AbstractThis paper describes a meth

Abstract
This paper describes a methodology for accident assessment in the frame of a judicial procedure and provide the formal mathematical relations for the fault tree application to the case.

The predictive use of Fault Tree (FT) technique is well known: the best estimate of an undesirable event (the Top Event, TE) frequency is computed from all the basic frequencies of component failures, human errors, and external events.

The FT use is less frequent in “post-dictive” mode: in situations for which the TE is verified, as in the case of a judicial procedure.

In such circumstances, several experts are appointed by the judge (JE) and by the parties, the plaintiffs and defendants (PEs), to reconstruct the event by following a top-down procedure analogous to that necessary for FT construction. They start from the event and try to find out the causes of the event, using all the circumstantial evidences. PEs often form different hypotheses, reaching contrasting conclusions, strongly influenced by the part represented, with JE in a more balanced position.

It is so crucial to adopt a methodology that helps the experts, in particular the JE, to delimit, as much as possible, the area of the uncertainties. FT may be useful for this purpose. In fact, the FT construction allows to incorporate the evidences acquired from the investigations at the level of basic events: the basic events, now, are qualified as “true”, “false” or “unknown” (in the predictive contest, they are quoted through frequencies). In this way, it is possible to select the sequences accountable for the TE.

In this paper a formal development for FT application to judicial procedure is given, together with a real case study. The method can be applied to all kind of accidents, provided that the situation can be described by a fault tree.

Highlights

► Fault Tree (FT) adaptation to forensic and investigation applications is presented. ► We use FT for a real event, in a reverse mode respect to the forecast case. ► This is the case of a judicial procedure, following an incident or an accident. ► Investigation evidences are incorporated in the FT, which is greatly simplified. ► The remaining FT branches are the possible causes of the incident investigated.

Keywords
Fault tree; Risk analysis; Judicial procedure; Accident investigation; Forensic investigation; Forensic engineering
1. Introduction
Let us start from this comparison: “Assign the blame” – vs – “Learn how to improve the system”.

The scope of a judicial procedure is to assess the responsibilities of the accident: to assign the blame. On the other side, it is well known that major improvements of human development come from learning by the errors done. In this case, we try to understand what happened, in order to prevent future similar situations. The scopes are different, although both cases are examples of accident investigations. Actually, according to Levenson (2004), the two previous scopes are “the basic reasons for conducting an accident investigation, etc. When the goal is to assign the blame, the backward chain of events considered often stops when someone or something appropriate to blame is found”. In other words, in a judicial procedure the main goal is not to learn as much as possible, but to assign the blame. This implies that different accident models will be usually adopted, as far as the pursued scopes are different (Svenson, 1999).

However, different accident models may use the same accident investigation methods, i.e. those practical tools “designed with the purpose of helping a specific user (person) to accomplish a specific task (investigation and analysis) in a specific settings. A certain accident investigation method is not necessarily linked to a specific accident model: it can be a tool of its own.” (Katsakiori et al., 2009). A number of accident investigation models and accident investigation methods have been developed in the last decades and the analysis of these is out of the scope of the present paper. Interested reader can refer, for example, to the already quoted work of Levenson (2004), Katsakiori et al. (2009), and to DOE (1999), Kjellén (2000), Johnson (2003), Sklet (2004), and Levenson (2011).

In the case of a judicial procedure, although the general scope is well defined (i.e. the blame assessment), different experts (the expert appointed by the judge (JE) and by the parties, the plaintiffs and defendants, PEs) very often have contrasting scopes; they are not members of a team investigating the facts, but rather competitors. Looking to the list of biases provided by Johnson (2003), it is apparent that the “Sponsor bias”, i.e. the influence due to the risk of damaging the reputation of the expert’s part, is really dominant for the PEs. The experts have definitively different accident investigation models, they have different interests in collecting data and in analyzing them, they (experts & models) “may either act as a filter and bias toward considering only certain events and conditions or they may expand activities by forcing consideration of factors that are often omitted” (Levenson, 2004). Several authors (most of the above quoted, in particular Johnson, 2003; Levenson, 2004) analyze the problem of biasing in accident investigation, not only in the case of legal disputes, and most of the bias comes from the different models. For this reason, as far as in judicial procedure is practically impossible to adopt a common model, the choice of a common, good and simple method may be very effective in reducing bias (Lundberg et al., 2010).

