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The use of parametric cost estimating and risk management techniques to improve project cost estimates during feasibility studies

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(1)THE USEOF PARAMETRIC COST ESTIMATINGAND RISK MANAGEMENT TECHNIQUESTO IMPROVE PROJECTCOST ESTIMATESDURING FEASIBILITY STUDIES. AMinor Dissertation Submitted in Partial Fulfilment for theDegree: MAGISTER INGENERIAE in ENGINEERING MANAGEMENT at the FACULTYOF ENGINEERINGAND THE BUILT ENVIRONMENT of the UNIVERSITY OF JOHANNESBURG. by. KHOTSO DANIEL MOLEFI FEBRUARY 2013 SUPERVISOR: PROF. J.H.C. PRETORIUS.

(2) University of Johannesburg – K. Molefi (201113613). ABSTRACT “A robust set of estimates puts a project on a firm footing from day 1, allowing the project manager to apply the right level of resources at the appropriate time. If the plan has been based on poor estimates, problems will occur during the execution of the project …” This statement places great importance on the ability to estimate costs as accurately as practicable early during a project life cycle.Many techniques have been proposed with the aim of aiding withthe production of early cost estimates,which have acceptable accuracies necessary for Feasibility Study purposes. One such technique is Parametric Cost Estimating for developing Parametric Cost Models used in producingthese conceptual estimates.At the heart of Parametric Cost Estimating Technique, is a fundamental statistical technique commonly known as Linear Regression Analysis.The problem that the research addresses is that of the general misconception found to prevail within project houses that some engineering systems are too complex to model using the Parametric Cost Estimating Technique. The objectives of this research are to investigate and demonstrate the effectiveness of this technique in predicting the costs of a system for Feasibility Study purposes. The objectives were achieved by conducting a secondary literature review of case studies of similar Parametric Cost Models that were developed by others for engineering systems of varying complexities. A second method used in achieving the objectivesincluded formulating a case study in which a Parametric Cost Model was developed to illustrate the concept and to prove that the accuracies produced by the model meet the requirementsfor Feasibility Studies.The research was limited to initial project costs required for Feasibility Studies,ignoring the effects of qualitative factors,focusing only on the acquisition costs and not the total lifecycle costs of the system.The case study was developed for a passenger motor vehicle as the system of interestbecause sufficient cost data in the form of vehicle retail price and performance specifications is publicly available in car magazines making it possible to build a meaningful Parametric Cost Model. The Parametric Cost Model wasdeveloped using Microsoft Excel 2007 and had a Mean Absolute Error Rate of 10.9% and the range of accuracy obtained, -20% to 10% with 67% confidence level and -30% to 30% with 95% confidence level, conforming to a Class 4 estimate which meets the accuracy requirements for a Feasibility Study.. Page i.

(3) University of Johannesburg – K. Molefi (201113613). Table of Contents ABSTRACT .................................................................................................................................. i Table of Figures ......................................................................................................................... iv CHAPTER 1: INTRODUCTION .................................................................................................. 1 1.1. Background on Parametric Cost Estimating ................................................................. 3. 1.2. Problem Statement ...................................................................................................... 3. 1.3. Research objectives..................................................................................................... 4. 1.4. Limitations ................................................................................................................... 5. 1.5. Significance ................................................................................................................. 5. 1.6. Brief Chapter Overviews .............................................................................................. 6. CHAPTER 2: LITERATURE REVIEW ........................................................................................ 7 2.1. Classification of Cost Estimates ................................................................................... 7. 2.2. The Parametric Cost Estimating Process ..................................................................... 9. 2.2.1. Determination of Parametric Cost Model Scope...................................................12. 2.2.2. Collection of Project Data.....................................................................................12. 2.2.3. Normalisation of Collected Data ...........................................................................13. 2.2.4. Analysis of Normalised Data ................................................................................14. 2.2.5. Model Testing and Validation ...............................................................................14. 2.2.6. Documentation.....................................................................................................15. 2.3. Uncertainty and Risk Considerations ..........................................................................16. 2.4. Secondary Literature of Empirical Research on Parametric Cost Models....................18. 2.4.1. Parametric Cost Estimating Model for Buildings...................................................18. 2.4.2. Comparison of construction cost estimating models based on regression analysis, neural networks, and case-based reasoning ........................................................19. 2.4.3. Parametric and Neural Methods for Cost Estimation of Process Vessels .............19. 2.4.4. Parametric vs. neural network models for the estimation of production costs: A case study in the automotive industry ..................................................................20. 2.4.5. Road Tunnel Early Cost Estimates Using Multiple Regression Analysis ..............21. 2.4.6. Chemical Process Equipment Cost Estimating using Parametric Models.............22. 2.4.7. Non-linear and Multivariate Regressions for Space Engineering Parametric Cost Models .................................................................................................................23. 2.4.8. Parametric Cost Model – Induced Draft Cooling Towers ......................................24. Page ii.

(4) University of Johannesburg – K. Molefi (201113613) CHAPTER 3: METHOD .............................................................................................................25 3.1. Introduction .................................................................................................................25. 3.2. Research Design ........................................................................................................25. 3.3. Methodology ...............................................................................................................27. 3.3.1. Research Instruments ..........................................................................................27. 3.3.2. Data .....................................................................................................................28. 3.3.3. Analysis ...............................................................................................................35. 3.4. Limitations ..................................................................................................................39. 3.5. Conclusions ................................................................................................................39. CHAPTER 4: CASE STUDY RESULTS AND ANALYSIS ..........................................................40 4.1. Relationships between Independent and Dependent Parameters ...............................40. 4.1.1. Graphical representation of parameter relationships ............................................41. 4.1.2. Correlation of the model parameters ....................................................................45. 4.2. Regression Analysis ...................................................................................................48. 4.2.1. Multivariate Regression Output Results ...............................................................48. 4.3. Model Verification .......................................................................................................52. 4.4. Final Parametric Cost Model .......................................................................................55. 4.5. Sensitivity Analysis .....................................................................................................56. CHAPTER 5: CONCLUSIONS ..................................................................................................58 5.1. Summary of Findings ..................................................................................................58. 5.2. Conclusions ................................................................................................................59. 5.3. Summary of Contributions...........................................................................................60. 5.4. Suggestion for Future Work ........................................................................................61. REFERENCES ......................................................................................................................62 APPENDIX A: Tables of data used in building and testing the cost model ................................65 APPENDIX B: Graphs of parameters vs. actual and estimated Retail Price ..............................69. Page iii.

