It is a fundamental human characteristic that a person engaged in a repetitive task will improve his performance over time. If data are gathered on this phenomenon, a curve representing a decrease in effort per unit for repetitive operations can be developed. This phenomenon is real and has a specific application in cost analysis, cost estimating,or profitability studies related to the examination of future costs and confidence levels in an analysis. It could be used in estimating portions of a project, such as the production of magnets for the supercollider. This chapter discusses the development and application of the learning curve.
The aircraft industry was the first to develop the learning curve. Based oncomparison of manufacturing and aircraft industry learning curves, it is evident that a typical curve exists. It is an irregular line that starts high, decreases rapidly on initial units, and then begins to level out. The curve shows that there is progressive improvement in productivity but at a diminishing rate as the number produced increases. Figure 21-1 shows the appearance of the curve.
Thissuggests an exponential relationship between productivity and cumulative production. When this data is plotted on log-log paper, the data plots as a straight line. This suggests the relationship of the form:
21-2 EN = KNS
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where EN = effort per unit of production (i.e., manhours) to produce the Nth unit K = constant, which is the effort to produce the first unit s = slopeconstant, which is negative since the effort per unit decreases with production. The above relationship will plot as a straight line on log-log paper. Take the logarithms of both sides, log EN = s x log N + log K which is the equation of a straight line Y = sX + b where Y = log EN, X = log N, and b = log K. Figure 21-2 represents the data on log-log paper.
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3.LEARNING CURVE FROM SINGLE-UNIT DATA
If the effort is available for each unit produced, any one of three curves can be plotted. They are the unit, the cumulative total, and the cumulative average. Following is Table 21-1, which includes single-unit data.
TABLE 21-1 PRODUCTION DATA ____________________________________________________________
_____________________ ITEM UNIT HOURS CUM. TOTALHRS CUM. AVG. HRS
________________________________________ 1 2 3 4 5 6 7 8 9 10 10.0 8.0 7.3 6.3 6.0 5.6 5.6 5.0 5.1 4.5 10.0 18.0 25.3 31.6 37.6 43.2 48.8 53.8 58.9 63.4 10.0 9.0 8.4 7.9 7.5 7.2 7.0 6.7 6.5 6.3
From this data the unit,cumulative total, and cumulative average curves can be drawn. A. Unit Curve If a set of data is available for the effort required for single, individual units of production, the data can be plotted on log-log paper and the best line drawn with the eye. Having established the best line, any two points on the line can be used to determine, graphically or analytically, the slope of the line and K, whichis the intercept at N = 1. This graphical method is quick, but it may require judgment when the data points are scattered. The most accurate method for determining the best straight line is to use the least squares method. B. Cumulative Total Curve For this curve, the effort is described as cumulative total. This curve produces a line with a positive slope.
21-4 C. Cumulative Average CurveDOG 430.1-1 03-28-97
The effort calculated for this curve is the cumulative average for each unit. It produces a curve that is usually a more regular curve than the unit curve.
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EFFECTS OF DOUBLING PRODUCTION
The equation, EN = KNs, implies a constant fractional or percentage reduction in effort for doubled (or tripled, etc.) production. For...