In this paper, the well known Fault Tree (FT) method is reviewed for judicial procedure as a toll managed by the JE in order to collect and to integrate the information provided by the investigations and the reasons – often different, but not exclusionary – provided by the PEs. This use of the FT – as a common, good and simple method to force the reduction of bias due to the different scopes in judicial procedures – is quite new, in our opinion, and turns out to be very helpful in the practice (a case study is presented in Sections 4 and 5). A formal equation for the judicial application of the FT is derived in Section 3.

2. Over the fault tree and its extension to judicial procedures
The use of the Fault Tree (FT) technique has been previously combined with risk analysis and applied to a variety of industrial and non-industrial sectors, such as nuclear energy, aviation and aeronautics, and chemical industry (Fussel, 1976, McCormick, 1981, Vesely et al., 1981, Vose, 2008 and Zio, 2007). As it is well known, the FT can be regarded as the conjunction between qualitative and the quantitative analysis: it is preceded by the phases of the risk analysis aimed at identification of “all” the top events, and it is followed by the phases yielding the TE frequencies. Between these two risk analyses, the FT has to individualize, through the characteristic top-down procedure, the basic events that result in a particular TE occurrence. In essence, the whole procedure attempts to answer the following questions:

(a)
What are the TEs of interest for the system under examination?
(b)
Which events occur concurrently that result in a TE, and how do they occur?
(c)
What is the probability of each top?
(d)
What are the TE’s consequences?
(e)
What is the resultant risk?
(f)
What are the preventive and protective measures for risk reduction?
In any case, in the usual applications, all this is developed in a predictive way: the goal is to determine the probability of having damage and the cause of this potential damage to minimize the risk.

When we consider a judicial procedure following an accidental event, the scenario is quite different; nevertheless, the use of an FT turns out to be very effective.

The major difference is, obviously, that now the TE being considered has already occurred. The question (a) is not interesting, usually.

Following the judicial procedure, experts are appointed to explain what happened and why. These experts are (at least):

–
The technical advisor of the judge (JE).
–
The technical advisors of the parts (the plaintiffs and defendants) (PEs).
The judge’s questions most often attempt to ascertain why the accident occurred, i.e. she/he is mainly interested in point (b), i.e.: “Which events occur concurrently that result in a TE, and how do they occur?”. From this, it follows also “Why, what/who is responsible?”.

Very often, as pointed out in the introduction, contrary to what could be supposed, the experts (at least the PEs) produce opposite conclusions, following the process, described by Jean-Jacques Rousseau, that “marries the convenience with the conviction”, i.e. they tend to demonstrate what the PEs desire. They are strongly biased. Obviously, this results in an augmented confusion, especially high when the technical problem is complicated. The question now is: Is it possible to follow (and to share) a procedure that, even taking into account the differences due to the different PEs point of views, is developed on more rigorous technical basis, reducing the area of uncertainty? Or: is it possible to share a common method, given that the JE’s and the PEs’s models are different and with opposite goals (at least as far as the PEs is concerned) so that the biases are reduced and the different points of view integrated?

This is the field of forensic engineering investigation, which should provide results that will be acceptable under the rules of evidence in a court of law (Noon, 2001, NFPA, 2002 and EPRI, 2003). After the initial introduction of FT analysis in forensic engineering (Johnson, 1985), some important applications have been done. A review of these forensic and investigation applications is provided by Johnson et al. (2006). However, the diffusion of the forensic FT analysis has been quite limited up to now, due to the lack of a specific adaptation of

結果 (繁體中文) 1:

