PERT Probabilistic Analysis - Worked Examples

A routine earthmoving activity for a lateral canal has an optimistic duration estimate of $5.00$ days (excellent weather), a most likely duration of $8.00$ days (typical conditions), and a pessimistic duration of $14.0$ days (heavy rains and equipment breakdown). Calculate the expected duration of this activity using PERT.

Securing Right-of-Way (ROW) for a main canal alignment is notorious for uncertainty. The optimistic estimate is $15.0$ days if landowners cooperate immediately. The most likely estimate is $30.0$ days based on average negotiation times. The pessimistic estimate is $90.0$ days if legal expropriation proceedings are required. Calculate the expected duration.

For a concrete canal lining activity, the optimistic duration is $5.00$ days and the pessimistic duration is $14.0$ days due to potential delays in aggregate delivery and failing compressive strength tests. Calculate the statistical variance of its duration.

Using the variance calculated in Example 3 ($2.25 \text{ days}^2$) for the concrete lining activity, determine the standard deviation.

Supplier A provides an estimate for manufacturing and delivering steel sluice gates with an optimistic duration of $10.0$ days, most likely of $12.0$ days, and pessimistic of $20.0$ days. Supplier B, located overseas but with better stock, provides an estimate of $8.00$ days optimistic, $13.0$ days most likely, and $15.0$ days pessimistic. Determine which supplier presents a higher uncertainty (variance) for the delivery schedule to aid management in procurement decision-making.

The critical path for constructing a pumping station consists of three sequential activities: Site Clearing, Foundation Excavation, and Concrete Pouring. Based on PERT calculations, the variances for these critical activities are $0.500 \text{ days}^2$, $1.20 \text{ days}^2$, and $0.800 \text{ days}^2$, respectively. A fourth activity, Perimeter Fencing, is non-critical and has a variance of $3.00 \text{ days}^2$. Calculate the total project variance.

The total project variance for the critical path of an earth-fill irrigation dam construction project is determined to be $14.4 \text{ days}^2$. Calculate the project standard deviation to be used for Z-score probability analysis.

An earthworks project to desilt a reservoir has an expected total duration of $120$ days and a standard deviation of $4.50$ days. The contractor wants to evaluate the feasibility of finishing the project in $125$ days, just before the monsoon season begins, to avoid massive rework. Calculate the Z-score for this target date.

A project to install a massive inverted siphon across a riverbed has an expected duration of $22.0$ days and a standard deviation of $1.12$ days. Using the Z-score of $1.79$ calculated for a target completion date of $24.0$ days, find the probability of completing the installation before the deadline using a standard normal distribution table.

Due to a rapidly approaching VIP inspection scheduled by local government officials, management requests that an ongoing canal lining project—which has an expected duration of $45.0$ days and a standard deviation of $3.00$ days—be completed in $42.0$ days. Calculate the Z-score and evaluate the schedule risk.

The construction of a diversion weir has three critical activities sequentially linked: Cofferdam Installation, River Diversion, and Weir Foundation Pouring.

• Cofferdam: $a=8.00$, $m=10.0$, $b=18.0$
• River Diversion: $a=3.00$, $m=5.00$, $b=7.00$
• Foundation Pouring: $a=12.0$, $m=15.0$, $b=24.0$

Calculate the total expected project duration and standard deviation.

Using the results from Example 11 ($T_e = 32.0$ days, $\sigma_p = 2.69$ days), the funding agency stipulates that the foundation must be poured and completed within $35.0$ days to avoid budget revocation. Calculate the probability of meeting this deadline and advise management.