(5) University of Johannesburg – K. Molefi (201113613). Table of Figures Figure 2.1: Graphical Representation of the Estimate Classification System [19] ....................... 9 Figure 2.2: The Parametric Cost Estimating Process [18] .........................................................11 Figure 2.3: Traditional vs. Risk-Based Estimate [22] .................................................................17 Figure 3.1: Engine Power Histogram.........................................................................................32 Figure 3.2: Maximum Speed Histogram ....................................................................................32 Figure 3.3: Acceleration Capacity Histogram ............................................................................33 Figure 3.4: Engine Capacity Histogram .....................................................................................33 Figure 3.5: Engine Torque Histogram .......................................................................................34 Figure 4.1: Relationship between Engine Power and Retail Price .............................................41 Figure 4.2: Relationship between Engine Torque and Retail Price ............................................42 Figure 4.3: Relationship between Engine Capacity and Retail Price .........................................43 Figure 4.4: Relationship between Maximum Speed and Retail Price [ref]..................................43 Figure 4.5: Relationship between Acceleration and Retail Price................................................44 Figure 4.6: Graph of Engine Power vs Actual and Estimated Retail Price .................................53 Figure 4.7: Model Output Error - Histogram ..............................................................................54 Figure 4.8: Sensitivity Analysis – All key parameters.................................................................56. Page iv.

(6) University of Johannesburg – K. Molefi (201113613). CHAPTER 1: INTRODUCTION “A robust set of estimates puts a project on a firm footing from day 1, allowing the project manager to apply the right level of resources at the appropriate time. If the plan has been based on poor estimates, problems will occur during the execution of the project …”Cost overruns in projects have always created problems for many projects throughout history including the Ancient Roman days. One research that was conducted recently has found that no improvement in the accuracy of the estimated project costs has been made [1]. Furthermore, several literature sources have revealed that over 50% of projects run over budget [1][2]. One of the identified causes of this problem is the low accuracy of budget estimates produced during the early stages of project conception, and not necessarily poor project or cost control and scope changes in the later execution phases of the project[2][3]. Various causes for underestimated costs could not be attributed to error only but also other factors such as failure to take into account risk and uncertainty in estimates and political reasons to keep estimates low in order to influence policy to get approval for projects[1] Despite the great importance of estimating costs as accurately as it is practicable, it is a not a simple task nor straightforward one to undertake because of the lack of information in the conceptual stages of a project[4]. Therefore, the methods and techniques used for estimating costs at this stage lend themselves to the level of project definition available at the time the estimate is prepared. Early in a project’s lifecycle, little information is available about the project and therefore conceptual cost estimatesare produced fordecision-making support to make“go or no-go” decisionson whether tocontinue development of a cost estimate for proposal purposes or to select between alternative designs[5][6]. According to A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Fourth Edition,. several cost estimating techniques exist, viz. analogous estimating, parametric. estimating, bottom-up estimating, three-point estimating, reserve analysis and many others and these can be used at differing stages of a project to produce estimates of differing accuracies [7]. It has been proposed by a number of researchers that parametric cost estimating technique has the capability of providing a systematic and consistent method of estimating initial project costs when project scope definition is low[5][8][9][10][11]. The models derived using this technique have economic value because when they are properly designed and used, they can improve the accuracy of project estimates, reduce the likelihood of severe overruns of budgets, and reduce the cost of preparing project proposals [12]. Page 1.

(7) University of Johannesburg – K. Molefi (201113613) The Practice Standard for Project Estimating describes parametric estimating as a technique that utilises statistical relationships between historical data and other variables to calculate estimates for project activity parameters such as scope, cost, and duration [13]. In parametric cost estimating, cost is expressed as a mathematical function dependent on a set of parameters. These parameters usually define the features of the system such as performance, structural features, type of materials used, etc., and they have an influence on the final cost of the system, thus earning the name ‘‘cost drivers’’[5][14]. Using this parametric cost estimating technique, system costs can be estimated to acceptable accuracies for feasibility study applications. The Association for the Advancement of Cost Engineering (AACE) International classify a feasibility study as a Class 4 estimate for engineering, procurement, and construction applications for the process industry. The Class 4 estimate is characterised by low project definition and very wide accuracy ranges, and typically engineering is 1 – 15% complete at this stage. Parametric estimating technique is one of the estimating methodologies identified as being appropriate for preparing a Class 4 estimate with an accuracy range of -30% to +50% [15]. In addition, Shabani and Yekta [16] have stated that by using parametric models, capital costs can be estimated to within an acceptable accuracy during the feasibility stages, despite only 15% of the design activities being complete at this stage. An important function of a parametric model should also serve to provide insight on the uncertainties and risks associated with project costs because modern projects are often extremely complex.Therefore due to thelittle information being available during the feasibility study stages, insufficient knowledge is available about the system parameters resulting in large uncertainty around the initial cost estimates [17]. A cost estimating model will provide a “point estimate” of costs; a point estimate being a single number, which will always be in error. A cost model that deals properly with uncertainty and risk will provide rather a “range estimate”. A range estimate is also called a probability distribution, that is, an estimate that tries to give some idea of the possible range of cost outcomes, and of the relative likelihood of particular outcomes[6][12].. Page 2.

(8) University of Johannesburg – K. Molefi (201113613) 1.1. Background on Parametric Cost Estimating. Parametric cost estimating originated during the World War II when the war created a high demand for military aircraft in quantities and models that the aircraft manufacturing industry could not keep pace with. Althoughthere was some elementary work that had been done to develop parametric cost estimating techniques, there was still no extensive use ofany cost estimating techniquesapart from the strenuous gathering of labor-hours and materials costs for the purposes of estimating costs[18]. In 1936, Theodore Paul Wright, a US Aeronautical Engineer and Educator suggested in the Journal of Aeronautical Science a type of statistical estimating equations that could be used to predict the cost of airplanes over long production runs, a theory which came to be known as the learning curve[11][18]. Learning curve is a theory that describes the decrease in unit costs as the manufacturing process is repeated [11].By the time the demand for military aircraft had blown up in the early years of World War II, industrial engineers were using Wright’s learning curve to predict the unit cost of airplanes[18]. Around 1950, the Rand Corporation was established to develop and conduct studies of parametric cost estimating in the airplane industry.In the mid 1950’s, Rand developed the most basic tool of the cost estimating discipline, the Cost Estimating Relationship (CER), and merged the CER with the learning curve to form the foundation of parametric aerospace estimating [18]. Parametric cost estimating evolved over the years until in 1995 when the Joint Government/Industry Parametric Estimating Initiative Steering Committee developed the Parametric Cost Estimating Handbook[11][18].. 1.2. Problem Statement. The problem that is being investigated in this research is concerned with the difficulty and timeconsuming effort that is being placed into producing cost estimates of engineering systems for use in feasibility studies. With the world becoming integrated daily, it is becoming increasingly difficult to compete on the global stage with western countries like China, Korea, Japan, and others in engineering projects in the African continent. A lot more effort needs to be devoted to becoming more efficient in our daily operations and processes. The particular problem being discussed is applicable to specific type of companies, known as the EPCM and the EPC companies. These are also known as the ‘project houses’. Having spent the past five years working for one such company, I came to realise recently the amount of time and effort being spent in preparing cost estimates for use in feasibility studies. There were no models developed for estimating costs for such studies that do not require a high Page 3.

