LEARNING CURVE APPLICATION IN FORMWORK CONSTRUCTION

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INIRODUCTION

Out of each dollar spent on cast in place concrete, formwork is a major portion, ranging from 35% to 60% of the total concrete cost depending on the type of structure. Formwork costs are made up of labor, equipment and material. Of these, formwork labor is the most important and can contribute up to 50% to the total formwork cost. This means that formwork labor can be as much as 30% of the total concrete cost, and can easily impact the profit or loss of a project.

Research and experience have shown that repetition can improve labor productivity. Contractors and designers can reduce formwork labor costs by creating repetition on the job [2,3,6]. This repetition increases productivity and contractibility, hence increasing the contractor's profit and saving the owner money. The more the number of repetitions, the higher the average productivity rate.

Learning curve theory can be used to investigate the effect of job repetition on the production rates. In this research, a straight-line learning curve model is utilized to quantify formwork productivity improvement. At first, the theory of learning curves is briefly presented and the straight line model introduced. Then the construction project used in this case-study is described. The developed learning curves are discussed and the impact of repetition on labor productivity is quantified. Quantifying the effect of repetition can help estimators to prepare more accurate bids for future projects.

LEARNING CURVES

The time required to complete a certain activity several times decreases as the number of repetitions increases. For example, if a carpenter takes 2 hours to install the first window in a house, he might install the second window in 1.75 hours and so on. Thomas et al [8] mention several reasons for this improvement in productivity. The most important ones are: increased worker familiarization, better crew and equipment coordination, improved organization, and development of more efficient work methods and material supply systems. According to the theory of learning curves, whenever the number of products doubles, the average man-hours or cost per product will decline by a certain percentage of the previous average rate. This percentage is called the learning rate, and establishes the slope of learning curve. The lower the learning rate, the higher the amount of productivity improvement.

Straight-Line Learning Curve Model

Several mathematical models have been developed to show the variation of productivity rates (or cost) with the number of units produced. Straight-line, linear piecewise, exponential and cubic models are examples of learning curve models. The straight­line model is most widely used in construction [1,4,5]. In the straight-line model, the learning rate is constant. When this curve is plotted on a log-log scale, it transforms to a straight line. The model is expressed as follows [8]:

Y = Ax ^–n                          (1)

where Y = cumulative average man-hours (cost) per unit of product, A = man-hours (cost) required for the first unit, x = the sequence number and n = slope of the logarithmic transformation of the learning curve. The learning rate is as follows

[8]:

S = 2^-n                              (2)

For a given job, n is constant and so the learning rate is constant as well. The expected range of learning rate for construction operations falls between 70% and 90% [5].

Figure 1 shows a 70% and a 90% learning curve. It shows that if a hypothetical product follows the 70% learning curve and if constructing the first unit takes 10 hours, then it will take 10 x 70% = 7 hrs/unit on average to construct the first two units and it will take 7 x 70% = 4.9 hrs/unit on average to construct the first four units and so on. It is apparent that the productivity gains due to learning decrease as the number of built items increases. In other words, a stabilization in the production rate is achieved after complete familiarization with the job. Still it should be noted that the learning rate remains constant during the whole process. As the logarithmic version of this learning curve model is a straight­line, it is easier to compare curves with each other. The straight-line model is used in this study to quantify the effect of repetition on formwork productivity.

PROJECT DESCRIPPION

The project studied was King County Correctional Facility located in Seattle, Washington. This correctional facility is the largest of its kind on the west coast and consists of 600,000 square feet. The building was designed as four interrelated, tiered towers with a ductile reinforced concrete frame. The west tower or wing is 8 stories high; the south wing is 16 stories; the east wing is 18 and the north wing is 20 stories high. The project

contains 3,000 tons of reinforcing steel and 23,000 cubic yards of concrete. The architect was NBBT and the contractor was Hensel-Phelps [6,7]. The project was completed in 1985.

Spandrel Beams

The writers studied the formwork for spandrel beams of this building. The objective was to investigate the effect of variations of the spandrel beam cross-sections on the project cost. Spandrel beams were the most variable structural component in this project. There were 59 different sizes and shapes of spandrel beams in this project. For example, there were 13 different spandrel beams' cross­sections in the 7th floor [2,6]. But in floors 9 through 18, the design repeated itself, requiring only five or six types of spandrel beams. On these floors, labor productivity (sq. ft/man-hour) rose by 25% compared to the average productivity for forming all spandrel beams in the building.

