The three-time estimates of a PERT activity, i.e. optimistic time, pessimistic time and most likely time, are 7 min, 13 min and 9 min, respectively. The expected time (in minutes) and the variance of the activity will be:

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HPCL Engineer Mechanical 04 Nov 2022 Official Paper (Shift 2)

Answer 1

Concept:

Expected time in a PERT activity is given by:

\({T_e} = \frac{{{t_o} \;+\; {t_p}\; +\; 4{t_n}}}{6}\)

Standard deviation,

\(σ = \left( {\frac{{{t_p} - {t_0}}}{6 }} \right)\)

variance = σ²

where,

to = Optimistic time, tp = Pessimistic time, tm = Most likely time

Calculation:

Given:

to = 7, tp = 13, tm = 9

TE = \(7~+~4 \times 9~+13\over 6\)

TE = 9.33 min

So,

\(\sigma = \frac{{13 - 7}}{6} = 1\;min\)

So, variance = 12 = 1

26 June 1

Optimistic time: It is the shortest possible time in which an activity can be completed if everything goes exceptionally well.
Most likely time: It is the time in which the activity is normally expected to complete under normal contingencies.
Pessimistic time: It is the time which activity will make to complete in case of difficulty. It is the longest of all the tree time estimates.