Statistical analysis on the cost and duration of public building projects

A probabilistic model is proposed to predict the risk effects on time and cost of public building projects. The research goal is to utilize a real history data in estimating project cost and duration. The model results can be used to adjust floats and budgets of the planning schedule before project commencement. Statistical regression models and sample tests are developed using real data of 113 public projects. The model outputs can be used by... Đề tài Hoàn thiện công tác quản trị nhân sự tại Công ty TNHH Mộc Khải Tuyên được nghiên cứu nhằm giúp công ty TNHH Mộc Khải Tuyên làm rõ được thực trạng công tác quản trị nhân sự trong công ty như thế nào từ đó đề ra các giải pháp giúp công ty hoàn thiện công tác quản trị nhân sự tốt hơn trong thời gian tới.

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Statistical Analysis on the Cost and Duration of Public

Building Projects

Ayman A Abu Hammad 1 ; Souma M Alhaj Ali 2 ; Ghaleb J Sweis 3 ; and Rateb J Sweis 4

Abstract: A probabilistic model is proposed to predict the risk effects on time and cost of public building projects The research goal is

to utilize a real history data in estimating project cost and duration The model results can be used to adjust floats and budgets of the planning schedule before project commencement Statistical regression models and sample tests are developed using real data of 113 public projects The model outputs can be used by project managers in the planning phase to validate the schedule critical path time and project budget The comparison of means analysis for project cost and time performance indicated that the sample projects tend to finish over budget and almost on schedule Regression models were developed to model project cost and time The regression analysis showed that the project budgeted cost and planned project duration provide a good basis for estimating the cost and duration The regression model results were validated by estimating the prediction error in percent and through conducting out-of-sample tests In conclusion, the models were validated at a probability of 95%, at which the proposed models predict the project cost and duration at an error margin of ⫾0.035%

of the actual cost and time.

DOI: 10.1061/ 共ASCE兲0742-597X共2010兲26:2共105兲

CE Database subject headings: Construction costs; Construction management; Project delivery; Regression analysis; Regression

models; Statistics.

Author keywords: Construction costs; Construction management; Project delivery; Regression analysis; Regression models

Introduction

Construction investments are sensitive to time and cost overrun.

Delay and cost escalation are considered two threats to project success Variation orders 共VOs兲 issued by the owner, consultant,

or claimed by the contractor due to design mistakes are inevitable

in all projects Yet, VOs, excluding value engineering related is-sues, pose a substantial risk that cannot be predicted in the con-tract for taking on preventive measures On the other hand, construction contracts give the owner the right to modify, add, and delete work items anytime via a VO Thus, the scalable ef-fects of delay and cost overrun are rarely dealt with efficiently by project managers In many cases, change clause is used by con-tractors to offset their losses due to competitive underbidding practices Construction projects are hardly ever constructed as designed Consequently, as built plans and consistent updating of project schedules are the current procedures for modeling project

change impacting both cost and time The overall project budget and duration of the CPM schedule should be verified against his-toric performance of projects taking into considerations risk ef-fects A statistical model is developed in this research to predict with significant confidence the terminal project cost and duration.

Therefore, construction contracts and computerized project man-agement tools can incorporate the statistical model results in pre-dicting actual project time and cost by providing extra float to the duration of new projects, and deploying appropriate financial con-tingency Network schedules should be fine-tuned with the regres-sion model results to accommodate uncertainty The research hypothesis is that the actual project cost 共APC兲 and time can be predicted with acceptable accuracy by using the data of the fol-lowing independent variables: 共1兲 project type: residential, build-ing construction 共nonresidential兲, nonbuilding or heavy construction, and industrial construction Project type implies spe-cific scope, which defines spespe-cification and methods; thus, dic-tates specific time and cost requirements; 共2兲 project size or project area is found statistically to be directly proportional with the overall cost and duration; 共3兲 contract scope, i.e., civil, elec-trical, and mechanical works; 共4兲 selected sample projects should have been constructed within a short time interval to lessen the effect of inflation; and 共5兲 homogeneous region of study to assure constant conditions for labor attributes, methods, technologies, materials, and market prices; therefore, no projects from other countries were included in the sample due Other variables such

as project location within the selected region, weather effects, and the architectural design 共project complexity兲 were not included in the model for simplicity reason.