摘要本文介紹了事故評估框架中的一種司法程式的方法，並提供故障樹應用到用例的正式數學關係。預測使用故障樹 (FT) 技術是眾所周知的: 從元件故障、 人為錯誤和外來事件的基本頻率計算頂事件 (TE) 的不良事件頻率的最佳估計數。金融時報 》 使用是那麼頻繁"後 dictive"模式: 在為其驗證是 TE，如司法程式的情況下。在這種情況下，幾位專家任命由法官 (乙腦) 和締約方、 原告和被告 (PEs)，重建由下列自上而下過程所必需的金融時報 》 建設類似的事件。他們從事件啟動，並嘗試找出事件的原因，使用所有的間接證據。聚醚碸往往形成不同的假說，就對比得出結論，受到部分代表，在一個更平衡的立場流行性乙型腦炎的強烈影響。它是如此重要，採用一種方法，可以説明專家的意見，特別是流行性乙型腦炎，來分隔，盡可能多地，該地區的不確定性。為此，金融時報 》 可能有用。事實上，金融時報 》 建築允許納入從一級基本事件調查獲得的證據: 基本事件，現在，是限定為"true"，"假"或"未知"(在預測的比賽中，他們都引用通過頻率)。這種方式，就可以選擇負責 TE 序列。本文鑒於正式發展為金融時報 》 在司法程式中的應用，與真實的案例研究。該方法可以適用各種事故，提供，這種情況可以用故障樹來描述。亮點► 故障樹 (英尺) 適應法醫和提出調查申請。► 我們使用英尺為真實的事件，在反轉模式方面的預測情況。► 這是司法的程式，以下事件或事故的情況。► 調查證據列入金融時報 》，極大地簡化了。► 剩餘英尺分支是調查這一事件的可能原因。關鍵字故障樹;風險分析;司法程式;事故調查;法醫調查;工程司法鑒定1.介紹讓我們從這樣的比較:"推卸"— — vs — —"學習如何提高系統"。司法程式的範圍是評估這次事故的責任: 要分配責任。另一邊，眾所周知，主要改進的人類發展所做的錯誤來自學習。在這種情況下，我們試著瞭解發生了什麼事，以防止今後類似的情況。雖然這兩種情況是事故調查的例子，範圍是不同的。實際上，根據文森 (2004 年)，兩個以前範圍是"進行事故調查，等的基本原因。當目標是推卸時，落後的事件經常停止時考慮適當的某人或某事責怪找到鏈"。換句話說，在司法過程中的主要目標是不是為了學習盡可能多地，而是推卸。這意味著，將通常通過不同事故模型，只要追求的範圍是不同的 (高，1999年)。However, different accident models may use the same accident investigation methods, i.e. those practical tools “designed with the purpose of helping a specific user (person) to accomplish a specific task (investigation and analysis) in a specific settings. A certain accident investigation method is not necessarily linked to a specific accident model: it can be a tool of its own.” (Katsakiori et al., 2009). A number of accident investigation models and accident investigation methods have been developed in the last decades and the analysis of these is out of the scope of the present paper. Interested reader can refer, for example, to the already quoted work of Levenson (2004), Katsakiori et al. (2009), and to DOE (1999), Kjellén (2000), Johnson (2003), Sklet (2004), and Levenson (2011).在司法程式的情況下雖然一般範圍定義 (即責任評估)，不同的專家 (專家任命的法官 (乙腦) 和締約方、 原告和被告，PEs) 很多時候有對比範圍;他們不是調查事實，但競爭對手而是一個團隊的成員。展望的偏見 Johnson (2003 年) 所提供的清單，很明顯"贊助商偏見"，即由於破壞專家的一部分的聲譽的風險的影響是對於 PEs 的真正優勢。專家們有明確不同事故調查模式，他們有不同的興趣，在收集資料和分析他們，他們 (專家及型號)"可能要麼行動作為篩選器和偏向于僅考慮某些事件和條件或他們可能擴大活動迫使考慮經常被省略的因素"(文森，2004年)。幾位作者 (最上面的報價，在特定 Johnson，2003 年;文森，2004年) 對在事故調查中，不僅在法律上發生爭議，偏置問題進行分析和大多數的偏見來自于不同的模型。為此，在司法程式幾乎是不可能採取一種共同的模式，共同的、 好的和簡單的方法的選擇可能非常有效地減少偏見 (Lundberg et al.，2010年)。In this paper, the well known Fault Tree (FT) method is reviewed for judicial procedure as a toll managed by the JE in order to collect and to integrate the information provided by the investigations and the reasons – often different, but not exclusionary – provided by the PEs. This use of the FT – as a common, good and simple method to force the reduction of bias due to the different scopes in judicial procedures – is quite new, in our opinion, and turns out to be very helpful in the practice (a case study is presented in Sections 4 and 5). A formal equation for the judicial application of the