we can use the lower/upper bound intervals obtained from evidence theory directly tocalculate the failure probability interval of the top event.The lower/upper bound intervals, may be viewed as a rectangularmembership function in fuzzy sets. That is, experts pay nosubject weight upon the intervals. As experts think someportion of the intervals is more confident than other portion,different kinds of membership function may be used to describethe subjective opinion, and then perform mathematical operationto evalute the fault tree quantitive analysis.