Page 278 - Industrial Process Plant Construction Estimating and Man Hour Analysis

Statistical applications to construction Chapter 12 257

Analysis of the historical data, for Waste Heat Boiler erection at project 1, unit 1,
spent 18,967 man-hours. Estimate the total man-hours to erect the four units, units
1–4, if the learning curve has a slope of 85%.

h i
ð 1þbÞ ð 1þbÞ
ð
ð
TM,N ¼ H1= 1þbފ N þ0:5Þ M 0:5Þ
½
ð
Value for b: b = log (S/100)/log (2) where S is slope convert to decimal
b = log(85/100)log (2) = log (0.85)log (2) = 0.02125
then, 1 + b =1 0.02125 = 0.9787
Compute H1 using Hn = Hm (n/m) b; H1 = (18,967) (1/4) ^ ( 0.02125) =
^
19,534
^
^
Calculate TM, N =[H1/(1 + b)][(N + 0.5) (1 + b) (M 0.5) (1 + b)], with N =4
and M =1
^
TM, N = (19,534)[(4.5 (0.9787)) ((0.5 0.9787))] = (19,534)(3.8507) = 75,219
^
man-hours
Actual historical man-hours to install the four units is 66650; results in a 11.39%
saving due to learning.
12.8.2 Linear regression—Fitting U model to unit historical data for
waste heat boiler erection
Where

^
y ¼ ax b
y ¼ hours required for the nth unit of production
a ¼ hours required for the first unit
b ¼ natural slope
The power function y ¼ ax b is transformed from a curved line on arithmetic
^
scales to a straight line on log-log scales; let

y ¼ log y
a ¼ log a
x ¼ log x

taking logarithms of both sides, log y ¼ log a + x log b, appears like, y ¼ a + bx
(Table 12.8.1).