(9) University of Johannesburg – K. Molefi (201113613) level of accuracy of estimated costs. Yet still we received endless enquiries to provide cost estimates of conceptual engineering systems for our clients. However, the level of effort placed in producing such a cost estimate was not commensurate with the procurement cycle of the project. As a result, the turnaround times for producing such cost estimates were long owing to the absence of cost models that could produce cost estimates quickly, consistently, and with ease. The essence of the problem being investigated is that companies commit many of their resources in producing these cost estimates and this ultimately leads to inefficiencies within the company. In isolated conversations with several experts and managers who have more than 25 years in the industry I was told that it was impossible to build a parametric cost model of a conveyor system to be of any use in predicting costs for feasibility studies due to their complex nature. If reliable data was readily available in the industry on conveyor systems as well as their cost data, the purpose of the research would have been to disprove that myth. However, since that kind of information is very difficult to come by, all is not lost since we can still work towards developing the body of knowledge on parametric cost models by building models for other systems. It is therefore the objective of this study to conduct an empirical research of parametric cost models by performing a secondary literature review and by developing a parametric cost model of an engineering system.. 1.3. Research objectives. The objectives of this research are: •. To investigate and demonstrate the effectiveness of the technique, parametric cost estimating in predicting the costs of a system during feasibility study stages of a project. It is the premise of the study to prove that the technique can be used to predict the costs of most systems to an accuracy that is needed duringfeasibility studies. Furthermore, it shall be proven that only quantitative key performance characteristics and specifications of the system are adequate in predicting these costs in the context of feasibility studies.The objective will be achieved by: o. Presenting parametric cost models that have been developed by othersthrough secondary empirical research by means of literature review,. o. Developing a parametric cost model of a system for which adequate information about its key performance characteristics is known and readily available so that it can be used to simulate a project in the feasibility study stages, and. Page 4.

(10) University of Johannesburg – K. Molefi (201113613) o. Interpreting the output results of the parametric cost model in the context of uncertainty and risk.. •. Tosubmit a report of this research to the University of Johannesburg inpartial fulfilment of the requirements for the degree of Magister Ingeneriae: Engineering Management.. 1.4. Limitations. The research will be limited to: •. Parametric cost estimating models only; no effect of project duration will be taken into account in the analyses although the two cannot be separated from one another in reality. It shall therefore be assumed that delays in duration play no role in the final costs of a system/project.. •. The effects of quantitative factors only. The author is well aware that qualitative factors also play a role in determining the final system costs.. •. Estimation of costs during the initial stages of a project viz., the feasibility study stages. Therefore these costs are high-level estimated costs that do not require detailed technical information such as engineering drawings, specifications, standards, etc.. •. The estimation of system costs,which do not denote the total life cycle costs of the system under consideration. The costs in this instance refer only to the costsrelated to the acquisition of the system by the owner whereas total life cycle costs include the total costs of ownership which include operating costs, service and maintenance costs, refurbishment costs, disposal costs, etc.. 1.5. Significance. Having mentioned the problem in the previous section, it is the belief of the author that this research will have both theoretical and practical significance. The theoretical significance is that the research will contribute to the knowledge in the field of parametric cost estimating in that it will reinforce what has already been researched in the past about the technique. Another theoretical significance of the research is foreducationalpurposesby using the results obtained from the parametric model to understand causal relationships, correlations between the parameters of the case engineeringsystem and how they affect the final output costs of the system. The practical significance of the research is that the procedure followed in the case study to develop the parametric cost model can be followed by any organisation in practice when they develop their own parametric cost model.. Page 5.

(11) University of Johannesburg – K. Molefi (201113613) 1.6. Brief Chapter Overviews. The remainder of the report is arranged as follows: Chapter 2: The chapter covers pertinent literature to the study of parametric cost models. A brief description of the accuracy classification of the cost estimatesis presented as background.An associated topic in risk management techniques is covered, in line with the topic of the research. The chapter is concluded by presenting literature review and an analysis of other research workconducted on parametric cost models. Chapter 3 presents the research methodologies adopted in this research and provides motivation and justification for the various methodologies employed. The chapter also highlights possible weaknesses in the methodologies adopted and suggests improvements for future studies. Chapter 4 presents the results of the research as well as the model developed. The results are analysed and comments made as well as sub-conclusions. Finally Chapter 5 presents the summary, principal findings, makesconclusions with regards to the results and objectives of the research, and makes recommendations for future research and development.. Page 6.

(12) University of Johannesburg – K. Molefi (201113613). CHAPTER 2: LITERATURE REVIEW Chapter 2 consists of four sections, namely,Classification of Cost Estimates, The Parametric Cost Estimating Process, Quantitative Risk Management Techniques, and Secondary Literature of Empirical Research on Parametric Cost Models.. 2.1. Classification of Cost Estimates. This section presents the cost estimate classification system. The classification is based on the expected accuracy for different estimate types and use. Table 2.1 presents a classification system according to the AACE International[15]. The first column includes the different estimate classes from Class 1 to Class 5 where Class 5 has the lowest accuracy and Class 1 the highest accuracy. The second column is an indication of the level of detailed project information available used to define each class of estimate. For an example, a Class 4 estimate is identified as an estimate that can be produced when there is only 1% to 15% of project deliverables defined or known about a project. This maturity level of definition is the sole determinant of class i.e. it is the primary characteristic of an estimate class. Consequently, in the third column the end usage of this Class 4 estimate is identified as a feasibility study i.e. a feasibility study by definition would have 1% to 15% maturity level of project deliverables defined. In the fourth column the methodology used in producing each estimate class is defined. According to the table, parametric models are befitting of a Class 4 estimate which will have the following accuracy ranges:. •. L: -15% to -30%. •. H: +20% to +50%. What this means is that for the lower limit (i.e. over estimation) the accuracy required is -15% to - 30%. Another way of interpreting this is that for a given feasibility study, worst-case accuracy will fall between -30% and +50% and for the best case scenario accuracy will fall between -15% and + 20% given the complexity of the project, the technology involved, risk associated with a project, etc. [15].. Page 7.

(13) University of Johannesburg – K. Molefi (201113613). Table 2.1: Cost Estimate Classification System for the Process Industry[15]. This table forms the foundation of this research as it quantifies the success criteria for the model that will be developed and therefore will be referred to a lot in this report.Figure 2.1 below presents the information presented in Table 2.1 in a graphical format. This way it is easier to visualise how the estimate classes related to each other as their accuracy ranges overlap. One can see just by looking at the figure that as the maturity of definition of the project deliverables increases, so does the level of accuracy because the accuracy ranges narrow down.. Page 8.

(14) University of Johannesburg – K. Molefi (201113613). Figure 2.1: Graphical Representation of the Estimate Classification System[15]. 2.2. The Parametric Cost Estimating Process. The parametric cost estimating model is a statistical representation of cost relationships that exists between the actual project historical costs and the key system parameters or cost drivers[5]. The cost relationships are known as the Cost Estimating Relationships (CER’s); CER’s are simple models consisting of only one cost driver [12]. The representation provides a logical, repeatable and predictable correlation between the systems’ cost drivers and its resulting cost[5]. The cost drivers are independent variables such as equipment’s physical, performance, operational characteristics and design parameters which relate to the system whilst the dependent variable is the final estimated system costs [5][18].. The methodology used in. building the parametric model is defined as a technique that employs validated cost estimating relationships (CER’s) to estimate project costs[8]. Multiple regression analysis is used to establish the CER’s that exist between the system costs and the cost drivers or key parameters [19].. Page 9.

