Senior management is scheduled to review the labor estimate

Senior management is scheduled to review the labor estimate for

developing software for Xi. The project manager requested an

analysis of past performance. The assigned analyst compared the

actual labor with the initial estimate for the 30 most recent projects.

The results, X= actual – initial estimate ( in thousands of hours), are

as follows:

15.2 7.2 0.1 10.9 2.5

14.1 4.8 -2.8 7.4 12.5

8.3 9.1 10.2 5.1 -4.2

6.0 13.2 3.8 18.1 5.5

11.5 3.9 4.2 3.1 -0.5

11.9 6.7 16.5 9.5 1.9

a) Analyze the results and summarize your conclusions.

b) Select an appropriate probability distribution and provide your

rationale.

c) If X has a normal probability distribution:

i. Estimate the population mean and standard deviation.

ii. Estimate the probability that the current labor estimate will

be exceeded. i.e., the project will experience an overrun.

iii. How much would the estimate need to be changed so that

there is a 50% chance of overrun? A 10% chance?

Solution

a) Most of the projects are overrun , only three estimates show negative overruns which implies there is high probability of overrun. The initial estimate of hours needs to be revised

b) Choose normal distribution for the data

c) Mean of the data   = 7.19

     Standard Deviation of the data = 5.499294

     Probability that the current labor estimate will overrun   = P( X >= 0)  

     = 1   - P( X < 0)

     = 1 - 0.095532    = 0.904468

     Or there is 90.4468 % probability of overrun.

     To reduce the overrun probability to 50 % the initial estimates has to be increased

     let the initial estimate incresase by A

     Then new mean   = 7.19 - A

     standard deviation is unchanged

     for 50 % overrun

     solving   P(X < 0) = 0.5     for   A

     we get A = 7.19   ( therefore initial estimate has to increase by 7.19)

     for 10 % overrun

     solving   P(X < 0) = 0.9     for   A

     we get A = 14.25 ( therefore initial estimate has to increase by 14.25)