--- title: "Network errors; expected time of engineers" subject: "Project Engineering" chapter: 3 key: "semester_7/project_engineering:network-errors-expected-time-engineers" source: https://www.bctengineer.com/q/semester_7/project_engineering/network-errors-expected-time-engineers site: BCT Engineering --- # Network errors; expected time of engineers Project Engineering · Chapter 3: Project Planning and Scheduling - Asked in: 2067 Asar (old course), 4+4 marks - Video: [Earliest start, finish and latest start, finish time](https://www.youtube.com/watch?v=qEhBgNn6pYk) — Meenu Kohli - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/project_engineering/network-errors-expected-time-engineers - Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-3 ## Question List out various errors in drawing a network diagram. Find out the expected time of each engineer mentioned below. Which engineer will you choose and why? Who is more certain in completing the job? | Type | to | tm | tp | |---|---|---|---| | NTC Engineer | 5 | 9 | 12 | | NCell Engineer | 4 | 5 | 9 | ## Short answer Errors: looping, dangling, redundancy, wrong logic, duplicate i-j, wrong numbering, multiple start/end events. Expected times: NTC 8.83, NCell 5.50 time units. Choose NCell because shorter expected time and lower standard deviation (0.83 vs 1.17), hence more certain. ## Answer #### Errors in drawing a network diagram 1. **Looping (cycle):** a chain of activities returns to an earlier event, e.g. 1-2-3-1. Time cannot go backward. 2. **Dangling (open end):** an activity, other than the last, ends at an event with no successor, or a non-first activity starts at an event with no predecessor. 3. **Redundancy:** an unnecessary dummy or a repeated dependence that does not change the logic. 4. **Wrong logic:** a wrong predecessor or successor is shown, or a dummy is missing, so dependence is incorrect. 5. **Same event numbers (duplicate i-j):** two activities with the same start and end event, without a dummy. 6. **Wrong numbering:** the head event number is smaller than the tail event number (i > j). 7. **Multiple start or end events:** more than one starting or finishing event. 8. **Unnecessary crossing of arrows**, or a dummy shown with a duration (a dummy must have zero duration). ```text Looping: (1)->(2)->(3) ^ | +---------+ Dangling: (1)->(2)->(3)->(5) \->(4) (4 has no successor) ``` #### Expected time (PERT) $t_e = \dfrac{t_o + 4t_m + t_p}{6}$, $\sigma = \dfrac{t_p - t_o}{6}$. **NTC Engineer** ($5, 9, 12$): $t_e = \dfrac{5 + 36 + 12}{6} = \dfrac{53}{6} = 8.83$, $\sigma = \dfrac{12 - 5}{6} = 1.17$, variance $= 1.36$ **NCell Engineer** ($4, 5, 9$): $t_e = \dfrac{4 + 20 + 9}{6} = \dfrac{33}{6} = 5.50$, $\sigma = \dfrac{9 - 4}{6} = 0.83$, variance $= 0.69$ | Engineer | $t_e$ | $\sigma$ | Variance | |---|---|---|---| | NTC | 8.83 | 1.17 | 1.36 | | NCell | 5.50 | 0.83 | 0.69 | **Choice:** the **NCell engineer** is chosen because the expected completion time (5.50) is much shorter than that of the NTC engineer (8.83). He is also **more certain** in completing the job since his standard deviation (0.83) and variance (0.69) are smaller. **Answer: $t_e$ = 8.83 (NTC) and 5.50 (NCell); NCell engineer is better and more certain.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is a looping error in a network diagram? A. Two activities share the same start and end events B. An activity ends at an event with no successor C. A chain of activities returns to an earlier event, such as 1-2-3-1 D. More than one starting event is shown Answer: C. A loop (cycle) is wrong because time cannot go backward. (Key point: Looping error) 2. Which is a dangling (open end) error? A. An activity, other than the last, ends at an event with no successor B. A dummy activity is given a duration C. The head event number is smaller than the tail event number D. Arrows cross each other Answer: A. Dangling means an activity other than the last leaves an event with no continuation, or a non-first activity starts at an event with no predecessor. (Key point: Dangling error) 3. NTC engineer has t_o = 5, t_m = 9 and t_p = 12. What is t_e? A. 9.00 B. 8.50 C. 8.83 D. 9.17 Answer: C. t_e = (5 + 36 + 12)/6 = 53/6 = 8.83. (Key point: Expected time of NTC engineer) 4. NCell has t_e = 5.50 and SD 0.83; NTC has t_e = 8.83 and SD 1.17. Which engineer is chosen and who is more certain? A. NTC for both B. NTC is chosen but NCell is more certain C. NCell is chosen but NTC is more certain D. NCell for both Answer: D. NCell has both the shorter expected time and the smaller SD and variance, so it is better and more certain. 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