(15) University of Johannesburg – K. Molefi (201113613) Parametric cost estimating has the following characteristics and advantages [5][[9][18][20]: •. Efficient: Not only do they allow estimates to be prepared in less time than required by more detailed techniques, they also require less engineering and level of project definition to support the estimate.. •. Objective: Parametric cost models require quantitative inputs that are linked to algorithms providing quantitative outputs; all costs are traceable.. •. Consistent and reproducible: If two estimators input the same values for parameters, they will get the same resulting cost. Parametric models also provide a consistent estimate format and estimate documentation.. •. Flexible: Parametric models provide costs for a range of input values, extrapolating to derive costs for systems of a different size or nature than you may have history for. The models can be easily adjusted to provide cost sensitivity analysis for proposed design changes.. •. Defensible: The models highlight the design parameters used, and can provide key statistical relationships and metrics for comparison with other projects. Statistical measures such as R2, and t- and F-statistics for individual CERs can provide validity to the model. R2 being the coefficient of determination; these statistical measures will be covered in more details later.. The steps involved in the development of a parametriccost model involve the following[5][9][19]: 1.. Determination of cost model scope;. 2.. Collection of project data. 3.. Normalisation of collected data. 4.. Analysis of normalised data. 5.. Model testing and validation. 6.. Documentation. In addition, Dysert [5]proposes that the scope of the model be determined and established before any data is collected. As a result, this step will be included as the first step in the process and in addition to the graphical representation contained in the Parametric Cost Estimating Handbook (PCEH), see Figure 2.1 below. However, the process presented by Dysert[5][9], Phaobunjong and Popescu[19] will be followed in this research as it more recent as compared to the one presented in the PCEH.. Page 10.

(16) University of Johannesburg – K. Molefi (201113613). Figure 2.2: The Parametric Cost Estimating Process [18] According to Figure 2.1, the following steps are followed in order to arrive at the final parametric cost model: 1. Data Collection 2. Data Evaluation and Normalisation 3. Selection of Variables 4. Data Analysis and Correlation 5. Multiple Regression and Curve Fitting 6. Relationships Testing 7. Selection or Development of CER’s 8. Development of Cost Models 9. Conversion of Parametric Output into a Cost Proposal 10. Documentation However, this process presented by the PCEH will not be followed as mentioned above; the process that will be used as a guide for the parametric cost model development in this. Page 11.

(17) University of Johannesburg – K. Molefi (201113613) researchis the combined one presented above by Phaobunjong and Popescu [19], and Dysert [5][9].. 2.2.1 Determination of Parametric Cost Model Scope The purpose of this step is to establish the scope of the cost model to be developed. The model scopeincludes information on the purpose of the model such as[5]: •. defining the intended use of the model;. •. defining the model’s physical characteristics;. •. identifying and defining the key design parameters that are the main project cost drivers;. •. defining the assumptions made in building the model;and. •. definingcost bases and definitions, model accuracy, limitationsand applicability.. The key design parameters used should have the ability to be predicted with ease to within acceptable levels of accuracy during the early stages of a project scope development. Usually, the values of these design parameters are already known and specified during the project scope development phase and therefore necessitates the need to ensure that thevaluesused in predicting the costs fall within the parameter ranges that were used to develop the model fromactual dataobtained from completed historical projects.This will ensure that parameter values that fall far outside the model parameter range are not used in predicting the costs[5].. 2.2.2 Collection of Project Data It can never be stressed any further the importance of the quality of the data used in developing the parametric cost model[18]. The quality of the model will therefore be only as good as the quality of the data used in developing it. Hence the level of effort required in collecting the data is of significant importance in building a meaningful parametric cost model[5]. The data that needs to be collected includes key design parameters, project location, and year for the cost data in order to ensure that all cost data can be normalised to the current or base year, and any other information or parameters that pertain to the complexity of the project or the technology used, etc. It is regarded good practice to devise a formal data collection form that can be used every time with consistency and that can be revised as needed. A universal format used in defining and collecting project data is known as a Work Breakdown Structure (WBS). The WBS breaks down the project data into cost and technical information [18]. As a result, in building a parametric cost Page 12.

(18) University of Johannesburg – K. Molefi (201113613) model, two types of data in the form of cost drivers is used, namely the cost-related data and technical non-cost-related data. Cost-related data includes historical cost and labour cost data whilst technical non-cost-related data defines the systems properties such as system performance, engineering characteristics, operating parameters, etc. Even though not much evidence is provided, it is the opinion of the author that at feasibility study stages, only technical non-cost data is available or is known with an acceptable level of accuracy at it is available from engineering specifications available at this stage[18]. There are generally many sources of data such as[18]: •. Basic Accounting Records. •. Cost Reports. •. Historical Databases. •. Functional Specialists. •. Technical Databases. •. Contracts. •. Cost Proposals. •. Technical Databases. 2.2.3 Normalisation of Collected Data Data normalisation is a process by which costs of projects with different conditions, locations, times, system specifications, site conditions, etc. are adjusted to a common reference point (a base date, base location, etc.) by making use of cost indices[5][19].Inflation indices are common cost indices used to adjust cost data]. Data normalisation allows for a larger sample of project data to be collected and analysed as it will be having a common reference point.There are two types of inflation indices i.e. those that are based on internal information and those that are based on external information. The indices based on external information include indices published by the government such as the Consumer Price Index (CPI) and the Producer Price Index (PPI) and the Commodity Prices Indices such as the All Share Index (ALSI), the Mining Index or the Resources Index. Once data normalisation is complete, the parametric cost model can be built[18].. Page 13.

(19) University of Johannesburg – K. Molefi (201113613) 2.2.4 Analysis of Normalised Data The purpose of data analysis is to allow the researcher to achieve a basic understanding of the data and the relationships that exist between the parameters [19]. A statistical analysis, of the independent parameters is performed to determine the strongest cost drivers. It is very important to note that when performing a statistical analysis, to ensure that functional specialists can provide realistic and reliable parameters for independent parameters, given the stage of the program being estimated. The statistical analysis used is multiple regression analysis between the independent design parameters and the dependent parameter [5][9].A mathematical function, multiple regression equation, which is the parametric cost model, is the result of the multiple regression analysis with a form[19]: Y = b0+ b1X1+ b2X2 + b3X3 +…+ bnXn. (1). Where: Y = Conceptual cost estimate b0= Regression constant b1= Partial regression coefficient of parameter V1 X1= independent parameter 1 b2= Partial regression coefficient of parameter V2 X2= independent parameter 2 b3= Partial regression coefficient of parameter V3 X3= independent parameter 3 The regression constant and partial regression coefficients in the equation above are determined using multiple regression analysis. In addition, statistical significance of theparameters as cost drivers is also assessed. If good results are obtained withtwo parameters instead of five,the model with fewer parameters is always preferred [19].. 2.2.5 Model Testing and Validation Having developed the parametric cost model, it becomes very important to test the model’s validity and accuracy. One key indicator that is an indication of how well a regression equation explains the data is the R2 value[12]. R2 is known as the coefficient of determination and it provides a measure of how well the model can explain the variability in the underlying data; in. Page 14.

