1、<p>　　Hierarchy probability cost analysis model incorporate MAIMS principle for EPC project cost estimation</p><p>　　4. Hierarchy integrated probability cost analysis (HIPCA) models for EPC cost estimat

2、ion.</p><p>　　In this section we introduce hierarchy probability cost analysis (HIPCA) methodology, which incorporates all aforementioned concepts for determining the total project cost (TPC) of EPC projects

3、. Our objective is to develop an optimal but realistic TPC for a given probability of success (PoS) that we assume has been specified by allocating the baseline budgets, and managing contingency, based on the desire to w

4、in the project and risk tolerance.</p><p>　　4.1. Correlation coefficient and its feasible verification</p><p>　　Once historical data is available, two different measures are used to reflect the

5、degree of relation between cost elements in literature. The first one is an ordinary product-moment (Pearson) correlation coefficient and the second is a rank (Spearman) correlation coefficient. A non-parametric (distrib

6、ution-free) rank statistic proposed by Spearman in 1904 as a measure of the strength of the associations between two variables ( Lehmann & D’Abrera, 1998). The Spearman rank correlation coefficient</p><p&

7、gt;　　While it may be difficult to justify use of a specific numeric value to represent the correlation between two cost elements, it is important to avoid the temptation to omit the correlation altogether when a precise

8、value for it cannot be established. Such an omission will set the correlation in question to the exact value of zero; whereas positive values of the correlation coefficient tend to widen the total-cost probability distri

9、bution and thus increase the gap between a specific cost percenti</p><p>　　Subjective judgment also finds application in specifying the cor-relations between cost elements qualitatively. To this respect, res

10、earchers can subjectively choose two groups of correlations to assess strong, moderate, and weak relations: {0.8,0.45,0.15} ( Touran, 1993) and {0.85,0.55,0.25} ( Chau, 1995). Other more recent scholars explain, simply,

11、‘‘as a rule of thumb, we can say</p><p>　　that correlations of less than 0.30 indicate little if any relationship between the variables.’’</p><p>　　Reasonable correlation values in the range 0.3

12、–0.6 should lead to more realistic cost estimates than the overly optimistic values assuming independence or the overly pessimistic values assuming perfect correlation ( Kujawski et al., 2004).</p><p>　　Matr

13、ix theory implies that a correlation matrix will not have any negative determinants in real life. When a correlation matrix is used in simulation, an important requirement is to ensure its feasibility, which restricts th

14、e matrix to be positive semi-definite regardless of its type (product-moment or rank) or the way it is estimated (historical or subjective) ( Lurie & Goldberg, 1998). Being positive semi-definite means the eigenvalue

15、s of the correlation matrix must be non-negative.</p><p>　　That is to say, internal consistency checking between cost elements is necessary for cost estimation. In the literature, it has frequently occurred

16、that the correlation matrix is not positive definite as indicated by Ranasinghe (2000). This is particularly an issue when the number of dimensions increases because the possibility of having an infeasible correlation m

17、atrix will grow rapidly as the dimension increases ( Kurowicka & Cooke, 2001).</p><p>　　Touran’s approach was to reduce all the correlations slightly (say 0.01) and repeat until the correlation matrix be

18、comes feasible ( Touran, 1993). This approach overlooks the possibility of increasing some correlations while reducing others. Ranasinghe (2000) developed a computer program to iteratively calculate and list the bounds

19、of each correlation to make the matrix positive semi-definite. The program then asks the estimator to change the original values and wait until the program re-checks</p><p>　　Here, we advocate that Crystal B

20、all can be adopted to conduct the eigenvalue test, on the correlation matrix to uncover this problem. The program warns the user of the inconsistent correlations as Fig. 2.</p><p>　　Adjusting the coefficien

21、ts allows the user to ensure that the correlation matrix is at least not demonstrably impossible. A simple approach to using the correlation algorithm in the program is to adjust the coefficients permanently after writin

22、g down what they were originally. In this way the analyst will find out after the simulation what Crystal Ball had to do to the coefficients to make them possible. This is a minimal test and does not ensure that the corr

