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The interdependence of a job consisting of 7 activities & time estimates are given in following table.
written 6.9 years ago by gravatar for teamques10 teamques10 ★ 68k •   modified 2.8 years ago

Mumbai University > Civil Engineering > SEM 8 > Construction Management

Marks: 12M

Draw Network & Determine:-

1) Project duration corresponding to 50 % probability.

2) Probability of completing the project in 35 days.

Z -3 -2 -1 0 1 2 3
P(%) 0.13 2.28 15.87 50 84.13 97.72 99.87
construction management
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written 6.9 years ago by gravatar for teamques10 teamques10 ★ 68k
Activity Preceding Activity Succeeding Activity $T_0$ $T_m$ $T_p$
A - C &E 6 9 12
B - D & E 5 8 17
C A G 4 7 22
D B G 4 7 16
E A - 4 7 10
F B - 2 5 8
G C & D - 4 10 22
Activity T0 Tm Tp $t_e=\frac{t_0+4t_m+t_p}{6}$ $\sigma = \frac{t_p-t_0}{6}$ $\sigma^2$
A 6 9 12 9 1 1
B 5 8 17 9
C 4 7 22 9 3 9
D 4 7 16 8
E 4 7 10 7
F 5 8 5
G 4 10 22 11 3 9
$\sum\sigma^2=19$

Step 2:

enter image description here

Project duration = 29 Days

Critical path = A-C-G =10-20-40-50

Step 3:

Probability % = 50 %

For probability 50 % the scheduled time will be same as that of the project duration.

∴ Duration= 29 Days

Probability of completing the project in 35 Days

$\mathcal{Z}=\frac{\text{Scheduled Time-Project Duration}}{∈}$

S.T.= 35 Days

P.D.= 29 Days

$∈=\sqrt{σ^2}=\sqrt{19} = 4.36$

$\mathcal{Z} =\frac{35-29}{4.36} =1.376$

By interpolation,

enter image description here

$\boxed{\therefore P\% = 89.23\%}$
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