(20) University of Johannesburg – K. Molefi (201113613) curve fitting, An R2 of greater than 0.80 is highly desirable [15]. However, a high R2 value by itself does not say much about the relationships that exist between the parameter inputs and the resulting cost being statistically significant. Once the regression analysis has been performed with a reasonably high R2 value, the obtained regression equation still needs to be checked to ensure that obvious relationships are present in the model. If the relationships from the model appear to be reasonable, then additional tests such as the statistical significance (t-test and Ftest) tests to verify that the model is providing results within an acceptable range of error can be run[5]. The t-statistic helps in identifying whether each individual independent parameter is a good predictor of costs, and the F-statistic is a measure of how well the regression as a whole describes the parametric model[12]. Firstly, a “null” hypothesis is made that the independent parameter concerned has no influence on the output of the parametric cost model.The null hypothesis is therefore accepted or rejected based on the value of the t-statistic for that particular parameter. A value of the t-statistic greater than five leads to the conclusion to reject the null hypothesis. On the other hand, the F-statistic should have a value greater than 4.0 or 5.0 to indicate that a good cost driver has been selected for the cost model and that the form of the equation is acceptable[15]. After all of the CER’s have been developed and assembled into a complete parametric cost model, it is important to test the model as a whole against new data.. 2.2.6 Documentation Documentation addresses the need to document the resulting parametric cost model thoroughly by[5]: •. Developing a usermanual showing the steps involved in preparing an estimate using the parametric cost model,. •. Describingthe data used to create the model, including adiscussion on how the data was adjusted or normalized for use in the data analysis stage,. •. Documenting all assumptions, exclusions and allowances designed into the parametric cost model,. •. Documenting the range ofapplicable input parameter values, and. •. Explaining the limitations of the model’s parametric equation.. Page 15.

(21) University of Johannesburg – K. Molefi (201113613) 2.3. Uncertainty and Risk Considerations. This section is presented in order to assist with being able to interpret the outputs of the parametric cost model in the context of uncertainty and risk. It was mentioned in the introduction that a cost estimating model would normally provide a “point estimate” of costs instead of a “range estimate”. A cost model that deals properly with uncertainty and risk will provide rather a “range estimate”.A range estimate is referred to as a probability distribution, i.e. an estimate that tries to give some idea of the possible range of cost outcomes, and of the relative likelihood of particular outcomes [6]. Figure 2.3 below presents two types of estimates i.e. traditional estimate and risk-based estimate (RBE)[21]. Traditional estimate does not take effects of uncertainty and risk into account. The traditional estimate requires an experienced estimator who has developed an appreciation for the contingencies required for different kinds of situations. The traditional method has the following disadvantages as opposed to the risk-based estimates[21]:. •. It doesn’t support the identification and management of events that could affect the cost estimate in a positively or adversely,. •. It does not allows adequate control over the project’s estimate, and. •. It is not proactive.. Page 16.

(22) University of Johannesburg – K. Molefi (201113613). Figure 2.3: Traditional vs. Risk-Based Estimate[21] On the other hand, whilst the cost of producing the traditional estimate may be lower for the same project, the advantages of RBE over traditional estimated values are[21]:. •. It has a way of accounting for and quantifyingtherisks that may change the project’s estimate,. •. It supports a what-if analysis considering the risks involved,. •. It enables sensible control over cost estimate through risk management, and. •. It gives management a better and far more realistic long-range view of the prospects awaiting their projects.. Range Estimating Defined The elemental cost subsets of a total cost estimate are considered to be random variables rather than known parameters. These elemental costs are fed into a probabilistic model that. Page 17.

(23) University of Johannesburg – K. Molefi (201113613) calculates a distribution of total costs paired with a confidence level for each cost in the distribution. Range estimating relies on deliberative input such as use of elemental data[21].. 2.4. Secondary Literature of Empirical Research on Parametric Cost Models. In this section, parametric cost models developed by others are presented and discussed. The parametric cost models considered are for both research purposes and corporate use, whatever the case may be. Of particular interest is the application for which the model was developed, the key parameters identified as cost drivers, the source of the data used, the methodology used to build the parametric cost model, the quality of results obtained, and analyses used in interpreting the results. The particular technical details of the model and the relationships of the parameters used in each study are of no importance to this research.. 2.4.1 Parametric Cost Estimating Model for Buildings Phaobunjong and Popescu[19] proposed a parametric cost model for the estimating of conceptual costs for building construction projects in their paper published in the 2003 AACE International Transactions. The model developed in this research is for estimating construction costs of new building projects and does not include other costs associated with a project such as design and engineering costs and so forth. The key parameters that were identified were Gross Square Footage Area, Assignable Square Footage Area, Usage Ratio, and Number of Floors whilst the dependent parameter being Building Costs. The data that was used to build the model was obtained from 139 construction projects for new buildings in Texas from 1990 – 2000. Since the historical cost data used was obtained from projects that took place at different locations and over different periods of time, the cost data was normalised to the base year 2001 using the following cost data indexes: Means Historical Cost Indexes and Means City Cost Indexes for cities in Texas. Normalisation is not necessary when projects take place in the same geographical location and within the same year as the increase in construction costs is negligible during a year under normal circumstances. The data was analysed using descriptive statistics in order to gain understanding its characteristics and using single linear regression analysing to understand relationships that exist between the parameters. A Pearson product moment-correlation was also used to assess the zero-order correlations between the parameters. The final parametric cost model was. Page 18.

(24) University of Johannesburg – K. Molefi (201113613) developed using multivariate linear regression. The chosen key parameters were tested for statistical significance to ensure that they are proper cost drivers. The final parametric model, produced estimates with errors ranging from -0.8% to 13.5% although R2 was 26.1%. It does not make sense that only 26% of the chosen parameters can explain the variability in the dependent variable and yet be able to predict the costs to within such good accuracies unless the data was modified to suit a predetermined outcome.. 2.4.2 Comparison of construction cost estimating models based on regression analysis, neural networks, and case-based reasoning Kim et al. [4] in 2004 presented a research paper in which three cost estimating models were compared, namely Multiple Regression Analysis (MRA), Neural Networks (NNs), and Casebased Reasoning (CBR). Although they prove that MRA is the least accurate method when compared to the other two methods, we will only concern ourselves with MRA because it relates to parametric costing. The cost models were developed using historical cost of 530 construction projects for residential dwellings in Korea that were built by general contractors between 1997 to 2000. The cost data that was used is direct household costs and do not include any mark-up. The data was broken down into two parts; 490 data points for developing the cost model and a further 40 data sets for the testing of the cost model. For the MRA, 28% of estimates had an error that falls within 2.5% of the actual value and 73% of the estimates falling within 10%. This is a very good result and perhaps it is attributed to the very large database that was used in compiling the model.. 2.4.3 Parametric and Neural Methods for Cost Estimation of Process Vessels Caputo and Pelagagge [22] present a parametric cost model that estimates the manufacturing costs for generally large pressure vessels with complex shapes based on the engineer-to-order manufacturing principle. At the outset, 62 parameters were identified as cost drivers but these were narrowed down to 42 with the help of experts. The dependent parameter in this case is manufacturing hours. The parameters were eventually narrowed down using linear correlation hypothesis between the 43 parameter and the manufacturing hours. The nine parameters are vessel volume (V), vessel. Page 19.