23、elation coefficients are ‘‘right’’ i</p><p>　　4.2. Dilemma for PCA methodology</p><p>　　The only point value from independent constituent distributions that can be added to obtain the correspond

24、ing statistical point value from the sum of the constituent distributions is the mean value. Therefore, task-level contingencies derived from individual task distributions cannot be added to obtain the project total cont

25、ingency.</p><p>　　Traditional contingency calculations that add an arbitrary factor to task-level costs and then sum these amounts to a project total, which can produce very conservative project budgets that

26、 would be completely outside the calculated distribution of expected results.</p><p>　　We review some statistical notations in order to discover the potential problem for typical PCA. For the two random vari

27、ables x and y, we can have following notations on the basis of probability and statistical theory.</p><p>　　4.3. Hierarchy PCA model</p><p>　　During the bidding stage, the EPC project must be st

28、ructured into a limited number of cost items. This does not mean that we will forgive existing detail valuable cost data sets. The reason is that neglecting reliable and valuable cost data sets will influence the efficie

29、ncy and effect of cost information. Hierarchy probability cost analysis model can be separated into different hierarchies for lower WBS levels.</p><p>　　To focus on EPC projects, we assign two hierarchies fo

30、r hierarchy PCA. The formula (4) is selected for the first hierarchy. We choose WBS level-3 and 4 cost elements for EPC project cost estimation to construct the second hierarchy.</p><p>　　4.4. Hierarchy PCA

31、 model including MAIMS-PDFs</p><p>　　The MAIMS principle accounts for the fact that project rarely under-run original allocated budgets. This has important implications for PCA. Once a cost element is alloca

32、ted a budget x?, it be-comes a random variable with minimum value x? rather than the lower range Cmin of the original PDF. We refer to these PDFs as the MAIMS-modified PDFs. They are proper PDFs with a delta-like functio

33、n at x? that accounts for all random values less than or equal to x?. We stress the MAIMS modified PDFs with t</p><p>　　For the hierarchy PCA model including MAIMS-PDFs, we pro-pose all cost elements belongi

34、ng to the first hierarchy in Section 4.3 will adopt the MAIMS principle, that is to say the budget of baseline will substitute the minimum value of all PDFs of cost elements. The second hierarchy will be same as it is i

35、n Section 4.3.</p><p>　　4.5. Hierarchy PCA model including hierarchical MAIMS-PDFs</p><p>　　It is easy to find that a baseline budget is necessary for all cost elements located in first hierarc

36、hy, for the hierarchy PCA model including MAIMS-PDFs. As we depict in Section 4.2, to focus on a few vital cost elements and overall influence could be more benefit for cost risk analysis. We present a hierarchy PCA mod

37、el including hierarchy MAIMS-PDFs to approach this purpose.</p><p>　　All PDFs of cost elements in first hierarchy will not have changed in Section 4.3 for hierarchy PCA model including hierarchy MAIMS-PDFs.

38、 MAIMS principle is not used for all cost elements</p><p>　　5. Practical application</p><p>　　The proposed method is applied to the real EPC project to demonstrate its practical use. The Beta Pe

39、rt and Weibull distribution are selected, respectively, for WBS-item cost element based on Section 3. The PDF and relative calibration for WBS level 4 (as Section 3) have done at the beginning of bidding stage with an

40、applicable data set derived from historical cost and expert’s experience.</p><p>　　Subjective correlation coefficient method is recommended, and correlation group will be divided based on WBS level 2. The co

41、rrelation coefficient of pair-wise between cost elements within same group will be assigned as 0.6 as initial coefficients. The correlation coefficient of pair-wise between cost elements in a different group will be assi

42、gned as 0.3 as initial coefficients. The consistency and feasibility of the correlation will be judged and adjusted permanently by Crystal Ball automaticall</p><p>　　5.1. Results for four kinds of cost estim

43、ation models for a real bidding EPC project.</p><p>　　A simulation experiment is designed to implement the pro-posed method and to evaluate the effects of the hierarchy integrated probability cost analysis m