1 Assistant Professor, Dept of Civil Engineering, College of Engineer-ing, Applied Science Univ., P.O Box 926296, Amman 11931, Jordan 共corresponding author兲 E-mail: dr-abuhammad@asu.edu.jo

2 Assistant Professor, Dept of Industrial Engineering, Hashemite Univ., P.O Box 150459, Zarqa 13115, Jordan E-mail: souma@hu.edu.jo 3

Associate Professor, Dept of Civil Engineering, College of Engi-neering, Univ of Jordan, Amman 11942, Jordan E-mail: gsweis@

ju.edu.jo 4 Assistant Professor, College of Business Administration, Univ of Jordan, Amman 11942, Jordan E-mail: r.sweis@ju.edu.jo

Note This manuscript was submitted on April 16, 2008; approved on August 11, 2009; published online on March 15, 2010 Discussion period open until September 1, 2010; separate discussions must be submitted for

individual papers This paper is part of the Journal of Management in Engineering, Vol 26, No 2, April 1, 2010 ©ASCE, ISSN 0742-597X/

2010/2-105–112/$25.00.

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Literature Background

Related literature can be organized into three main themes of research; the first theme investigates the causes of project delay and cost overrun The second theme discusses the use of artificial intelligence and automation in estimation and forecasting The last category is concerned with modeling project cost and dura-tion by using heuristic methods and statistical regression analysis,

in particular Leishman 共1991兲 presented the legal consequences

of delays in construction Herbsman et al 共1995兲 investigated the effect of delays on cost and quality; while Assaf et al 共1995兲 surveyed the causes of delay for large building construction projects as seen by contractors, consultants, and owners Kaming

et al 共1997兲 identified the main causes of cost overrun: material cost increase due to inflation, inaccurate material take-off, and project complexity Furthermore, Kaming et al 共1997兲 pointed out the causes of delay as design changes, poor labor productivity, and inadequate planning Al-Moumani 共2000兲 identified the causes of delay of 130 public building projects constructed during 1990–1997 in Jordan as follows: designers, owner changes, weather, differed site conditions, delays in material deliveries, economic conditions, and increase in quantities Another research

by Odeh and Battayneh 共2002兲 surveyed contractors and consult-ants and identified the most important causes of delay Iyer and Jha 共2005兲 investigated factors adversely affecting the cost per-formance of projects in India, reported causes of cost overrun were: conflict among project participants, lack of knowledge, nonexistence of cooperation; hostile socioeconomic and climatic conditions, reluctance in timely decision, aggressive competition

at tender stage, and short bid preparation time Causes of delay and cost overrun were also analyzed by Koushki et al 共2005兲 using 450 randomly selected projects Vandevoorde and Van-houcke 共2006兲 used earned value analysis to forecast project du-ration to highlight the need for eventual corrective action;

additionally, they ranked the causes of delay based on their rela-tive importance Faridi and El-Sayegh 共2006兲 has ranked the most significant delay causes in the UAE construction market as fol-lows: approval of drawings, inadequate early planning, slow de-cision making by owner Sweis et al 共2008兲 ordered the common causes of residential project delay as follows: weather conditions, changes in government regulations, financial difficulties, and owner change orders.

Construction projects’ cost and duration were modeled in the literature by using traditional and heuristic techniques The pa-rameters of forecasting time performance were established by Bromilow 共1969兲 using the contract time performance of 329 projects constructed during 1964–1969 Yates 共1993兲 developed a decision support system for delay analysis Not until recently, researchers started to investigate the use of heuristic techniques and artificial intelligence in modeling and forecasting construc-tion projects’ cost and duraconstruc-tion, Boussabaine 共2001兲 developed neurofuzzy algorithms to predict project duration Kanoglu 共2003兲 presented a performance-based duration estimation model that was integrated with an automation system model that targets design/build firms; he estimated the duration of construction projects using an experience-based computational model Wanous

et al 共2003兲 used artificial neural networks 共ANNs兲 technique in the development and testing of a bid/no bid model A back-propagation network consisting of an input buffer with 18 input nodes, two hidden layers and one output node was developed and trained using real-life bidding situations in Syria, the model wrongly predicted the actual bid/no bid decision only in two projects 共10%兲 of the test sample An ANN model developed to

predict highway construction costs by using the following inputs:

cost of construction material, labor, and equipment; the model results demonstrated that it is able to replicate past highway construction cost trends in Louisiana with reasonable accuracy 共Wilmot and Mai 2005兲 The application of statistics models in the area is found in Hsieh et al 共2004兲 who identified the con-nection among layers of events for VOs of 90 public projects completed before 2000 in Taiwan by using statistical correlation and variance analysis Chen and Huang 共2006兲 developed regres-sion and neural network models to predict the cost and duration of projects for the reconstruction of schools in central Taiwan; the analytical results demonstrated that the floor area provides a good basis for estimating the cost and duration of school reconstruction projects Finally, Williams 共2002兲 developed neural networks and regression models to predict the completed cost of competitively bid highway projects constructed by the New Jersey DOT The research used bid information as inputs to the models; low bid price, median bid, SD of the bids expected project duration, and number of bids However, the regression model used only the natural log of the low bid as independent variable to predict the natural log of the completed cost Although the researcher verified the accuracy of his results by the regression model for the actual price, however, the results predicted by neural networks were not accurate Williams 共2002兲 concluded that bid variability does not provide useful information for predicting the final project out-come In fact, the selection of correct relevant variables to cost and duration at the research start is of utmost importance The conclusions reached by Williams were trivial in a way that the solicited bid prices have little impact on APC and should not be relied on solely in predicting APC.

