Question

A PERT analysis of a small project determined that the duration of the critical path is 10 weeks with a variance of 2 weeks. What project duration can be promised that will have only a 5% chance of time overrun? A. 11 weeks B. 10 weeks C. 12.3 weeks D. 13.3 weeks

Answer 1

The project duration that can be promised with only a 5% chance of time overrun is approximately 12.3 weeks, based on the PERT analysis result of a 10-week critical path with a variance of 2 weeks.

Step-by-step explanation:

The question deals with Project Evaluation and Review Technique (PERT) which is a tool used in project management to analyze and represent the tasks involved in completing a given project. The PERT analysis has determined a critical path duration of 10 weeks with a variance of 2 weeks. To answer what project duration can be promised with only a 5% chance of time overrun, we can use the concept of the standard deviation and the Z-score associated with the 5% probability in the normal distribution. The Z-score for a 5% chance of time overrun (one-tailed as we are only looking at overruns) is approximately 1.645. Since variance is the square of the standard deviation, the standard deviation is the square root of the variance, which in this case is √2.

Thus, the project duration can be calculated as follows:

1. Find the standard deviation: √2 = 1.41 weeks (approximately).
2. Calculate the time overrun threshold: (1.645 × 1.41 weeks) + 10 weeks = 2.3 weeks + 10 weeks = 12.3 weeks.

Therefore, the project duration that can be promised to have only a 5% chance of time overrun is approximately 12.3 weeks.

Answer 2

To determine the project duration with only a 5% chance of time overrun using a PERT analysis with a duration variance of 2 weeks, the Z-value for a 95% confidence level is multiplied by the standard deviation and added to the mean duration, resulting in approximately 12.3 weeks.

Step-by-step explanation:

The PERT (Program Evaluation and Review Technique) analysis involves calculating the expected project duration and assessing the risk associated with meeting project deadlines. To find the project duration with a 5% chance of overrun, we can use the concept of standard deviation and the Z-value associated with a 95% confidence level (5% chance of overrun corresponds with the 95th percentile).

The Z-value for a 95% confidence level is approximately 1.645. Since the question states that the variance of the critical path duration is 2 weeks, we can calculate the standard deviation as the square root of the variance, which equals √2 or approximately 1.414 weeks.

To find the duration that has only a 5% chance to be exceeded, we multiply the Z-value by the standard deviation and add it to the expected duration:

Expected duration + (Z-value × Standard deviation) = 10 weeks + (1.645 × 1.414) = 10 weeks + 2.33 weeks ≈ 12.33 weeks

Therefore, the duration of the project that can be promised with only a 5% chance of time overrun is approximately 12.3 weeks.