Engineering Statistics Questions

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W02-01 Assume a beta-distribution of the duration (weeks) of each of 10 activities (A - J) of a project. Calculate the mean (μ) and the variance (σ2) of the duration of each activity. The optimistic time, the pessimistic time and the most likely time are denoted respectively by a, b and c in the following table: W02-02 The following figure illustrates the flow chart of the project including the 10 activities (A - J) of Discussion Problem W02-02. The duration of the path A-D-E-F-H-J is the sum of the mean durations of the activities A, D, E, F, H, J in the path. Calculate the mean and the standard deviation of the duration of the path. In fact, the path is longest in duration among all paths of the project. We call the longest path "critical path". In the flow chart, node (1) marks the start event, and node (END) marks the ending event. Discussion Problem WO2-01: Expected Activity Time and SD? 62 1+4x3+5 D = = 3 ? 6 ? V= =12-4; -1.78 6 Act a А 1 B 4 C 2 D 1 E 1 F 1 G 2 H 10 I 6 J 1 PERT с b 3 5 5 12 3 10 8 9 2 3 3 5 4 6 17 18 13 14 2 3 SEEM 3530 4 Discussion Problem W02-02: a) The mean time of path A-D-E-F-H-J? b) The standard deviation of the time of the path? 1,12 (B,6 (J, 2 End 1 (E,2) (6,4) (F,3 (A,3 3 (0,7) G,4) H,16 PERT SEEM 3530 5 Discussion Problem WO2-03 The longest path in the mean time is A-D-E- F-H-J. Assume that the length of the longest path is the whole project duration. What is the probability to complete the project within 36 weeks? Use the longest path to assess the probability PERT SEEM 3530 7 Discussion Problem WO2-04 The longest path in the mean time is A-D-E- F-H-J. Assume that the length of the longest path is the whole project duration. What is the time T for which the probability to complete the project is 95%? Use the longest path to assess the probability PERT SEEM 3530 10
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Engineering Statics
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Engineering Statics
Engineering Statics
DISCUSSION PROBLEM W02-01
Given the following:
𝜇=

𝑎+4𝑐+𝑏
6

, 𝜎2 =

(𝑏−𝑎)2
36

𝑎𝑛𝑑 𝑆𝐷 =

𝑏−𝑎
6

.

We use the above formulas to calculate the expected time, variance, and SD follows:
For...


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