Page 292 - Industrial Process Plant Construction Estimating and Man Hour Analysis

272 Appendix B

Method of least squares
Least-square line
The least-square line approximating the set of points (x1, y1), (x2, y2) … (xn,
yn) has the equation
y ¼ bx + a
where
b¼the slope of the line
a¼y-intercept
The best fit line for the points (x1, y1), (x2, y2) … (xn, yn) is given by
y y ¼ bx xð Þ
where the slope is

2
b ¼ Σ xi xð Þ yi yÞ=Σ xi xÞ
ð
ð
and the y-intercept is
a ¼ y bx
Formula correlation coefficient r:
h ih i
P P P P 2 P 2 P 2 P 2 1
ð
r ¼ nð XYÞ ð XÞð YÞ= n X ð XÞ n y ð YÞ 2
^
Define the U model: Hn¼H1 (n b)
where
Hn¼hours required for the nth unit of production
H1¼hours required for the first unit
^
Natural slope b is defined by the formula S¼10 blog(2)+2 logarithm to
base 10
Prediction for the total hours for a “block” of production

Define man-hours for a block of erection as the total man-hours required to erect
all units from unit M to another unit N, N>M.
TM, N is defined as

^ ^ ^ ^
TM,N ¼ H1 M b+ M+ 1ð Þ b+ M + 2Þ b+ ⋯ +N b
ð
Approximation formula:

^ ^
ð
TM,N ¼ H1= 1+ bފ N+0:5Þ 1+ bð Þ M 0:5Þ 1+bÞ
ð
ð
½
ð
Linear regression—Fitting U model to unit historical data
^
y ¼ ax b