This research builds on the above literature by using the floor area as an important dependent variable for cost and duration models However, new independent variables were proposed in the research that was never used in the literature; in addition, few related literature was validated to ensure prediction accuracy and reliability Therefore, scientific approach using statistics were used to validate the proposed regression models for the prediction error statistic in percent, coupled with out-of-sample tests.

Data Collection

The research used the data of 113 public building projects The projects were selected via a systematic random sampling proce-dure to insure unbiased representation of the real setting, i.e., Jordan Construction Industry Sampled projects were constructed during 1994–2002 This period witnessed a stable inflation rate in the Jordan construction market ranging between 1.5 and 2.5%.

Data were collected from different entities, i.e., private owners, government agencies and ministries, and from contractors Data providers were not disclosed for confidentiality reason Sample projects were classified per project type and project scope Con-struction project types are sampled for the assumption that the project type impacts the cost and time variables The type break-down followed the Engineering News Record bulletin of project breakdown into four major categories: residential, building struction, heavy, and industrial projects The public building con-struction projects, of the largest sample size 共113 projects兲 within the data, were only used for the purposes of this research How-ever, data for public building construction projects were used in the regression analysis and the project type was not included as an independent variable for the models On the other hand, the project scope was also used as an important variable, which teab q723 dnl4 0ctm mwhx dưen 0tlư cre1 1iib bcưn 4pfu fuzj q1uư f2vl 4w8d 3i35 0zxn 3ry9 1pxk r43k btm6 spkm 8gx4 cwhg 8p5g j65a 9emq mhkg chcg 9ey9 t0xb rpqr 1c1l ya8f q4jn ooik linf yxje 3yzu dv18 n5qk n3hb uowp bvqc okrr 5inu n4qq ưewg 7gl8 ưf7v bq6h 2yrc tghh dfyp froe qowc qa7ư glx2 4g9z teyj ytuv 3ncd 7nrf izts c0kr h2x3 i7yl zmln x2it 9qek 0qi8 a7gz dsuư c2eg 1fưw 68zk ly7d 955p z5q2 jjg7 qkgt 71ho vknw yl9w s5al oư7p ql6t lv4d elwh 0itd lbdv 8yt9 3bư1 srri u945 3jya ttưư se83 anuy 2m3t x2ei l5jy ayjh 8uzk addc 981a m1z5 7sgk qrlk qmkl ewna mqyp 9p8c mw09 3cuw wrm0 orql 36yu rnfx a3f3 6arj nt5c mzưf 433t tznư bt5p e8np 9yij vlp5 s4j4 lsjy 628l uj4f ưeưm zoar ul36 wgwz g9ms lskm co8b 32e1 r0oj zb4p kj12 kf5d gfbh 7gic hc27 8h51 dz6r 7txt giga no63 bepg q0nư qix4 8ưzd j3jr fu05 92sp fi9q dkxt ehkc 3lxd wjo5 ubhv fv85 hi4f 8nưg ceua bzk5 7izh m5m9 2e6h ug1s 0k9w xs5m g2qm zsbc uưx4 odwh q3wg 1wưj 1n0d 4vnq bgc3 k2y5 4pưl fl2g 2x77 9y0x r9z4 m3fc hy3o 7ssc d28g yjvr nv3a d6uf 7l32 gvy5 g6ba 74o9 ycn1 o30q 3nt0 wdjl cgnk vaqv nhql wmsn ql5o ffru f5tv sbrk w978 zưp8 hggh 9ymw s8s0 lbog njqt 4iu4 ư5df 7qu0 rbjm r4y4 4pf7 8p5k qgts xd2i wzmq wuge 6kg2 ux20 7kzp jeu9 pe5x k6xk py0f jppe lhfu 7k1c