(25) University of Johannesburg – K. Molefi (201113613) external surface (S), the weight of the support (PS), the weight of wall plates (PB), the total weight (PT)and the weight of the auxiliary, welding volume (VSC), nozzles welding length (SB) and heads type (CF). The parametric cost model was developed using a database of 23 vessels whilst another 45 vessels were used to validate the model. The resulting equation is shown below: NOF = K + A1 x PB+ A2 + PT + A3 x PA0.15 + A4 x V0:52+ A5 S0.95 + A6x VSC + A7x PS08+ A8x SB + A9x CF0.55. (2). The final coefficients of the above equation could not be published in the research paper due to privacy issues. The MAER obtained was 9.4%, the result which once more proves the good accuracy that can be achieved with parametric cost modelling. In this particular paper, it has been proven that parametric costing can also be used for other estimating applications such as manufacturing in this case. It seems as though the suitability of parametric costing for other applications apart from feasibility studies are possible, but very detailed and large amount of data would probably be required to achieve such a requirement.. 2.4.4 Parametric vs. neural network models for the estimation of production costs: A case study in the automotive industry Cavalieri et al. [14] present a case study in their research in which they were comparing the accuracy obtained between estimating using parametric cost estimating with using neural networks. In this research only the results of the parametric model will discussed. These researchers developed a parametric cost model that can estimate unitary manufacturing costs of a new type brake disk for a real case company in Italy. The data used to develop the models was obtained internally in the Design and Engineering Department, Procurement Department, and the Accounting Department; the data integrity therefore is very high in terms of reliability, quality, and sufficiency. Five key parameters were identified as cost drivers of the manufacturing costs of these brake disks, namely, raw disk weight, kind of material, number and type of foundry cores, type of disk, and geometric shape. Many of these cost drivers are qualitative in nature and they would need to be converted into a quantitative form to be useful in parametric cost modelling. Page 20.

(26) University of Johannesburg – K. Molefi (201113613). The results obtained in terms of the accuracy indicate a MAER percentage of 6% minimum and 15% maximum. Once more this proves the suitability of parametric cost modelling during the manufacturing phase.. 2.4.5 Road Tunnel Early Cost Estimates Using Multiple Regression Analysis In this paper, Petroutsatou et al. [10] present a parametric cost model for a road tunnel. In the field of construction, this type of a project is seen to be a high risk project due to uncertainties of the underground conditions. Data for the parametric cost model was obtained from thirty three (33) single bore line road tunnel projects constructed for the Egnatia motorway in northern Greece. A total of forty six (46) kilometres of tunnel was under consideration in this case study. Data such as geotechnical properties of encountered rock masses and the corresponding quantities of support was gathered and used to compile a database for the parametric cost model. One geometrical and four geotechnical parameters were investigated and four models were developed for steel sets and shotcrete of the primary support and for steel and concrete of the permanent support. The results of the accuracies obtained in shown in table 2.1 below. Table 2.2: Results obtained from the parametric cost model of a road tunnel [10]. The accuracy obtained ranges from 6.47% to11.54% of the actual costs. These results are astonishing for such a complex engineering field. This case study goes a long way in proving that there can never be an engineering system too complex that developing a parametric cost model for it would be impossible.. Page 21.

(27) University of Johannesburg – K. Molefi (201113613) 2.4.6 Chemical Process Equipment Cost Estimating using Parametric Models In 2006 MohammedShabani and Reza Yekta[16]in their paper titled “Chemical Process Equipment Cost Estimating using Parametric Models” refer to parametric cost estimation as a ‘shortcut method’ in estimating equipment costs fast. This view if theirs is in agreement with the view of the author in as far as the Problem Statement is concerned. Too much time is spent in organisations preparing conceptual estimates whereas there are quick methods of deriving the costs and more consistently as well. They present seven parametric models that they developed for various mechanical equipment found in a process plant. Components that were analysed were Carbon Steel Pressure Vessels, Stainless Steel Pressure Vessels, Carbon Steel Atmospheric Storage Tanks, Carbon Steel Separation Towers, Stainless Steel Separation Towers, Carbon Steel Shell and Tube Heat Exchanger BEU Type, and Oil Injected Screw Compressors. This type of equipment has a common principle of operation since they are all found in process plants and therefore the author does not expect their performance parameters to differ greatly. The key performance parameters that they identified were weight (W) in kg and operating pressure (P) in bars for most of the equipment.. Other key parameters identified were. Length/Diameter (L/D) andfor the Screw Conveyors the key parameters were power (W p) in kW and operating pressure. The data used to build the models was obtained from the Research Institute of Petroleum Industry’s (RIPI) project archives and the regression analysis was carried out using SPSS software - SPSS is statistical analysis software. Linear regression was used to derive the coefficients for the key parameters and statistical tests F, t-statistic, and confidence levels were then used to verify the derived models. The results obtained are presented in the table below. In the table, the second column contains the derived parametric equations for each type of equipment, and the third column the parameter ranges within which the parametric equations remain valid.In the fourth column is Absolute Average Deviation percentage (AAD%), a performance indicator, which indicates the overall accuracy of the parametric cost model and in the last column are the coefficients for the parameters of the regression equation. The highest AAD% produced was 37% for the Stainless Steel Separation Towers and the lowest AAD% was 4.2% for the Carbon Steel Atmospheric Storage Tank. These accuracies. Page 22.

(28) University of Johannesburg – K. Molefi (201113613) correspond to the class 4estimates for process engineering projects. An uncertainty analysis was performed using 95% and 90% confidence intervals to quantify the uncertainty involved with the parametric cost model’s coefficients. This research provides evidence of the usefulness of parametric cost models and that they can be built for various engineering systems, some complex than others. Table 2.3: Results of the Parametric Cost Model by Shabani and Yekta[16]. 2.4.7 Non-linear and Multivariate Regressions for Space Engineering Parametric Cost Models Lamboglia et al.[20]in their paper as titled in the heading define parametric estimation as: “a technique that develops estimates based upon the examination and validation of the relationships between technical, technological, programmatic, and financial aspects, using an accurate estimate from limited data available during concept formulation when only mission and performance envelopes are defined.” This description embodies the essence of what parametric cost estimating is about. However, the author has observed that usually the technological aspects are only applicable for describing the different systems used, for interpreting the results of the parametric cost model or for explaining discrepancies in the results obtained. Only those, parameters which are quantitative in nature find their way into the parametric equation.. Page 23.