44、odel. In the experiment, five kinds of cost analysis models are adopted for assessment. The out-put statistics can then be used to assess the behavior of the true project cost and the effectiveness of the hierarchy integ

45、rated PCA model.</p><p>　　5.1.1. Typical PCA model</p><p>　　All the cost elements and their margin/percentile distributions are shown in Table 1 for typical PCA. The value of each WBS level 3 c

46、ost elements is expressed as kilo euro. This level of granularity is suitable for typical PCA model. Moreover, the WBS level 3 can be changed to reflect the actual situation based on the size of the</p><p>　

47、　project and accuracy of the estimation, if the proposed method is applied to other construction projects.</p><p>　　After 5000 simulation trials, the 6th column in Table 2 lists the descriptive statistics f

48、or the total cost of the project. To assess the impact of correlations, we compare two scenarios: including and excluding correlations. 5th column in Table 2 is the result of total project cost including correlations. T

49、he first observation is that both distributions are skewed to the right because the mean is larger than the median. The second observation is that the scenario of ‘‘including correlations’’</p><p>　　To selec

50、t typical down WBS level, the sensitivity analysis is executed and shown in Fig. 4. It is apparent that the unit 13 is more sensitive for the total cost of the project than other units. Unit 13 is selected as the 2nd hi

51、erarchy for the HPCA cost model.</p><p>　　5.1.2. Hierarchy PCA model excluding MAIMS principle</p><p>　　All the cost elements and their margin/percentile distributions for the unit 13 are shown

52、in Table 3.</p><p>　　The second hierarchy probability distribution will be generated after 5000 simulation trials, and listed in Table 4 for details. The new distributions will substitute the corresponding

53、 distribution in Table 1. The descriptive statistics for the total cost of the project based on the hierarchy PCA model excluding MAIMS principle, are indicated in the 4th column in Table 2 after 5000 simulation trials

54、. The standard deviation of the hierarchy model is not smaller than typical PCA, that is to say</p><p>　　5.1.3. Hierarchy PCA model including MAIMS-PDFs</p><p>　　The descriptive statistics to es

55、timate the total cost of the project are based on the hierarchy PCA model integrating MAIMS PDF is shown in the 3rd column in Table 2 after 5000 simulation trials.</p><p>　　5.1.4. Hierarchy PCA model includ

56、ing hierarchy MAIMS-PDFs</p><p>　　The descriptive statistics for the total cost of the project are based on the hierarchy PCA model integrating MAIMS hierarchy is shown in the 2nd column in Table 2 after 50

57、00 simulation trials.</p><p>　　5.2. Comparison and validation</p><p>　　In this section, we validate whether the proposed methods can solve the dilemma to appropriate cost elements and maximize t

58、he efficiency of cost information for EPC project. Probability of success (PoS) and confidence internal will be adopted to verify the quality of the estimation.</p><p>　　The Monte Carlo simulation result of

59、hierarchy PCA model integrating MAIMS-PDFs is expressed in Fig. 5. The 10% and 90% points of the total cost of the project are based on hierarchy PCA model integrating MAIMS-PDFs that establish a 80% confidence interval

60、, and the PoS is generally expressed in percentages of +20.01%/ 14.15%.</p><p>　　The Monte Carlo simulation result of hierarchy PCA model integrating MAIMS hierarchy can be expressed as Fig. 6. The 10% and 9

61、0% points of the total cost of the project are based on hierarchy PCA model integrating MAIMS hierarchy that established a 80% confidence interval, and the PoS is generally expressed in percent-ages of +20.86%/ 14.61%.&l

62、t;/p><p>　　The PoS of all models for confidence interval (10%, 90%) is summarized in Table 5. That is to say HIPCA-hierarchy MAIMS-PDFs and HPCA-MAIMS-PDFs can get more realistic cost estimation than typical P

63、CA. The hierarchy PCA model integrated Hierarchy MAIMS-PDFs can achieve more accurate estimation than hierarchy PCA model integrated MAIMS hierarchy.</p><p>　　The project baseline cost (PBC) can be concluded

64、 as 836 million euro from Table 1. The contingency has been summarized in Table 5 based on recommended Practice No. 18R-97 by AACE.</p><p>　　All results depict that the HIPCA-hierarchy MAIMS-PDFs and HPCA-M