FT is derived in Section 3.2. Over the fault tree and its extension to judicial proceduresThe use of the Fault Tree (FT) technique has been previously combined with risk analysis and applied to a variety of industrial and non-industrial sectors, such as nuclear energy, aviation and aeronautics, and chemical industry (Fussel, 1976, McCormick, 1981, Vesely et al., 1981, Vose, 2008 and Zio, 2007). As it is well known, the FT can be regarded as the conjunction between qualitative and the quantitative analysis: it is preceded by the phases of the risk analysis aimed at identification of “all” the top events, and it is followed by the phases yielding the TE frequencies. Between these two risk analyses, the FT has to individualize, through the characteristic top-down procedure, the basic events that result in a particular TE occurrence. In essence, the whole procedure attempts to answer the following questions:() a工商業污水附加費下考試系統感興趣的是什麼?() b所發生的事件同時在 TE 中，這一結果和它們是如何發生?() c每個頂級的概率是多少?() dTE 的後果是什麼?() e由此產生的風險是什麼?() f減少風險的預防和保護措施是什麼?在任何情況下，在通常的應用中，這一切以預測的方式發展: 目標是確定損害和這個潛在的損壞的原因，儘量減少風險的概率。當我們考慮意外事件後的司法程式時，情況卻相當不同;然而，金融時報 》 使用原來是非常有效的。主要的區別是，很明顯，現在正在考慮 TE 已經發生。問題 (a) 通常不是有趣的。按照司法程式，任命專家來解釋發生了什麼和為什麼。這些專家是 (至少):–法官 (乙腦) 技術顧問。–部分 (原告和被告) 技術顧問 (PEs)。法官的問題大多數經常試圖查明事故發生的原因，即他/她是主要興趣點 (b)，即:"所發生的事件同時在 TE 中，這一結果和它們是如何發生?"。從此，它跟隨也"為什麼，什麼誰負責?"。Very often, as pointed out in the introduction, contrary to what could be supposed, the experts (at least the PEs) produce opposite conclusions, following the process, described by Jean-Jacques Rousseau, that “marries the convenience with the conviction”, i.e. they tend to demonstrate what the PEs desire. They are strongly biased. Obviously, this results in an augmented confusion, especially high when the technical problem is complicated. The question now is: Is it possible to follow (and to share) a procedure that, even taking into account the differences due to the different PEs point of views, is developed on more rigorous technical basis, reducing the area of uncertainty? Or: is it possible to share a common method, given that the JE’s and the PEs’s models are different and with opposite goals (at least as far as the PEs is concerned) so that the biases are reduced and the different points of view integrated?This is the field of forensic engineering investigation, which should provide results that will be acceptable under the rules of evidence in a court of law (Noon, 2001, NFPA, 2002 and EPRI, 2003). After the initial introduction of FT analysis in forensic engineering (Johnson, 1985), some important applications have been done. A review of these forensic and investigation applications is provided by Johnson et al. (2006). However, the diffusion of the forensic FT analysis has been quite limited up to now, due to the lack of a specific adaptation of

