A Manufacturing Company Is Planning to Use PERT to Setup

question 11

Essay

A manufacturing company is planning to use PERT to setup a project for a new production line. For this project, they have established the following activities, precedence relationships, and time estimates in days:
$$\begin{array} { c c r r r } \text { Activity } & \text { Immediate Predecessors } & \text { Optimistic t }_p & \text { Most Likely t }_m & \text { Pessimistic t } _p\\\hline \text { a } & \text { none } & 8 & 10 & 12 \\\text { b } & \text { none } & 6 & 7 & 9 \\\text { c } & \text { b } & 3 & 3 & 3 \\\text { d } & \text { a } & 10 & 15 & 20 \\\text { E } & \text { d } & 6 & 7 & 8 \\\text { f } & \text { c } & 9 & 10 & 11 \\\text { E } & \text { d } & 5 & 7 & 10 \\\text { h } & \text { ef } & 14 & 15 & 16\end{array}$$
a. What is the expected duration for activity b?
b. What is the variance of activity d?
c. How many paths are there in the network?
d. What is the earliest finish EF) time for activity e?
e. What is the slack in days for activity c
f. What is the critical path
g. What is the duration of the critical path in days
h. What is the standard deviation of the critical path
i. What is the probability of completing the project within 50 days?

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Definitions:

Expected Frequencies

The counts that one would expect in a statistical distribution, based on a specific hypothesis or model.

Chi-Squared Test Statistic

A statistical measure used to determine the goodness of fit between observed values and values expected theoretically.

Level of Significance

Another term for significance level, indicating the threshold below which the null hypothesis is rejected in statistical tests.

Degrees of Freedom

refers to the number of independent values in a statistical calculation that can vary without violating any given constraints.