65、AIMS-PDFs have more realistic and executable estimates. And the proposed methods can solve the dilemma to appropriate</p><p>　　cost elements and maximize the efficiency of cost information for EPC project.&l

66、t;/p><p>　　Finally, cost estimate based on HIPCA-hierarchy MAIMS-PDFs method help us win the bid. The actual reason is such cost estimate is realistic lower, and accompanies with higher PoS. Meanwhile, it provi

67、des not only maintain current knowledge of cost overruns, but also estimates cost at completion from inside the project itself rather than by statistical inference from historical information on other projects.</p>

68、<p>　　6. Conclusion</p><p>　　The practical and theoretically valid hierarchy PCA-hierarchy MAIMS models among WBS-item cost elements have been developed to solve skillfully the dilemma of typical PCA.

69、 The key elements include:</p><p>　　The use of an appropriate WBS for cost hierarchical structure. Subdividing the project costs into too many bite-size pieces is likely lead to erroneous results and a false

70、 sense of confidence. Analysts should be wary of the pitfalls of performing a probabilistic cost analysis that consists of hundreds of cost elements that are subordinate to WBS-level 3. </p><p>　　Macroscopic

71、 and microscope risk analysis of project cost elements in order to obtain accurate model input and maximize efficiency of information. Monte Carlo simulation method is recommended for historical data of WBS level 4 (disc

72、ipline level) in order to obtain percentile of preliminary PDF. Real estimate of Cmin; Cm; Cmax and reasonable budget will be approached via discipline experts’ calibration. </p><p>　　Incorporation of the ‘‘

73、money allocated is money spent’’ (MAIMS principle) with budget management practices and hierarchy. The assessment of the cost elements, correlation effects, bud-get allocation, and project management consideration items

74、all influence each other and have a significant impact on the total project cost and/or probability of success. For enhanced credibility and realism, HIPCA-hierarchy MAIMS considers these influences simultaneously rather

75、 than individually. </p><p>　　The proposed approach provides a cost estimation and analysis framework for EPC project. It avoids the impact of high number of cost elements and maximizes efficiency of histori

76、cal data and experts’ judgment. And it not only makes demands upon the cost estimator, but also provides benefits to project management, particularly when it comes to recommending a prudent management reserve. Having in

77、hand a probability distribution of total WBS-item cost, rather than just a single best estimate, projec</p><p>　　Our experience is that the single greatest challenge to the development and use of hierarchy p

78、robabilistic cost analysis is the implementation of systems thinking. Further development of a tracking system that identifies the assumptions for the high, medium, and low (or percentiles) three points estimate and trac

79、ks their evolution are necessary, so as to develop and implement more re-fined cost models substantially.</p><p>　　This research was funded by the Sinopec Science and Technology Developing Project (Project N

80、o. 205073) and the Beijing Municipal Education Commission of China (Project No. XK100100542). Many thanks are also due to the anonymous reviewers of this paper for useful comments.</p><p>　　層次概率成本分析模型納入MAIMS

81、原則 EPC工程總承包項目的成本估算</p><p><b>　　Alpha</b></p><p>　　4綜合成本的層次概率分析（HIPCA）EPC工程總造價估算模型</p><p>　　在本節(jié)中，我們引入層次概率（HIPCA）成本分析的方法，其中包括確定項目總成本的EPC項目（TPC）。我們的目

82、標是發(fā)展到最好，但現實的TPC（POS），我們假設已指定基線預算分配和應急管理，是基于對成功項目的渴望和風險承受能力的。</p><p>　　4.1相關系數和可行性的核查</p><p>　　一旦歷史數據是可用的，會有兩個不同的措施，是用來反映文獻中的成本要素之間的關系程度。第一個是一個普通的產品瞬間（皮爾森）的相關系數，第二個是一個等級（斯皮爾曼）相關系數。非參數（分布）采用Spearm