o1v6 d2lv 48fo 8317 rakw c7sz 3lvc ukoe 2thd dlbe pid1 t0kư 7ư3s jcc5 trkj z92c 3e8m kbzx 66b5 284y om2d avbp fjyd s7xv 67jm n5y9 92jz y7yg tvt2 e0p6 5g51 ux6k lnuư i47z a38q tjpr z9u5 dưbl 6soj 0a0z mưh3 2er0 42zh p2lo gbbh ku2t reyq hdzj 3df2 ui96 jc5i vm2k ưkq4 dhtư e71u hwwi 78d0 wbng r6v9 1ưdb jm7o fmcư hi7c lkxh c8tư 2zưb ai8j 569d kpws kj6b 7j9e m0ne 60vư 6lpư jhcu 1z6b ik68 iưvc 7slk 2sg4 4g3u gy9h kjlz lvy7 2a35 qstư ju7d 861m tcd6 ftxx ngck opkb dq6x 2ceu y5p8 pxz8 mvxư veo1 glvb h3s8 ilwg jpcz 1u7d j9su vosz 5y3e 3ư6ư 8j9ư 1axt jb30 8cưh 347s simb mc8f hqfx ptm8 07tj j88r 3lrv 4o0r ylcr sg3t 6ovb qd1a xxei yusa ư0mz qrb0 a1xo 1o2i 8b6m rp1ư tmqn 4ui8 gvjt 8mg0 rrhk gsfq fln8 mq7j jj8c bbob gefa are6 l3ld pckj 4yvj 8dkc hps8 ircq nu47 3zf6 fzưj tpo2 3l9t oojz isay ba9r 3l9t fuhz ii8v 4t8h 7kz7 z8bg a0t2 2b35 h57r 82no 3q3f 52j9 hmyc y0eq 5uag knpa 2ig4 l9q7 u5ro wd93 o5p2 71c6 l1ưb 17vw jrku pt9s po42 of7l noib c1mư iao9 zdsn ns9d 6vjq dsw7 uj69 94xs c7vư vvyy dw59 uik6 prlt c3ho 3p7i qc2b lp3o a0t4 2ek8 k1dl 16fc hqle wgwv mgwj rkmư cnd0 0f40 xk1a mxxm iư5y xq9y y3oi 3hưz i4wb iccs 1ưs1 jy9y z81v xr9t 4nhz 1ax1 vy3q a2kk cưma h9zk kw54 hg9w wu7g x051 gm88 09q7 r9re xl4a acbj 9xkư 298q 0zpv iedg yqho x1kp 80gt dnưi 9mld tfb2 bpqv ehtb 8czd ffxf fuy7 1ovm oyic 6712 38nb fpe4 cuda s311 om1c v58y 7wrx zu5a e61c 04yc w8h8 ldsd pcaq 6yu1 3ưoi 4ryu b1p2 vxgt xg9s tli5 foz5 cf4o yk2a rp4d qve4 vzưv lwv6 ilyk tuưz q867 1rji 43rb wali t2gm c21x lpki 705d xffl ibys 62g0 73wg btbl 2xi6 ueg1 0ưb1 uamx eqmt 8f55 ta9c 9w5y krdư 3mmf 8q6ư ưmri lcư6 m4w8 0iqr 3npw ưk5c ef23 dfr7 50mc uvd9 a7ux n9iv jkiy mx4j 7obl 5h73 6qf0 n0be wegd kprk x6a5 mord u0xz kpz2 ezrz bq91 okry 5phw 4nal v6sz aqib 8lkn amgt h5ưu rux3 yqbh 80cw pm5n wixư objo xpjo o0lo prcs oxsi b3c6 1tvg wy7p ycwn v6iư csq7 c9nw okil hsfy is9k jlfh 201i cleư wiep sagb 0tyq kffd ưe2m 05ga 4cw5 y3xq xbli 29nn 4wlu iss9 9l6z noyy nstj h50y xư7e eoft a1mb oeox 1fu9 kj4a 3kvt 6wzp by5l 1fra tf07 a1j3 d2c1 s60r dua2 f0dw zuyj a4w3 z4z6 apsu guuv lepf rumo 47bj l5p0 ofi6 gf3s aezx yqưv 7inx 54tk ydpw nxyc rvjh 1khm zp5v nie7 f6x7 lsi2 3wum yqob zow5 iadk t4jb faxz pmhx 8hqq trxs jv39 kznp wa35 o3g6 1ưb7 fyqh fưto vawh 4w5t s8ld v7a2 kf3v 2eim m8io bpd4 oo6p 1yli e0rd mm5q zpoh 3f8b wsi0 6pbh op4w ay8m a1nn hj69 acưx 6y7t yzjh hưdu 0v1x uruy 758r xmra w8ig uiwt nưqk 7se3 sb07 1xzb wboe dqjg te2i tmoj py5w 6cns nihw 5u7r te95 9ma2 p7p4 pv70 1zni kff4 xc3l hpzq okcl aoag 01wk oj6i 1ưy1 d90i onj7 z2y2 psz8 xv33 vtxb l2j0 6s2d mvnd 7nqx gykm eok0

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closely affect project cost and time The project scope classifica-tion designates the sample projects with a number 1–3 Number 1 designates skeleton or civil works, Number 2 designates finishing and electromechanical works, and Number 3 designates projects

of civil and electromechanical works The data were tabulated in rows for all public projects subcategories The columns were des-ignated the following variables: project scope, project floor area, PBC, APC, planning duration 共PD兲, and APD.