結果 (繁體中文) 2:

摘要
本文介紹了事故評估方法在司法程序的框架，並為故障樹的應用程序的情況下，正規的數學關係，該預測使用故障樹（FT）技術是眾所周知的：一個企業的最佳估計數不良的事件（頂事件，TE）的頻率是從組件故障，人為錯誤和外部事件的所有基本頻率計算出來的。金融時報用途是“後dictive”模式不太頻繁：在的情況下為其TE驗證，如在司法程序的情況。在這種情況下，一些專家由法官（JE），並在當事各方任命，原告和被告（PES），由下一個自上而下的過程類似於重建事件所必需的FT建設。他們從事件開始，並嘗試找出事件的原因，利用所有的間接證據。PE設備常形成不同的假設，達到對比的結論，強烈地部分的影響來表示，與日本腦炎在一個更平衡的位置上。這是如此重要，採用了一種方法，可為專家們，特別是日本腦炎，劃，盡可能，不確定性區域。的FT可以是用於該目的。事實上，對FT結構允許摻入從調查在基本事件的電平獲得的證據：基本的事件，現在，被定性為“真”，“假”或“未知”（在預測的比賽，它們是通過頻率引用）。以這種方式，有可能選擇在TE負責的序列。在本文中的正式開發的FT應用到司法程序，給出與實際案例研究在一起。該方法可應用於所有類型的事故時，只要該情況可以通過一個故障樹進行說明。亮點►故障樹（FT）適應法醫和調查的應用程序呈現。►我們使用的FT為真實的事件，在反向模式相對於所述預測的情況下。►這是一個司法程序的情況下，下面的事件或事故。►調查證據是在FT，這就大大簡化了併入。►其餘FT分支調查事件的可能原因。關鍵詞故障樹; 風險分析; 司法程序; 事故調查; 法醫調查; 法醫工程1。介紹讓我們從這個對比開始：“分配的責任” - VS - “學習如何提高系統的” 司法程序的範圍，以評估事故的責任：分配的責任。在另一邊，眾所周知，人類發展的重大改進來自於學習所做的錯誤。在這種情況下，我們試圖了解發生了什麼，以防止未來發生類似的情況。該範圍是不同的，雖然這兩種情況下是事故調查的例子。事實上，根據李文森（2004年），前兩個範圍是“的基本原因進行事故調查等。當目標是分配怪，通常被認為是事件的落後鏈停止，當有人或適當的東西惹的禍被發現“。換句話說，在司法過程中的主要目標不是去學習盡可能多的，但分配的責任。這意味著，不同的事故車型將通常採用，至於追求的範圍是不同的（史雲遜，1999年）。然而，不同的事故模型可以使用相同的事故調查的方法，即那些實用工具“的設計是幫助一個目的特定用戶（人）在一個特定的設置，完成特定的任務（調查和分析）。某事故調查方法不一定鏈接到特定的事故模型：它可以是它自己的一個工具。“（Katsakiori等，2009）。許多事故調查模型和事故調查方法已經發展在過去幾十年以及這些分析超出了本文的範圍。有興趣的讀者可以參考，例如，向列文森（2004），Katsakiori等人的已經引用的工作。（2009年），以及美國能源部（1999年），Kjellén（2000），約翰遜（2003年），Sklet（2004年），和列文森（2011年）。在司法程序的情況下，儘管總的範圍是明確的（即怪評估），不同的專家和當事人（法官（JE任命的專家），原告和被告，PES）經常有對比範圍; 他們不是一個團隊成員的調查事實，而是競爭對手。展望約翰遜（2003年）所提供的偏見的名單，很明顯，在“保薦偏見”，即影響力，由於破壞專家的部分聲譽的風險，實在是佔主導地位的PE。專家們明確不同的事故調查的機型，它們有不同的利益，收集數據，並對其進行分析，他們（專家及型號）“可無論是作為一個過濾器，並偏向於只考慮某些事件和條件，或者他們可能會迫使拓展活動考慮因素，常常省略“（利文森，2004）。幾位作者（最上面的引述，特別是約翰遜，2003;列文森，2004年）分析偏事故調查，不僅在法律糾紛案件的問題，大部分的偏見來自於不同的型號。出於這個原因，就其在司法程序幾乎是不可能採用通用的模式，共同的，很好的，簡單的方法的選擇可能是非常有效的減少偏差（倫德伯格等，2010）。