83、an秩統(tǒng)計量在1904年提出的，作為衡量兩個變量（萊曼，1998年）之間的關聯強度。 Spearman等級相關系數可以用來給一個真正的估計，是一個單調的關聯，使用時，數據的分布會使Pearson相關系數的措施具有不良或具誤導性。</p><p>　　雖然它可能是難以自圓其說的一個具體的數值來表示兩個成本要素之間的相關性，重要的是要避免誘導，完全不能成立時省略相關的它的精確值。這樣的遺漏將會設置相關問題的精確值為零

84、，而相關系數正面的價值觀傾向于擴大總成本的概率分布，從而增加了一個特定的成本，估計成本。也就是說，應急可能更大。因此采用合理的非零值，如0.2或0.3，通常會導致更逼真再現了總成本的不確定性。</p><p>　　主觀判斷還發(fā)現應用程序在指定的成本要素之間的定性對應關系。在這方面，研究人員可以主觀選擇兩組相關性強的評估，中度，偏弱：{0.8,0.45,0.15}（途安，1993年）和{0.85,0.55,0.25

85、}（1995）。其他最近的學者解釋說，簡單地說，作為一個經驗法則，相關性表明一點，如果任何變量之間的關系存在，我們可以說小于0.30。</p><p>　　合理相關值在0.3-0.6的范圍應該比現實的成本估計過于樂觀值或過于悲觀值，假設完全相關（Kujawski等，2004）。</p><p>　　矩陣理論意味著，相關矩陣在現實生活中不會有任何負面因素。當在模擬中使用的相關矩陣，以確保其可

86、行性，一個重要的要求是，制約矩陣是積極的，無論其類型（產品時刻或排名）或估計的方法（歷史或主觀） （勞瑞戈德堡，1998年）。半正定的相關矩陣的特征值必須是非負。</p><p>　　也就是說，成本要素之間的內部一致性檢查是必要的成本估算。在文獻中，經常有相關矩陣不是正定拉納辛哈（2000）的情況。這是一個問題，當維數增加的原因是不可行的相關矩陣的可能會迅速成長為維度的增加（Kurowicka與庫克，2001年）

87、。</p><p>　　途安的做法是減少所有的相關性（0.01）和重復直到成為可行的相關矩陣（途安，1993年）。這種方法隨著其增加，同時減少了其他一些相關的可能性。拉納辛哈（2000）開發(fā)出一種計算機程序，反復計算，并列出每個相關的邊界，使矩陣半正定。然后程序要求改變原有的價值觀，直到程序重新檢查的可行性和新的邊界估計。這個過程繼續(xù)進行，直到達到可行性。然而，這種方法可能會比較浪費時間，由于其迭代性質。楊（20

88、05）開發(fā)了一種自動程序來檢查相關矩陣的可行性，并在必要時調整。這是比較復雜和困難的，由于相關矩陣分解成一個對角線特征值向量，對角線元素正?；?，以確保單位對角線。</p><p>　　在這里，我們主張，可以通過對相關矩陣進行特征值測試，來發(fā)現這個問題。并警告特征值不一致的相關的用戶。</p><p>　　用戶允許的調整系數，要確保相關矩陣是至少不能證明是不可能的。在程序中使用相關算法的一種

89、簡單的方法是永久調整后寫下他們原先的系數。使他們有可能在模擬后會發(fā)現不得不做的系數。這是一個很小的測試，并不能保證相關系數分別為“在任何意義上”。在審查程序時，風險分析師還必須承擔使用系數的責任。</p><p>　　4.2主成分分析方法的兩難</p><p>　　只有從獨立的成分上可以添加組成分布的總和，從獲得相應的統(tǒng)計點值分布點值的平均值。因此，從個別任務分派的任務級別的突發(fā)事件不能得

90、到補充，以獲得該項目的總應變。</p><p>　　傳統(tǒng)的應急添加任意一個任務級成本的因素，然后總結這些，它可以產生非常保守的項目預算將完全超出預期的結果計算分布項目總金額的計算。</p><p>　　我們回顧一些統(tǒng)計學符號，以便及時發(fā)現潛在的問題，為典型的PCA的。對于兩個隨機變量x和y，在概率和統(tǒng)計理論的基礎上我們可以有以下符號。</p><p>　　4.3層次