(29) University of Johannesburg – K. Molefi (201113613) In this paper, two case studies were developed for the power and structure spacecraft subsystems. The function of the power subsystem is to generate power, regulate it and store itin the spacecraft for peak periods when the demand for power is high. The life of the spacecraft is limited by the solar cells and hence the battery used for this power system. The purpose of the firstcase studies was to develop a parametric cost model of the batterybased on a single quantitative parameter, battery capacity and a qualitative parameter,technology. The reason being that the cost of a battery depends highly on the battery technology used i.e. a nickel cadmium battery. 2.4.8 Parametric Cost Model – Induced Draft Cooling Towers In this paper published in 2008, a parametric cost model of the cooling towers is presented. Dysert [5] in this paper develops a parametric cost model using a trial and error method to establish the regression equation from only six projects. The ability of the results obtained from this study to be generalisedis brought into questioning given the small sample of six projectsused as well as the trial-and-error method adopted. Three key parameters were identified as cooling range, approach, and flow rate. The cooling range is determined by calculating the difference between the hot water entering the cooling tower and the cool water leaving the cooling towers. The Approach on the other hand is the difference in temperature between the cool water leaving the cooling tower wet bulb temperature of the atmosphere. The flow rate provides the cooling capacity of the cooling tower. A non-linear regression model resulted as shown below. Cost = $86,600 + $84,500(Cooling Range in Deg F).65 - $68,600(Approach in Deg F) + $76,700(Flow Rate in1000GPM).7. (3). GPM stands for gallons per minute. Astonishingly, the parametric cost model produces an error that ranges between -1.3% and 7.1%. This accuracy corresponds to a class 1 estimate for engineering projects. However, not much information has been provided in this study about the source of the cost data used to build the parametric cost model and hence the credibility of the model cannot be fully established.. Page 24.

(30) University of Johannesburg – K. Molefi (201113613). CHAPTER 3: METHOD 3.1. Introduction. The research deals with the problem associated with the disproportional time andeffort placed in producing cost estimates of engineering systems for use during conceptual stages of a project.The purpose of the research is to demonstrate the effectiveness of parametric cost estimating in producing cost estimates of engineering systems for purposes of feasibility studies.Another aim of the study is to contribute knowledge towards the advancement and understanding of parametric cost estimating. The aim of this chapter is to provide a description of how the objectivesof this research will be achieved. The method used to achieve the objectives is by undertaking an extensive secondary literature reviewof empirical research done by others on this subject. A second method used is by developing a parametric costmodel of an engineering system that will help to demonstrate the effectiveness of parametric cost estimating technique. Therefore, the aim of the sections that follow will describe the method usedfor achieving the objectives described above. The following section will discuss the type of research design employed, followed by a section on the methodology followed to obtain the research results. The limitations of the methodology adopted will be discussed followed by concluding remarks in subsequent sections.. 3.2. Research Design. The type of research design employed in this study is that of simulation/statistical modelling[23][24]. Due to the quantitative nature of the subject i.e. parametric cost modelling, the research design lends itself to the simulation/statistical modelling research design by default.At the heart of parametric cost modelling is a statistical technique known as regression analysis. In this research study a linear multiple regression analysis is used. It shall be proven that the parametric cost model developed has the capability to produce cost estimates relatively quickly, consistently, with ease, and with acceptable levels of accuracies required for feasibility studies. As discussed in the literature review chapter, the accuracy of a feasibility study conforms to a Class 4 estimate as defined by the AACE International. The researchwill also demonstrateby way of a case studyhow to develop a parametric cost model for most engineering systems where key performance parameters of the system are known; this is. Page 25.

(31) University of Johannesburg – K. Molefi (201113613) usually the case during the feasibility study stages of a project and the system will be simulated to resemble this stage of a project. An advantageof using this type of research design for the study underway is that due to the fact that engineering systems are generally complex in nature, statistical modelling will help simplify the complexity of the system being studied[24].Simplifying the system helps with understanding the relationships that exist in the systemand to be able to predict parameters better[23]. Another advantage is that large-scale modelling of data is possible. The premise of the research is to prove that the parametric cost estimating technique can be used on most engineering systems to produce cost estimates with acceptable accuracies for use in feasibility studies. Therefore it is highly advantageous that the type of research design chosen is supportive of this. On the other hand, the weakness of using this research design isthat it relies heavily on the availability of sufficient good quality data tobuild and test the model. Another weakness is that the research design requires statistical skills to be able to interpret the results obtained[24]. Kim et al [4]in their paper quote other authors who provided four disadvantages of using regression analysis, which is at the heart of the research design in this research. Firstly they claim that there is no clear method available to guide estimators to choose between the cost models that fit the historical data in the case of different costing applications. However, this concern does not affect this research since the parametric cost model will be developed only for one application i.e. estimating costs for feasibility studies. Secondly they question why an assumption has to be made about certain types of multiple equations and their data being suitable for regression equations.Another disadvantage they mention is that the method becomes difficult with in increasing number of input variables and that these variables need to be previewed in advance. This disadvantage does not apply to this research because during the feasibility stages not much information is available on the specifications of the system; therefore, the number of variables at this stage is at a minimum level. Having mentioned the strength and weaknesses of the chosen research design, there is absolutely no doubt that simulation/statistical modelling technique is the most suitable design for this research.. Page 26.

(32) University of Johannesburg – K. Molefi (201113613) 3.3. Methodology. The research design described above for this study is that of simulation and statistical model. Therefore, two things were performed in the research; firstly an engineering system that has data readily available was used to simulate the conditions which resemble a project in the feasibility study stage. Secondly, this engineering system was then used to develop a parametric cost model for predicting costs of similar systems. The purpose of the case study is to provide a practical approach to developing a parametric cost model using regression analysis. As a result, the approach employed was to analyse a system which is reasonably understood in the engineering field and for which data on the different system costs is readily available from public sources. Such a system is the passenger motor vehicle. The different systems referred to above include the different types of vehicle makes with their differing specifications. It has been assumed in the study that the key performance parameters of a motor vehicle are represented by the data published in car magazines when the retail value of the different vehicles is compared based on technical specifications. All the parameters considered are quantitative; the effect of qualitative parameters are ignored in this study as it the object of the study to prove that an acceptable level of accuracy can be obtained in estimating system costs (in this case motor vehicle retail values) even when qualitative factors are not considered. The motor vehicle models selected in the case study do not fall into the category of any sophisticated technology such as hybrid models in order to ensure that the qualitative parameter of technology does not have a significant effect on the value of the vehicles.. 3.3.1 Research Instruments Due to the difficulties that are normally experienced in many quantitative research studies in obtaining sufficiently good andreliable data to use in the research, it has been the strategy of this research to steer clear of this obstacle and use good quality data that is readily accessible. The criterion for choosing a system was to focus on a system whose key performance parameters and cost data arepublicly available in the retail market. There was really no need to focus on modelling an industrial system since there are many engineering systems that are available in the public domain that could be analysed with ease due to the availability in part due to what has already been mentioned above about data integrity. The main problem the research. Page 27.

