There are three different estimates of activity duration in PERT: 1. Positive 2. Cynical 3. Most Likely.

1. Positive time, expressed together ‘to‘,represents calculation of minimum possible time through which an activity can be completed assuming that every little thing is in order follow to the plan and there have the right to be just minimum amount of difficulty.

2. Cynical time, expressed together ‘tp’ represents estimate of maximum feasible time through which an activity can be perfect assuming the things may not it is in in accordance through the plan and also there can be incidence of challenges in delivering out the activity.




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3. Most most likely time, expressed together ‘tm‘, represents estimate of time because that completion of an activity, i m sorry is neither positive nor pessimistic, assuming the things need to go in a typical way, and also if the activity is repetitive several times, in many of the cases, it will be completed with time represented by t.

From the above three different estimates, PERT argues work the end of the expected time, expressed as ‘te‘ assuming that the probability distribution of the activity duration follows beta-distribution and, thus, dare is the median of to tp and also tm calculate as,

te=to + 4 x tm + tp /6

This averaging is described with the presumption that, for every activity, as soon as the tij is estimated 6 times, the sample of such estimated time will be once t0 four times tm and, again, when tp. This have the right to be illustrated in a time range as follows when to = 3, tp = 9 and also tm = 6 then, together per the formula,


te =to + 4 x tm + tp/6= 3+ 24 + 9/6 = 6; as soon as the three estimates are put in time scale.

Three estimates, as above, when placed in time scale, will show up as:

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When the probability complies with beta distribution (as suspect in PERT), and also in the range of time, time systems 12 to represent 100 every cent probability, then time systems 6 is 0.5 or 50 every cent probability. The most likely estimate is a probability that 0.5. As we have noted in the averaging formula the weightage because that to tm and also tp room 1, 4, and 1, respectively.


The 0 to 2 in the time scale representing 1/6 th = 0.17, 2 come 6 is 0.33, 6 to 10 is 0.33 and also 10 to 12 is 0.17. Therefore, the probability of tm will certainly lie in between 2 to 10 i.e. 0.33 + 0.33 = 0.66.

PERT considers car as an ext probable time estimate for tasks and climate the network construction and the crucial path is attracted considering te-s for the respective activities.

The estimate of te as described here is an ext reliable as it takes right into account the longest and the shortest feasible time estimates additionally and it gives a probability the 50 per cent.

Once the dare is settled for each of the activities the network can be built following the same principle disputed earlier and is portrayed below:


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From the three different time estimates, car is cleared up for each activity shown above.

The network is created in PERT together per the te occurred from the three various time estimates as displayed below:

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All the various estimates that time as well as the cleared up te are presented in the above network diagram against the relevant activity. There is, however, no certain rule for writing such estimates on the network.

We will now redraft the network (to have a cleaner diagram) with only the te and also work out the vital Path together per the complying with steps:

Step 1. Calculating ESTs and also plotting castle on the network as thorough below:

event ① = begin with 0;


event ② = EST that tail +te i.e. 0+5=5 work

event ③= 0+ 14 days;

event ④ = 5+15=20 days

event ⑤ = highest of 14 +9, 5+8, and 20+4(as over there are different tail events) = 24 days;


event ⑥ = 24+5=29 job

Step 2. We are to come backward from the end event ⑥.

Calculating the LFTs and plotting them on this network together follows:

of occasion ⑥ = EST of event (6) = 29 days, as already found in action 1;

of event ⑤ = LFT that head occasion minus te, i.e. 29 – 5 = 24 days;

of occasion ④ = 24 – 4 = 20 days;




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of occasion ③ = 24 – 9 = 15 days;

of occasion ② = shortest of 24 – 8,20 – 15 and also 15-9 (as there space three different head events) = 5 days;

of event ① = 5-5 = 0 day.

With the ESTs and also LFTs calculation as in-depth in action 1 and also Step 2 over we will create the network diagram as:

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Step 3:


We recognize the occasions having very same EST and LFT are on the vital path and now we uncover those space 1, 2, 3, 4, 5 and 6. The vital path is now shown by double-line arrows and also the job duration is 29 days.

This is topic to the arbitrarily variation the the actual performance time as versus te (time approximates for PERT) the 5, 15, 4 and also 5 time units for tasks on the vital path.

Therefore, the actual time to execute the four activities A, D, G and H represents the moment to complete the project and also PERT works out by way of statistical theory the probability the meeting the time target.