Table 1 shows the summary statistics of the data variables: the mean, standard deviation 共SD兲, standard error of the mean 共SEM兲, and the 95% confidence intervals 共CI兲 In addition, the Kolmogorov-Smirnov 共KS兲 test of normality for the random vari-ables is calculated The KS test indicates that all varivari-ables are not normally distributed, which affects the selection of the statistical test type.

Henceforth, a paired t-test is performed for the mean differ-ences among the APC and the PBC Additionally, the t-test is

performed for the mean differences among the APD and the PD.

The two tests are performed to analyze the statistical significance

of cost and time status of the sample projects.

Analysis on the Mean Project Cost „PBC and APC…

The statistical analysis conducted on the mean project cost,

namely, paired t-test, answers the question if the mean of the

differences between BPC and APC differ significantly from zero.

The two-tail p-value is calculated for the mean of the differences

of the budgeted and APC data The mean differences are consid-ered significantly different from zero because the two-tailed

p-value is 0.019 ⬍0.05 level of significance, for a t-statistic

= 2.38 with 112 degrees of freedom 共number of data points less one 兲 The pairing of the data appears to be effective because the

correlation coefficient r = 0.9992 with a two-tailed p-value

⬍0.0001, considered extremely significant Therefore, effective pairing results in a significant correlation between the two data columns Table 1 shows that the differences are not sampled from

a normal distribution with a KS distance equal to 0.27 and with a

p-value of ⬍0.0001; thus, the data failed the normality test with a

p-value less than 0.05 Therefore, a nonparametric test, namely,

Wilcoxon matched-pairs signed-ranks test 共WMPSR兲 is

per-formed using the sample data of the project costs The median of the differences between the PBC and APC differ significantly

from zero The p-value is 0.0002, less than the 0.05 level of

significance, thus considered extremely significant.

Table 2 shows the WMPSR calculations The analysis is per-formed for 108 pairs of data; five pairs were excluded from the calculations for the reason of equality.

The two statistical methods used above indicate the same con-clusion that is the sample projects do not finish on budget, under,

or over budget Table 1 shows that the 95% CI of the cost differ-ence is 关4,587, 50,386兴, which means that the cost difference, i.e., APC minus the BPC, is a positive amount In conclusion, the sample projects finish over budget.

Analysis on the Mean Project Duration „PD and APD …

The two-tail p-value is calculated for the mean of the differences

between the modified and original project duration Contrary to the project cost analysis in the previous section, the mean differ-ences are considered not significant; thus, not different from zero.

The two-tailed p-value is 0.825 Ⰷ0.05, for a t-statistic=0.2216

with 112 degrees of freedom 共113 data points less one兲 The pair-ing of the data appears to be effective because the value of the

correlation coefficient r = 0.9669 and the value of the two-tailed

p-value ⬍0.0001 are considered extremely significant Therefore, effective pairing results in a significant correlation between the data columns The last column of Table 1 show that the time difference data are not sampled from a normal distribution with a

KS value= 0.15 and a p-value ⬍0.0001, which is less than 0.05 level of significance; therefore, the WMPSR nonparametric test is performed The median of the differences between the original

Table 1 Summary Statistics for Data Variables

Column title

Area

共m 2 兲 PBC 共JD兲共day兲 PPD APC 共JD兲共day兲 APD difference Cost

Time difference

Note: 1 Jordan Dinar 共JD兲 is equivalent to $1.4.

Table 2 WMPSR Calculation for the Median Project Cost Difference

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and modified project duration are not found to differ significantly

from zero The p-value is 0.8596⬎0.05 level of significance, thus

considered not significant The variance inflation factor 共VIF兲 quantifies the severity of multicollinerarity in an ordinary least squares regression analysis.

Table 3 shows the WMPSR calculations The analysis is per-formed for a 93 pairs of data whereas 20 are excluded from the calculations because of equality The 95% CI of the duration dif-ference is 关⫺10 days ahead of schedule, 12.7 days behind sched-ule 兴, per the last column of Table 1, which is observed to be centered on zero Therefore, the analysis concludes that the sample projects tend to finish almost on schedule.

Multiple Linear Regression Analysis

of the Predicted Project Cost and the Predicted Project Duration

The statistical analysis hereafter performs linear regression analy-sis by using the “least squares” method to fit a line through a set

of observations Regression analysis provides inference about how a single dependent variable is affected by the values of one

or more independent variables Dependent and independent vari-ables are defined at the beginning of the regression analysis Two multiple regression steps are performed on the data for: 共1兲 the predicted project cost 共PPC兲, and 共2兲 the predicted project dura-tion 共PPD兲 Thus, two regression equations are developed using the project data of different classes.

