W7.0_FZ_Cost Estimating Relationship (CER)

1. Problem Definition

Company had planned to build Fuel Storage Tank with capacity 40.000 KL on Center of Java Province. In association with efforts preparation of the Owner Estimate for the Fuel Storage Tank construction project, the Author requires price data from Carbon Steel Gate Valve of API 600.

For that, the Author had asked for vendor quotation from five company, but not all the needs that we ask for can be met by vendors so a further estimation process is needed to find out the price of valves with sizes 1 and 10 inches.

2. Feasible Alternative

The Author used the Unit Technique which involves using a per-unit factor that can be estimated effectively. For this case, it would be selected diameter as unit factor.

To conduct the estimation process, Parametric Cost Estimation will be applied to find the desired value by utilizing statistics to derive CERs. Parametric Cost Estimating is a method of predicting costs utilizing historical cost data and statistical techniques [1]. This section below, describes two commonly used estimating relationships, namely:

• Power-Sizing Technique

The power-sizing technique, which is sometimes referred to as an exponential model, is frequently used for developing capital investment estimates for industrial plants and equipment. This CER recognizes that cost varies as some power of the change incapacity or size. That is [1],

* This may be calculated or estimated from experience by using statistical techniques.

• The Learning Curve

A learning curve is a mathematical model that explains the phenomenon of increased worker efficiency and improved organizational performance with repetitive production of a good or service. The learning curve is sometimes called an experience curve or a manufacturing progress function [1].

The basic concept of learning curves is that some input resources (e.g., energy costs, labor hours, material costs, engineering hours) decrease, on a peroutput- unit basis, as the number of units produced increases. Most learning curves are based on the assumption that a constant percentage reduction occurs in, say, labor hours, as the number of units produced is doubled. [1]

Although the two CERs above are commonly used, in principle the CER Equation can be developed by utilizing statistic from the data collected. Table 1 lists four general equation types commonly used in CER development. A simple, yet very effective, way to determine an appropriate equation form for the CER is to plot the data. If a plot of the data on regular graph paper appears to follow a straight line, then a linear relationship is suggested. If a curve is suggested, then try plotting the data on semilog or log-log paper. If a straight line results on semilog paper, then the relationship is logarithmic or exponential. If a straight line results on log-log paper, then the relationship is a power curve [1].

Table 1. Typical Equation Forms

3. Develop The Outcomes For Each Alternative

The following are the results of vendor quotations from five companies and the author processes the data using the average method to obtain prices that can represent each unit.

Table 2. Vendor Quotation

As mention on step 2, the Author will develop the curve from plotting between Diameter of Valve and Price. The curve will be drawn in regular graph, semilog and log-log paper, whichever produces a straight line is preferred.

Figure 1. Plot Diameter of Valve vs Price in Regular Graph

Figure 2. Plot Diameter of Valve vs Price in Semilog Graph

Figure 3. Plot Diameter of Valve vs Price in Log-Log Graph

4. Selection For Applicable Criteria

Once the CER equation has been developed, validation can be accomplished with statistical “goodness of fit” measures such as standard error and the correlation coefficient. There are two methods that can be used to validate, namely [1]:

• The standard error (SE) measures the average amount by which the actual cost values and the predicted cost values vary. The SE is calculated by

where Cost_i is the cost predicted by using the CER with the independent variable values for data set i and yi is the actual cost. A relatively small value of SE is preferred.

• The correlation coefficient (R) measures the closeness of the actual data points to the regression line (y = b0 + b1x). It is simply the ratio of explained deviation to total deviation.

Values of R close to one (or minus one) are desirable in that they indicate a strong linear relationship between the dependent and independent variables.

For this case the author will choose the Correlation Coefficient (R). The CER equation that has the closest R value to one will be selected.

5. Analysis & Comparison Of Alternatives

From Figure 1, 2 and 3, it can be concluded semilog and log-log graph are preferable to produce straight line. The following is the result of the validation by finding the R square of the conditions below:

1. Regular Graph : Linear relationship (Figure 4)
2. Semilog           : Logarithmic or exponential relationship (Figure 5 and 6)
3. Log-log           : Power relationship (Figure 7)

Figure 4. Linear Regression in Regular Graph

Figure 5. Exponential Regression in Semilog Graph

Figure 6. Logarithmic Regression in Semilog Graph

Figure 7. Power Regression in Log-log Graph

To enrich the analysis that has been made, the author will add polynomial relations to the regular graph as shown in Figure 8, 9 and 10.

Figure 8. Polynomial 2^nd order Regression in Regular Graph

Figure 9. Polynomial 4^th order Regression in Regular Graph

Figure 10. Polynomial 6^th order Regression in Regular Graph

6. Selection Of The Prefered Alternatives

From all the curve that has been made, the following is a summary of all the data.

Table 3. Summary R² of Regression

From table 3 it can be concluded that the 6th order polynomial regression on a Regular Graph has the R value that is closest to one, so this relation is chosen as the CER equation.

7. Performance Monitoring & Post Evaluation Result

With R value so close to one, the price of valve developed using CER can be used in the actual project. The CER should be validated using another price from other times to ensure the robustness of CER.

Reference

1. Sullivan, W. G., Wicks, E. M., & Koelling, C. P. (2019). Engineering economy. Pearson Higher Ed. Chapter 3 – Cost-Estimation Techniques, pp129. Problem 3-21 & 3-22
2. PTMC & Giammalvo, P. D. (2021). 1.4.1.10 unit 10- Managing Cost Estimating and Budgeting. Retrieved from https://build-project-management-competency.com/1-4-1-10-unit-10/
3. Yonathan, S. (2023, June 23). W2.0_sy_estimating carbon steel (Cs) pipe prices for small diameter size api 5l grade B cs pipe using parametric model to develop CER. RETRO MERCI. Retrieved from https://retromerci2023.wordpress.com/2023/06/24/w2-0_sy_estimating-carbon-steel-cs-pipe-prices-for-small-diameter-size-api-5l-grade-b-cs-pipe-using-parametric-model-to-develop-cer/
4. Hastak, M. (2015). Skills & Knowledge of Cost Engineering (6th ed.). AACE International. pp. 106-109
5. Irawan, Harnadi.(2015). W2_HI_Cost Estimating Relationship (CER) Application to Develop Cost Estimate Quickly from Historical Data. Retrieved from https://garudaaace2015.wordpress.com/2015/03/05/w2_hi_cost-estimating-relationship-cer-application-to-develop-cost-estimate-quickly-from-historical-data/