Question

A chemical plant is due for a major overhaul and the manager has to make an assessment of a number of uncertainties associated with the project. These include the time the overhaul will take to complete (after 35 days the losses of production caused by the overhaul could have serious consequences for the company) and the risks that there will be leakage of dangerous chemicals into local watercourses during the cleaning process. The following extracts have been taken from the manager’s draft report which details plans for the overhaul.

(i)‘I assessed the most likely duration of the overhaul to be 30 days. I then tried to take an optimistic view and assumed that, if all goes well, we could finish the work 5 days earlier than this (i.e., in 25 days). I then took a pessimistic perspective and estimated that the longest the project will take is 34 days. I am therefore certain that we should complete the overhaul within 35 days.’

(ii)‘Essentially the overhaul will be split into eight independent phases. I think the chances of us completing each phase without a pollution problem are high, say 90%. Overall, I therefore estimate that we have almost a 90% chance of avoiding a pollution problem during the project.’

• Please make an assessment of a number of uncertainties associated with the project.

Answer 1

SOLUTION:

i.Here we are given the following :

Most likely duration of over haul = m = 30 days

Optimistic View of duration of over haul = o = 25 days

Pessimistic View of duration of over haul = p = 34 days

Expected Time of completion = E = (o+4m+p)/6 = (25+4*30+34)/6=179/6=29.83 days

Variance here is given as V = square of ((p-o)/6) = square of (9/6) = 2.25

Standard deviation is given as = S = square root of V = square root of 2.25 = 1.5

Now number of standard deviations the due date or target date lies from expected time of completion = Z = (Due date - E)/S = (35-29.83)/1.5 = 3.446

For a Z score of 3.446 probability of over haul getting completed under 35 days is 99.98% so uncertainty is 100-99.97=0.02%.

ii Now considering 90% chances of avoiding a pollution problem let us calculate what should be the due date for completion .

Now Z value closest to 90% probability is 1.282 .

Now formula foe due date = Z*S+E = 1.282*1.5+29.83= 31.753 days

So line haul should be completed before 31.753 days to have 90% chance of avoiding a pollution problem.