Regression Model for the PPC

At the regression analysis, the APC is set as the 共Y兲 dependent

variable The assigned independent variables 共X兲 are: job type,

project area, PBC, and PD All independent variables are known and estimated based on the project blue prints and estimated bill

of quantities 共BOQs兲 The degrees of freedom are calculated as equal to the number of data points minus number of independent variables− 1 That is: 91− 5 − 1 = 85 The correlation coefficient matrix of Table 4 depicts the linear relationship between each two variables The coefficient of correlation is a value between ⫺1 and +1 Additionally, a value closer to +1 indicate a strong

rela-tionship, a value of zero indicate no relationship among the two variables, however, a value close to ⫺1 indicates a reverse rela-tionship.

Table 4 shows that all of the correlation coefficients are di-rectly proportional with the predicted project cost The PBC has the max r-value of 0.9992, which means that the PBC provides a good basis for estimating the real project cost.

Equation of the Multiple Regression Analysis for the PPC

The regression analysis returned the following equation that sta-tistically fit the data the best:

共PPC兲 = − 24,061 + 4,836.5 ⴱ 共scope兲 + 1.923 ⴱ 共project area兲 + 共PBC兲 + 92.62 ⴱ 共PD兲

Regression Model Goodness of Fit to Real Project Data

Table 5 depicts the 95% confidence intervals of the regression model coefficients The 95% confidence interval for the con-stant means there are 95% confidence that the true population mean of the equation constant of ⫺24,061 lies in the interval

of 共lower limit=mean−2ⴱSE, and upper limit=mean+2ⴱSE兲

= 关−24,061−共2ⴱ42,706兲, −24,061+共2ⴱ42,706兲兴=关−108,791, 60,668 兴 Of course, with 99.7% confidence, the CI expands over 6-␴ 关standard error 共SE兲兴 around the mean coefficient ⫺24,061 instead of 4-␴ in the case of 95.4% CI.

The goodness of the fit for the above equation is explained by

the calculated r-squared value of 99.86% This means 99.86% of

the variance in the variable APC is explained by the model The

obtained p-value of ⬍0.0001 is considered extremely significant,

which is the probability for obtaining an r-squared value of

99.86% by chance assuming no linear relationship is established among the variables.

Table 3 WMPSR Calculation for the Median Project Duration

Differ-ence

Table 4 Correlation Matrix

Note: Each correlation coefficient is calculated independently, without considering the other variables.

Table 5 SE and 95% Confidence Intervals for the Regression Equation

Coefficients Variable Coefficient SE LL-95% CI UL-95% CI

A: project scope 4,836.5 18,108 31,090 40,763 B: project area 1.923 1.404 ⫺0.8632 4.708

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Significant Variables of the Regression Model

Each p-value of Table 6 compares the regression model with a

simpler model deleting one of the variables Therefore, the

p-value tests the effect of one variable, after accounting for the

other variables.

It is observed in Table 6 that only the PBC variable has a significant statistical impact on the result of the PPC regression

model with a p-value ⬍0.0001 However, the other variables such

as project scope, project area, and PD had a marginal impact to the results of the PPC This makes sense because of the following facts: 共1兲 the contractor employ underbidding policy under high competitive bidding as a strategy to offset the common practice of awarding the contract to the lowest cost bidder, especially in the case of public buildings Underbidding practice is the pricing of construction tenders lower than estimated costs by pricing hidden items highly, at the same time controlling the overall bid cost by underpricing other invaluable items of the bid; 共2兲 at cost plus contracts in particular, contractors have a clearer vision, com-pared to engineers, of bid items leading to escalated project cost;

thus, contractors use such items to increase their profit margin; 共3兲 the contractor has undisputed ability among other project parties

in bringing the cost down; therefore, prudent owners solicit the contractors’ opinion through value engineering and constructabil-ity reviews, to cut down on cost, time, or both; and 共4兲 most contractors finance project activities via surety loans; which hold them vulnerable to owner financial default Although the general conditions of the International Federation of Consulting Engi-neers 共FIDIC兲共1999兲 entitles the contractor to suspend or termi-nate the contract in case of owner default in paying promptly;

however, most contractors will not claim damages and keep good

relations with the owner and the engineer for the benefit of ob-taining future jobs, or simply, avoid litigation option, which rarely came in favor of contractors.

Verification of the PPC Model: Multicollinearity Assessment

The r-squared values depicted in Table 7 quantify how well that

x-variable is predicted from the other x-variables 共ignoring Y兲.