(33) University of Johannesburg – K. Molefi (201113613) is addressing is that there are some engineering systems that are so complex that it is impossible to develop a meaningful cost model based on the system’s performance parameters for purposes of conducting feasibility studies. Hence it is the objective of this research to prove that a parametric cost model can be developed for almost any engineering system whose key performance parameters are available during feasibility study stages. The research instrument used in this study to obtain data for developing the model is a car magazine publication. A car magazine provides a large database of different motor vehicle models with different specifications that can be used as key system performance parameters. In addition, cost information in the form of motor vehicle retail price for a brand new motor vehicle is provided. The motor vehicle is a very sophisticated engineering system especially nowadays when technology has advanced so enormously in the automobile field. A particular magazine was used in building the database of vehicles used in this research, namely, Car. Car magazine is one of South Africa’s leading car magazines and it contains upto-dateand reliable information on new vehicle models. The data available in the Car magazine was randomly verified against the information published on the various vehicle manufacturers’ websites. This kind of data therefore meets all the requirements for data integrity as the information is readily available from reliable sources and cannot be tempered with. Even some of the retail prices were verified from the vehicle manufacturers’ websites and the discrepancies that existed could not even equate to a 10th of a percentage. Therefore, thedata used for the parametric cost model can be taken to have 100% integrity. The choice of this engineering system is in line with the strategy of this study as mentioned above. Whilst a challenge with many engineering systems is to obtain a sample population large enough for statistical analyses, the motor vehicle in this instance does not suffer from the challenge as data is readily available and accessible.. 3.3.2 Data 3.3.2.1 Collection of data The data that was obtained from the Car magazine publication is the primary data used in this research to develop the parametric cost model. A total ofeighty (80) vehicle models were selected from the car magazine and used for developing the parametric cost model such that the final database is equally representative of all the model engine power for the power ranges. Page 28.

(34) University of Johannesburg – K. Molefi (201113613) involved. Sixty (60) of the vehicle models were used to build the parametric cost model whilst an additional fifteen (15) vehicle models were used for the testing of the parametric cost model.A further five vehicle models were used to test the parametric cost model beyond the parameter limits. Before I proceed in detailing the kind of information that was used to build the database, perhaps it is imperative at this stage to take a step backwards and put things in perspective. 3.3.2.2 Assumptions and simplifications made to the data In essence what has been donein the study is that the motor vehicle data obtained from the car magazine was used to simulate an engineering system which is still in the “development phase”, viz. in the feasibility study stage. What we know about feasibility studies is that at this stage of the lifecycle of any system, very little information is known about the system. Complete system specificationsare not yet available as the system has not yet been fully developed; only performance parameters of the envisaged system are known at this point and are not sufficient to produce detailed cost estimates. On the other hand, the data contained in the car magazine is for a fully developed system. However, to simulate a condition that closely resembles that of a feasibility study, many of the quantitative vehicle specifications available in the car magazine were left out. Only those specifications that were deemed to be typical of the kind of information available during feasibility study stages were included in the parametric cost model database as the key performance parameters. 3.3.2.3 Selection criteria of key parameters The criteria used to select these key parameters were based on the experience of the author in dealing with feasibility studies. The information available is usually just basic information about the overall performance characteristics of the system such as the conveyor design throughput in tons per hour, running length in metres of the conveyor, overall conveyor lift in metres etc. So for our parametric cost model, the criterion was to select the most basic information about the vehicle but yet which still had some effect on the performance of the vehicle. In Table 3.1 below I present all the quantitative specifications presented in the car magazine. The specifications I chose that I believe are representative of the kind of information that would be available during a feasibility study stage are highlighted in yellow.. Page 29.

(35) University of Johannesburg – K. Molefi (201113613) Table 3.1: Motor Vehicle Specifications Published in the Car magazine Engine. Engine Capacity. Max Power. Acceleration 0. -. 100 Max Speed. km/h. Power/mass. Engine. ratio. Torque. Fuel. Number. Consumption of Airbags. Amount. of. Transmission Gears. CO2. The key performance parameters of a motor vehicle that I have selected against the vehicle retail price are: •. Engine maximum power,. •. Vehicle maximum speed,. •. Vehicle acceleration from 0 – 100 km/h,. •. Engine capacity, and. •. Engine torque.. A process of elimination and engineering logic was used in deciding on the key parameters given the available data as follows: •. Engine Capacity – likely.It is related to the engine maximum power because the bigger the capacity the more the power produced.. •. Engine max power – most likely.To the author this represents the design throughput in the conveyor belt example.. •. Power/mass ratio – most likely. However, this information is not provided formost vehicle. models listed. Moreover, it is the opinion of the author that this parameter would. not be. known during the feasibility stages. •. Engine max torque – most likely. It is related to engine power and it is also commonly referred to when talking about vehicle performance.. •. Amount of transmission gears –likely. However, according to the author this kind of information would only be available after the detail design phase.. •. Acceleration from 0 – 100 km/h. Most definitely–This is the most referenced performance parameter in any vehicle performance conversation.. •. Maximum speed. Most likely –This is also referenceda lot in vehicle performance discussions.. Page 30.

(36) University of Johannesburg – K. Molefi (201113613) •. Fuel consumption – likely. Big engines produce big power and consume more fuel. However, this parameter is unlikely to be available at feasibility stage.. •. Number of airbags –not likely.. •. CO2 emissions – not likely.. Although many of these parameters are related, only a few would be known in the early stages of the development of the system viz., Engine Power, Engine Torque, Engine Capacity, Acceleration, and Maximum Speed. However, these parameters were tested for statistical significance before including them in the final parametric cost model, the details to follow in the results chapter. The test that was used to test the statistical significance of these parameters is contained in the next subsection 3.3.3. In addition, Khan and Manarvi[25] in their research paper titled “Selecting a Spots Car through Data Mining of Critical Feature” were able to come to the conclusion that the vehicle parameters that have an influence on superior performance, which correspond to my designation above are Retail Price, Engine Capacity, Engine Power, and Top speed. This is piece of information is used as a guiding principle to indicate that we are headed in the right direction. 3.3.2.4 Characteristics of the selected data This section describes the characteristics of the data obtained and used in developing the parametric cost model. The full database of motor vehicle models is contained in Appendix A. Please note that the different vehicle models are referred to as systems; the exact description of the vehicle model has no significance on the outcomes of the research. The aim of this section is to discuss the method followed when selecting the data i.e. the criteria used to select the vehicle models and rationale behind the criteria.The criteria that was used in selecting the models was based on the model’s maximum engine power output. The vehicle models were selected in such a manner that at the end there will be equal number of vehicle models in an interval of 30 kW starting from the lowest power vehicle model to the highest in the database. The rationale forusing this criterion was to ensure that that all vehicle models are represented equally in the database as far as the engine power is concerned. Emphasis is placed on engine power by the author as he believes it is the single most-weighing parameter on the retail price of a vehicle in the database of the three selected key parameters.The resulting histograms are presented in Figure 3.1 to 3.5 below.. Page 31.

(37) University of Johannesburg – K. Molefi (201113613). Histogram - Engine Power Frequency of Occurence. 12 10 8 6 4 2 0 51 - 80. 81 - 110. 111 - 140 141 - 170 171 - 200 201 - 230 Engine Power [kW]. Figure 3.1: Engine Power Histogram. Histogram - Maximum Speed 16. Frequency of Occurence. 14 12 10 8 6 4 2 0 141 - 160. 161 - 180. 181 - 200. 201 -220. 221 - 240. 241 - 260. > 261. Maximum Speed [km/h]. Figure 3.2: Maximum Speed Histogram. Page 32.

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