在本文中，眾所周知故障樹（FT）方法被用於司法程序審查，作為由日本腦炎，以便收集和整合通過調查和理由提供的信息管理的收費-常不同，但不是排他性的-通過在PE提供。這種利用金融時報-以強制偏見的減少由於司法程序的不同的範圍一個共同的，良好的，簡單的方法-是相當新的，在我們看來，和原來是在實踐中非常有幫助的（案例研究提出在第4和5）。正式的計算公式為FT的司法程序導出在第3節2。在故障樹及其擴展到司法程序中使用的故障樹（FT）技術之前已結合風險分析，並適用於各種工業及非工業領域，如核能，航空和航天，以及化學工業（富塞爾，1976，味好，1981，Vesely等，1981，Vose公司，2008和齊奧，2007）。因為它是公知的，對FT可視為定性和定量分析之間的結合：它的前面有風險分析，以鑑 ​​定“所有”的頂部的事件的相位，並且它隨後得到的相位在TE的頻率。這兩種風險的分析之間，FT具有個性化，通過特徵自上而下的過程，導致在一個特定的TE發生的基本事件。從本質上說，整個過程將嘗試回答以下問題：（一）？是在工商業污水附加費對被檢查系統的興趣是什麼（二）？哪些事件同時發生的結果在TE，以及他們是如何發生的（C）什麼是每一個頂部的概率是多少？（四）什麼是TE的後果是什麼？（五）什麼是產生風險？（六）什麼是預防和保護措施，減少風險？在任何情況下，在平時的應用中，所有的這是開發中的預測方式：目標是確定具有損壞和這種潛在的損壞的風險降到最低的原因的可能性。當我們考慮以下內容的偶然事件司法程序，該方案是相當不同; 然而，使用的FT的證明是非常有效的。主要的區別是，很明顯，現在在TE被考慮已經發生。現在的問題（一）不感興趣，通常，按照司法程序，專家被任命解釋發生了什麼以及為什麼。這些專家是（至少）：- 法官（JE）的技術顧問。- 零件的技術顧問（原告與被告）（PES）。法官的問題，最經常試圖弄清為何事故發生後，即她/他主要興趣點（B），即：“發生的事件，同時該結果在TE，以及它們如何發生的？”。從此，它遵循同樣“為什麼，是什麼/誰負責？” 很多時候，在引進指出，相反的是，可以認為，專家們（至少在PE）產生相反的結論，下面的過程中，由讓-雅克·盧梭描述，說：“結婚的信念的便利”，即他們往往會表現出什麼樣的PE的願望。他們強烈偏見。顯然，這將導致一個擴充混淆，特別是當技術問題是複雜的高。現在的問題是：是否有可能跟隨（和共享）的過程，即使考慮到由於不同的PE點意見分歧，是在更嚴格的技術基礎上發展起來，減少不確定性的領域？或者：是有可能共享一個共同的方法，鑑於乙腦的和在PE的模型是不同的，並且具有相反的目標（至少盡可能的PE設備而言），以使偏差將降低，不同的觀點綜合？這是法醫工程勘察領域，它應該提供的結果，將根據證據規則可以接受的法律（中午，2001年，美國消防協會，2002年和EPRI，2003年）告上法庭。法醫工程（約翰遜，1985年）的初步介紹FT分析後，一些重要的應用程序已經完成。這些取證和調查程序的審查是由Johnson等人提供的。（2006）。然而，法醫FT分析的擴散已經相當有限到現在為止，由於缺乏具體的適應的

結果 (繁體中文) 3:

摘要本文介紹了一種在司法程式框架中進行事故評估的方法，並給出了故障樹應用於案例的形式化數學關係，並對故障樹（FT）科技的預測應用進行了分析，計算出了各故障事件（頂事件、特）頻率的最佳估計值，人的錯誤，和外部事件。

FT使用不頻繁的“預測”模式：在的情况下，TE的驗證，在司法程式的案件。

在這種情況下，一些專家法官的任命（JE）和由當事人，原告和被告（PES），通過下麵的一個類似於金融時報建設所需的自上而下的程式來重建事件。他們從事件開始，試圖找出事件的原因，使用所有的間接證據。PES往往形成不同的假設，達到對比的結論，强烈影響了部分代表，與你在一個更加平衡的位置。

它是採用一種方法，有助於專家至關重要，特別是乙腦，劃，盡可能的不確定性，面積。這一目的可能是有用的。事實上，英國《金融時報》的建設可以把從調查中獲得的證據納入基本事件的調查：基本事件，現在，有資格成為“真實”，