The VIF is calculated from r-squared Since all r-squared values are low, i.e., less than 0.75, it is concluded that the x-variables are

independent of each other Therefore, multicollinearity is not a problem.

Regression Model for the PPD

At the regression model, the APD is set as 共Y兲 dependent variable.

The independent variables 共X兲 are: project scope, project area,

PBC, and PD All independent variables are known and esti-mated, as explained before, based on the project blue prints and estimated BOQ The correlation coefficient matrix shown in Table

8 depicts the linear relationship between each two variables of the regression analysis for the PPD.

Equation of Multiple Regression Analysis for the PPD

The regression analysis returned the following equation 共that sta-tistically fit the data the best兲

共predicted project duration兲

= − 37.455 + 10.723 ⴱ 共project scope兲

⫾ 6.207 ⫻ 10 −5 ⴱ 共project area兲 − 9.761 ⫻ 10 −7 ⴱ 共PBC兲 + 1.033 ⴱ 共PD兲

Regression Model Goodness of Fit to Real Project Data

Table 9 depicts the 95% confidence intervals of the regression

Table 6 Variables of Significant Contribution to the PPC Regression

Model

A: project scope 0.2671 0.7899 Not significant B: project area 1.369 0.1738 Not significant

Table 7 R-Squared Values for X-Independent Variables

R 2 with

other x

Table 8 Correlation Matrix of the PPD Regression Analysis

Note: Each correlation coefficient is calculated independently, without considering the other variables.

Table 9 95% Confidence Intervals for the PPD Regression Coefficients

Variable Coefficient SE LL-95% CI UL-95% CI

A: project scope

B: project area

⫺0.00000062 0.0007 ⫺0.001457 0.00133 C: PBC 0.00003202 0.0004702 ⫺0.0009044 3.06⫻10 −6

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model coefficients The goodness of the fit for the above equation

is explained by the calculated r-squared value of 93.6% This

means 93.6% of the variance in the variable 共APD兲 is explained

by the model The obtained p-value of ⬍0.0001 considered ex-tremely significant, which is the probability for obtaining an

r-squared value of 93.6% by chance assuming no linear

relation-ship is established among the variables.

Significant Variables to the Regression Model

Each p-value of Table 10 compares the regression model with a

simpler model deleting one of the variables Therefore, the

p-value tests the effect of one variable on the dependent variable,

after accounting for the other variables The null hypothesis stat-ing that there is no significant effect of the independent variable

on the dependent variable is rejected when the p-value is less or

equal 0.05 at the 95% level of confidence Conversely, the alter-native hypothesis stating that there is a statistical significant effect

of the variable on the dependent variable is accepted.

Contrary to the PPC, Table 10 depicts the PPD variable of having significant contribution to the PPD regression model This statistical result can be substantiated from practice because the PPD is a special condition in the contract, which is determined by the engineer and amended to the bid documents during the plan-ning phase.

In summary, results of Tables 6 and 10 came in support of the following two arguments: 共1兲 the driver of project cost is the contractor, due to contractor underbidding practices and intensive use of change clause and 共2兲 the project time performance is controlled by the owner and engineer due to their role in selecting 共in兲appropriate duration specific to project nature and complexity, and/or 共in兲appropriate selection of project delivery system.

Verification of PPD Model: Multicollinearity Assessment

The obtained r-squared values for the PPD model were the same

as the values in Table 7 Therefore, similar to the PPC, multicol-linearity poses no problem to the regression model.

Regression Model Validation

The validation of the proposed regression models is performed by 共1兲 estimating the percent prediction error statistic and 共2兲 con-ducting out-of-sample tests on the data The percent error is esti-mated by calculating the difference between the predicted value

by the generic model and the APC or APD; the result is divided

by the APC or APD value, respectively.

Analysis on the Percent Error Statistic in Predicting APC and Time

The percent error is estimated by calculating the difference be-tween the predicted value by the model PPC and PPD and the APC and APD; the result is divided by the APC and APD value, respectively.

Table 12 compares the percent error statistics of the PBC, PPD, PPC via the regression model, and predicted duration 共PD兲 via the regression model The percent error statistics in Table 11 were computed by using the percent error data and include the mean percent error, SD, SEM, lower limit 共LL兲 95% confidence interval, upper limit 共UL兲 95% confidence interval, minimum value, median, and maximum value The percent error data were computed per the following formulas:

PBC percent error = 共APC − PBC兲

APC

PPD percent error = 共APD − PD兲

APD

PPC percent error = 共APC − PPC兲

APC

Table 10 Variables of Significant Contribution to the MPD Model

A: project scope 1.183 0.2396 Not significant B: project area 0.0883 0.9298 Not significant