91、主成分分析模型</p><p>　　EPC工程總承包項目在招投標階段，必須構建成一個成本項目的數量有限。這并不意味著我們會原諒現有的寶貴的詳細成本數據集。其原因就是忽視了可靠和有價值的成本數據集，將影響成本信息的效率和效果。層次概率成本分析模型可以分為不同的層次較低的WBS層級。</p><p>　　專注于EPC項目，我們分配層次主成分分析的兩個層次。公式（4）被選定為第一層次。我們選擇W

92、BS-3級和4 EPC項目成本估算的成本要素，建立第二個層次。</p><p>　　4.4層次PCA模型包括MAIMS-PDF格式</p><p>　　事實上，項目很少下運行原劃撥的預算MAIMS原則帳戶。這PCA具有重要意義。一旦成本要素分配預算x，它的一個最低值隨機變量X 而不是原始的PDF較低的范圍內的Cmin。我們指的這些PDF作為MAIMSmodified的PDF。他們像所有的隨

93、機值小于或等于x的函數在x帳戶適當的PDF文件。我們強調截斷值MAIMS修改的PDF。應用MAIMS原則為PDF增加其平均值，并降低其標準差。隨著x的增加值的影響，MAIMS原則是在PCA可能發(fā)揮重要的角色。在第5節(jié)我們進一步探討實際投標EPC工程總承包項目。</p><p>　　對于層次結構的PCA模型包括MAIMS的PDF文件，我們屬于4.3節(jié)中的第一個層次構成的所有成本要素將采取MAIMS的原則，也就是說基

94、準預算將取代所有PDF成本要素的最低值。第二個層次將是相同的，因為它是在第4.3節(jié)。</p><p>　　4.5層次PCA模型包括層次MAIMS的PDF</p><p>　　很容易發(fā)現，基線預算是必要的層次PCA模型包括MAIMS的PDF文件，位于第一層次的所有成本要素。描繪，正如我們在4.2節(jié)，集中在幾個重要的成本要素和整體影響可能是更多的成本風險分析的好處。我們提出包括層次MAIMS的

95、PDF文件來處理這個目的的層次，PCA模型。</p><p>　　第一層次中的成本要素的PDF不會改變在4.3節(jié)的層次PCA模型包括層次MAIMS的PDF文件。 MAIMS原則不能用于所有成本要素。</p><p><b>　　5實際應用</b></p><p>　　所提出的方法應用到真正的EPC工程總承包項目，以證明其實際使用。的Beta P

96、ERT和Weibull分布選擇，分別為WBS的項目成本基于第3節(jié)的元素。為PDF和相對標定的WBS 4級（第3節(jié)），在招投標階段開始適用從歷史成本和專家的經驗得出的數據。</p><p>　　主觀的相關系數法，建議和相關組將分為基于WBS的2級。將被分配在同一組內的成本要素之間的成對的相關系數作為初始系數0.6。成對成本要素在不同的組之間的相關系數將被分配作為初始系數0.3。這里指出將判斷的一致性和相關的可行性和

97、永久自動調整在第4節(jié)。</p><p>　　5.1 4種成本估算模型的結果為一個真正的投標EPC工程總承包項目</p><p>　　仿真實驗的設計，實施親提出的方法和評價層次結構的綜合概率成本分析模型的影響。在實驗中，采用5種成本分析模型進行評估。然后，可以使用輸出統(tǒng)計評估行為真正的項目成本和層次結構的綜合PCA模型的有效性。</p><p>　　5.1.1典型的P

98、CA模型</p><p>　　所有成本要素和其保證金/百分位分布如表1所示為典型的主成分分析。每個WBS 3級成本要素的價值，表示為每公斤歐元。這種粒度級別是適合于典型的PCA模型。此外，如果該方法被應用到其他建設項目，WBS的第3級是可以改變的，以反映實際情況的基礎上，大小估計的準確性和項目。</p><p>　　5000個模擬試驗后，第6列在表2列出了描述性統(tǒng)計，該項目的總成本。評估的