As part of the study on spandrel beams a learning curve analysis was performed on formwork productivity. Since beams in the project varied drastically from floor 1 to 8, it was decided to exclude them from learning curve analysis. Therefore the learning curves were constructed for the formwork productivity for spandrel beams from floor 9 to 18. On these floors the formwork activities were continuous, the formwork crew did not change and formwork configurations were reasonably similar. Two types of learning curves were developed in this process. One type of curve was based on unit data and the other one on cumulative average data. In preparing unit data, the productivity rate at each floor was plotted against the floor number. In the cumulative average curve, the cumulative average productivity rate up to each floor was computed and plotted against the floor number. The cumulative average approach tends to smooth out the data and generally makes the data appear better by reducing the amount of variation as compared to the unit data [8]. Thomas et al [ 8 ] suggest that the unit data curve be used for controlling current operations, and detecting short-term changes. The cumulative average curve, on the other hand, can be used for estimating purposes. Table 1 shows the data used in plotting learning curves for spandrel beams. Columns (2) and (3) were used in plotting Figs 2 and 4 (unit data) and columns (2) and (4) were used in plotting Figs. 3 and 5 (cumulative average data).

Curves were fit to the plotted data using the method of least squares. Figures 4 and 5 are logarithmic curves and hence are straight lines because straight-line models were used. The coefficient of determination (R²), correlation coefficient (R) and learning rate (S) were computed for this data set (Table 2). Large values of the coefficient of determination indicate that the independent variable explains most of the variance associated with dependent variable. In this case, the large R² shows that the straight line model is an appropriate model for the data. Also note that the learning rate for this job (i.e. 88% cuimnulative, 84% unit) falls in the range of learning rate expected for construction operations (70% to 90%) [5].

Elevator Core Walls

Learning curve analysis was also conducted on the formwork for the elevator core walls of the building [6]. Elevator core walls were chosen because they were continuous, repetitious and performed by the same crew. There was a major change in the core wall configuration in floor 9 which resulted in a different plan view. For this reason, the core wall was constructed in two stages. The first stage was from floor 1 to 8 and the second stage consisted of constructing the core walls in floors 9 to 15. Discontinuity or change of work scope has a profound effect on the learning curve. This point is proven in this case because after the data was plotted it became apparent that fitting one curve to all data (floors 1 through 18) would result in a very low coefficient of determination. Therefore two learning curves were fit to the data using Table 3.

columns (2) and (3) of Table 3 were used in plotting Figure 6 which shows the best curves fitted to the data using least squares. This is a classical configuration of a learning curve for discontinuous or interrupted activities. Columns (2) and (4) of Table 3 were used to plot Figure 7 which shows the learning curves for the cummalative average data. Values of R², R and S were computed and presented in Table 4. R² is rather low for unit data, especially for floors 1 to 8. One reason for this can be that the straight-line model is not the best model to use in this case. Another reason for the low R² is the few number of data points. Note that the learning rate, S, is still within the 70% and 90% limits. Also note that the values of R and R² are very high for the cumulative average data. This could be expected also because by averaging the data, the variations of the single data points were eliminated.

CONCLUSION

Productivity gains due to work repetition was quantified using a straight-line learning curve model. The developed equations can be used as a forecasting tool in similiar projects. More data is needed for developing reliable forecasting systems, while the methodology would be similar. Referring to the data presented in Table 1, it is seen that an average productivity of 0.178 manhours/square foot was realized on spandrel beam formwork in floors 9 to 18. This is 33% "better" than the productivity rate achieved on floor 9 (i.e. .272 manhours/square foot). Estimators should take the effect of learning curves into consideration to prepare more accurate bids.

The choice of the most appropriate learning curve model is very important. Low value of R² in the core wall analysis suggests that the straight-line model might not have been the best model to be used in that case. Also, changing the plan view and intern.ption in the construction process affected the learning curve drastically. So the learning curve analysis would be more valid in cases where there are rather a large number of repetitions and the products are alike. Also, the high value of R² in core walls when working with cumulative average data reveals the power of cumulative average data in soothing out the variations. So this type of data should be used with care and preferrably as a complement to unit data analysis. In the case of core walls, the average productivity rate in formwork construction in floors 1 to 8 improved by 40% compared to the first floor and in floors 9 to 15 improved by 47% compared to floor 9 (Table 2). Also note that in almost all the developed learning curves, the productivity rates dropped in the last few cycles. Authors' experience shows that in most construction jobs this happens due to the time allocated to finishing and cleaning small items of work that might have remained from earlier cycles. These times are usually reflected in the productivity reports of the last few days or weeks.

ACKNOWLEDGEMENT

REFER NOTES