1、 1 Using Weibull Analysis for Evaluation of Cost and Schedule Performance Khaled M. Nassar1； Hordur G. Gunnarsson2； and Mohamed Y. Hegab, P.E.3 Large amounts of money are lost each year in the construction industry because of poor schedule and cost control. Few contractors specify and follow systema
2、tic schedule monitoring practices. Traditionally, the earned value method EVM is used to control and monitor schedule performance using the schedule and cost performance indices which compare the budgeted cost of work performed to what was originally scheduled or what is actually expended. This pape
3、r presents a statistical approach, namely Weibull analysis, to evaluate stochastically the schedule performance of construction or design projects. The approach can be used in conjunction with the EVM to enhance the evaluation and control of schedule performance. Weibull analysis is a common method
4、for failure analysis and reliability engineering used in a wide range of applications. In this paper, the applicability of Weibull analysis for evaluating and comparing the reliability of the schedule performance of multiple projects is presented. The various steps in the analysis are discussed alon
5、g with an example in which two projects are analyzed and compared. The authors conclude that Weibull analysis has several advantages and provides a relatively robust and effective method for construction managers to better control and monitor their projects. Construction projects are seldom on-sched
6、ule all the time. The amount of work performed on the project usually fluctuates from one period to the other. In fact, according to the 80 / 20 rule. suggested by the 18th Century economist, Pareto 80% of the effort will be expended during 20% of the project duration. This creates a significant pro
7、blem in trying to monitor the actual performance of the project schedule and specifically trying to decide whether or not the project can finish on time., the reliability of the project schedule performance .The earned value method EVM is often used as a project control technique to provide a quanti
8、tative measure of schedule performance. In the EVM, the schedule and cost performance indices C/SPI are used for constant monitoring of the projects cost and schedule based on an original critical path method CPM schedule Chang 2001 . Unfortunately, CPM scheduling in general creates an unrealistic e
9、xpectation regarding project schedule performance. Starting a project one day and expecting that the project will finish on an exact date some two or three years in the future is unrealistic. Therefore, there is a need to extend schedule analysis techniques, like the EVM, to provide means for probab
10、ilistically analyzing the schedule performance and measuring the risks involved. In other management domains like software projects and business management, tools from the area of reliability, availability, and maintainability RAM engineering are now used to predict and avoid sudden system failures
11、. RAM engineering is emerging as the newest discipline in product development due to new accurate, quantitative methods. Weibull analysis is foremost among these tools . Weibull analysis is a widely used method in the field of manufacturing and industrial engineering. It has mainly served for simula
12、ting failure rates or lifetime of certain products. By using this particular analysis one can make predictions about products life, compare the reliability of competing product designs, and manage spare parts inventories to name a few common industrial applications Dorner 1997, 1999 . The objective
13、of this study is to discuss and present the applicability of Weibull analysis for evaluating schedule performance using cost and performance indices C/SPI and to provide construction 2 managers with an effective tool for stochastically evaluating the C/SPI. A number of probabilistic techniques were
14、checked against the data using Anderson-Darling measure AD value and the Weibull distribution was found to be the best representative for evaluating schedule performance and cost performance having the lowest AD value . In this paper, an example is provided, in which two projects are compared and an
15、alyzed. The first part of this paper briefly covers the EVM and performance indices. The second part discusses the Weibull distribution, it sharacteristics and its application to EVM. This is followed by an example of Weibull analysis using actual data of C/SPI, in which two projects are compared. L
16、astly, conclusions are drawn. Earned Value Method and Performance Indices The goal of the EVM is to control costs and schedule performance during the project. This is accomplished by calculating a number of measures. First, the budgeted cost for work scheduled BCWS within a given time period is calc