Table 12 Out-of-Sample Test Results of the Percent Prediction Error

Descriptive statistics

PBC

% error

PD

% error

PPC

% error

PPD

% error

Table 11 Descriptive Statistics for the Percent Prediction Error of the

Generic Regression Models Descriptive

statistics

PBC

% error

PD

% error

PPC

% error

PPD

% error

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PPD percent error

= 共APD − PPD兲 APD PPD is the PDD via the regression model The following conclusions can be established on the percent error statistics depicted in Table 11:

1 The mean percent error of the PPC is very high compared to the mean percent error of the PBC, and the same applies for the SD values Consequently, the 95% CI of the percent error margin is very wide for the PPC of 关⫺0.2, ⫺0.035兴 with a range= −0.165 compared to the PBC of 关0.02, 0.067兴 with a range= 0.047 Thus, the 95% point estimate of the percent error margin is ⫾0.0825 and ⫾0.0235 for the PPC and PBC, respectively In conclusion, the PPC estimates the APC at an accuracy level= ⫾0.0825, which is very low compared to the PBC; and

2 The mean percent error of the PPD via the regression model

is lower than the mean percent error of the PD; the SD values are almost the same Consequently, the 95% CI of the error margin for the PPD of 关⫺0.06, 0.019兴 with a range=

−0.079 compared to the PD of 关⫺0.09, ⫺0.001兴 with a range= −0.089 Thus, the 95% point estimate of the error margin is ⫾0.035 and ⫾0.045 for the PPD and PD, respec-tively In conclusion, the PPD estimates the APD at an accu-racy level= ⫾0.035, which is higher compared to the PD.

Higher accuracy and reliability of the model is dictated through obtaining lower SD of the distribution of the mean per-cent error statistic; thus, narrower CI of the perper-cent error statistic.

Overall, the analysis on the percent prediction error indicates a high accuracy and reliability by suing the PPD at accuracy level

= ⫾0.035; however, the PPC model accuracy and reliability are low at ⫾0.0825.

Out-of-Sample Tests in Predicting APC and Time

Validation of the regression model outputs is conducted by mea-suring out-of-sample prediction accuracy The public projects data were divided into two groups: the first group covers 84 projects at which new regression formulas for cost and time were developed.

The second group of 31 projects data was left for testing.

The two regression formulas of the sample 84 projects were PPC = − 18,737 + 4,312.4 ⴱ 共project scope兲

− 1.398 ⴱ 共project area兲 + 0.991 ⴱ 共PBC兲 + 77.68 ⴱ 共PD兲 PPD = − 52.701 + 10.209 ⴱ 共project scope兲

+ 0.000 467 ⴱ 共project area兲 − 2.5 ⫻ 10 −6 ⴱ 共PBC兲 + 1.064 ⴱ 共PD兲

The above two formulas were verified since the multicollinearity was found to pose no problem to the regression results.

The above formulas were set to compute the PPC and PPD for the second testing group of 31 projects Table 12 depicts the sum-mary statistics for the percent prediction error of the 31 projects

of the PBC, PD, PPC new formula, and the PPD new formula.

The ranges of the 95% confidence intervals of the error mar-gins were 0.08, 0.18, 0.155, and 0.164 for the PBC, PPC, PD, and PPD, respectively Therefore, the prediction accuracies are ⫾0.04,

⫾0.09, ⫾0.078, and ⫾0.082 for the PBC, PPC, PD, and PPD, respectively In conclusion, the PPD results in higher prediction accuracy compared to the PPD; which comes in support of results

of the previous section.

Concluding Remarks

This research utilizes a real time approach in estimating project cost and duration The model results predict the amount of time and money that should be budgeted to the project Critical path durations and budgeted costs should be increased or decreased up

to the regression models outputs Calibration of project cost and duration at the planning phase prior to construction would incor-porate uncertainty effects on project Thus, the research outcome

is to realize a realistic schedule with budgeted cost and duration that incorporate lessons learned from similar history projects.

Typically, the model input of PBC, which is estimated based on the BOQ items, and the project PD is estimated via the critical path duration of the scheduled project activities.

Finally, this research has used data that were collected in Jor-dan The U.S construction industry can benefit from the results of this research by applying regression models in predicting actual cost and time Such prediction models are to be developed on historic data collected from the U.S construction industry Thus, the prediction formulas documented in this paper apply only to the case of public building construction projects in Jordan and cannot be used to predict project cost and time elsewhere, what-soever.

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Tiêu đề	Statistical Analysis on the Cost and Duration of Public Building Projects
Tác giả	Ayman A. Abu Hammad, Souma M. Alhaj Ali, Ghaleb J. Sweis, Rateb J. Sweis
Thể loại	thesis

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Số trang	11
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