17、ulated. Second, the actual cost of work performed ACWP during the given time period and the budgeted cost for work performed BCWP are calculated. The performance indices are determined next to show the percentage of variation, between planned and actual performance. Weibull Analysis Weibull analysis
18、 essentially entails fitting a Weibull distribution to a collected data set about some characteristic of a system usually a quality or performance characteristic , and analyzing the reliability of the system based on the fitted distribution. Collection of percent-complete data of the first project a
19、nd calculating the SPI/CPI； Ranking SPI/CPI smaller value is given a rank of 1 ； Calculating the median rank rank No. 0.3/ No. of points+0.4 ； Calculating in 1/ 1-median rank values and drawing a straight line trendline in MS EXCEL between them and ln SPI and ln CPI in separate charts and choosing t
20、he option of showing the straight line equation in the form of y = mx + b ； = m and = eb/ ； Calculating the PDF for Weibull distribution in MS EXCEL using Weibull function WEIBULL index value, shape parameter , scale parameter , TRUE ； Drawing the PDF against the index value； Benefits of the Weibull
21、 Analysis in Evaluating Cost and Schedule Control The three advantages, mentioned in section 2 above, make the use of Weibull distribution in the analysis and valuation of the schedule and cost performances of projects highly suitable. Firstly, since the C/SPI are essentially performance measures, t
22、he robustness and flexibility of the Weibull distribution in modeling performance characteristics, can be utilized effectively to model C/SPI. Moreover, since the Weibull distribution is robust enough to assume a number of different distributions including the normal, exponential and beta distributi
23、ons one can utilize the Weibull distribution to model the C/SPI data of the project, without the limitations of a predefined distribution assumption. Predefined distribution assumption is often used for example when modeling activity durations forprobabilistic scheduling techniques like PERT. The du
24、rations of the various activities in the project are often assumed to follow either normal distribution Fentetal. Secondly, the parameters and represent a meaningful measures of the data at hand, namely C/SPI. In SPIs terms, the shape parameter indicates whether the performance of the project in ter
25、ms of C/SPI is increasing, constant or decreasing. A 1.0 indicates that the project has an increasing index rate, i.e., there is an improvement in the performance of the project from one period to another. A = 1.0 indicates a constant index rate and a1.0 indicates a decreasing index rate. The desire
26、d rate is therefore 1. The scale parameter or the Weibull characteristic life is a measure of the performance variability. A high alpha means more variability in the project performance in terms of the index values. 3 Thirdly, one of the strongest advantages of Weibull analysis is the ability to pro
27、vide accurate performance analysis and risk pre- dictions with extremely small samples. Abernathy and Fulton Small sample can be defined as any sample less than 25. When controlling the schedule and cost of the project using the EVM, the frequency of calculating the performance indices is determined
28、 depending on the duration of each project and the required level of control. In most cases however, relatively few C/SPI data points are available, which makes the Weibull distribution an ideal fit. Conclusion Keeping the project on schedule and within budget is a primary objective in every project
29、. This is one of the main functions of cost and schedule control and is vital to monitoring the progress of design and construction projects and keeping these projects on track. The earned value method is a common technique for cost and schedule control through sampling C/SPIs during the project. In
30、 this paper, Weibull analysis for probabilistic analysis of the C/SPI was presented. The Weibull distribution is very flexible and robust which allows the distribution to assume a wide variety of shapes by appropriate selection of the parameters and Characteristics of the Weibull distribution functi
31、on and Weibull analysis that renders them pertinent for monitoring construction and cost schedule performance were discussed. References Abernathy, R., and Fulton, W. 2000 . The new Weibull handbook, 4th Ed., Gulf, West Orange, N.J. AbouRizk, S. M., and Halpin, D. W. 1992 . Statistical properties of
32、 construction duration data. J. Constr. Eng. Manage., 118 3 ,525544. Chang, A. S. 2001 .Defining cost/schedule performance indices and their ranges for design projects. J. Manage. Eng., 17 2 , 122130. Dorner, W. W. 1997 . Using Excel for data analysis. Quality Dig.,4 10 , 4246. Dorner, W. W. 1999 . Using Microsoft Excel for Weibull analysis. Quality Dig., 6 1 , 1519. Evans, J. R., and Olson, D. L. 1998 . Introduction to simulation and risk analysis, Prentice-Hall, Englewood Cliffs, N.J. .
