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Project Management and Statistical Process Control Homework Assignment

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Project Management
PERT Network Diagram 1 illustrates the ten interrelated activities that comprise a certain project.


PERT Network Diagram 1
The information presented in Table 1 represents the optimistic activity time (a), most probable activity time (m), and pessimistic activity time (b) in weeks for each activity associated with the project.


Table 1

ActivityOptimistic (a)Most Probable (m)Pessimistic (b)
A234
B135
C258
D123
E246
F135
G246
H135
I246
J147

PERT Network Diagram 2

  1. Using the information provided in Table 1, calculate the expected activity time (t) in weeks for each activity and then enter this information in the appropriate data field provided for each activity in PERT Network Diagram 2 in order to complete this diagram. Which of the following sequences accurately reflects the expected activity time in weeks for the ten activities arranged in alphabetical order by activity beginning with activity A and ending with activity J?
    • 3, 3, 4, 2, 4, 3, 4, 3, 4, 4
    • 3, 3, 5, 2, 4, 3, 4, 3, 4, 4
    • 3, 3, 5, 2, 4, 3, 5, 3, 4, 4
    • 3, 3, 4, 2, 4, 3, 4, 3, 5, 4
  2. Using the information provided in Table 1, calculate the variance for the estimated activity time for each activity in order to identify which of the following sequences accurately reflects the variance for the ten activities arranged in alphabetical order by activity beginning with activity A and ending with activity J.
    • 0.11, 1.00, 1.00, 0.11, 0.44, 0.44, 0.44, 0.44, 0.44, 1.00
    • 0.11, 0.44, 1.00, 0.11, 0.44, 0.11, 0.44, 1.00, 0.44, 1.00
    • 0.11, 0.44, 1.00, 0.11, 0.44, 0.44, 0.44, 0.44, 0.44, 1.00
    • 0.11, 0.44, 1.00, 1.00, 0.44, 0.44, 0.11, 0.44, 0.44, 1.00
  3. Using the information in completed PERT Network Diagram 2, calculate the overall estimated activity time in weeks for each of the following paths through the network in order to determine which of the following paths constitutes the critical path.
    • ABCDG
    • ABEFJG
    • ABCFJG
    • HIJG
  4. Using the information provided in Table 1, calculate the standard deviation for the project.
    • 1.86 weeks
    • 2.05 weeks
    • 1.69 weeks
    • 1.94 weeks
  5. Using the information provided in Table 1 and completed Project Network Diagram 2, calculate the probability of the project critical path activities being completed in less than or equal to 24 weeks.
    • 0.63
    • 0.78
    • 0.86
    • 0.90

The information presented in Table 2 represents the calculated Earliest Start, Earliest Finish, Latest Start and Latest Finish times for each activity.


Table 2

ActivityEarliest StartEarliest FinishLatest StartLatest Finish
A0303
B3636
C611611
D11131618
E610711
F11141114
G18221822
H03710
I371014
J14181418
  1. Using the information provided in Table 2, calculate the slack time in weeks for each activity in order to identify which of the following sequences accurately represents the slack time for each activity arranged in alphabetical order by activity beginning with activity A and ending with activity J.
    • 0, 1, 0, 5, 1, 0, 0, 7, 7, 0
    • 0, 0, 0, 5, 1, 0, 0, 5, 7, 0
    • 0, 0, 0, 5, 5, 0, 0, 7, 7, 0
    • 0, 0, 0, 5, 1, 0, 0, 7, 7, 0

The information presented in Table 3 represents the total budgeted cost for each activity associated with the project.


Table 3

ActivityTotal Budgeted Cost
A$22,000
B$30,000
C$24,000
D$8,000
E$7,000
F$9,000
G$10,000
H$12,000
I$23,000
J$11,000
  1. Using the information provided in Table 2 and Table 3, calculate the budgeted costs for week seven of the project based upon using the Earliest Start Date for each activity and calculate the budgeted costs for week seven of the project based upon using the Latest Start Date for each activity in order to then calculate the difference in the cashflow for week seven between these two scenarios.
    • $29,780
    • $31,900
    • $36,750
    • $42,640
  2. Using the information provided in Table 2 and Table 3, calculate the budgeted costs for week eighteen of the project based upon using the Earliest Start Date for each activity and calculate the budgeted costs for week eighteen of the project based upon using the Latest Start Date for each activity in order to then calculate the difference in the cashflow for week eighteen between these two scenarios.
    • $0
    • $3,900
    • $6,750
    • $12,640

Table 4 represents the percentage of completion and actual cost of work performed data for each activity associated with the project at a certain point in time during the project.


Table 4

ActivityTotal Budgeted CostPercent of CompletionActual Cost of Work Completed
A$22,000100%$23,000
B$30,000100%$28,000
C$24,000100%$27,500
D$8,00085%$7,300
E$7,00065%$9,800
F$9,0000%$0
G$10,0000%$0
H$12,00045%$5,100
I$23,0000%$0
J$11,0000%$0
  1. Using the information provided in Table 4, calculate the value of work completed and activity difference for each activity. Which activity evidences the single largest activity difference (regardless of whether it is a cost overrun or cost underrun) at this particular point in the project?
    • Activity A
    • Activity B
    • Activity C
    • Activity D
    • Activity E
    • Activity F
    • Activity G
    • Activity H
    • Activity I
    • Activity J
  2. Using the information provided in Table 4, calculate the overall cost overrun or cost underrun for the project at this particular point in the project.
    • $7,950 cost overrun
    • $22,700 cost overrun
    • $7,950 cost underrun
    • $22,700 cost underrun

Table 5 represents the estimated crash time in weeks and associated total crash cost for each activity.


Table 5

ActivityCrash Time
(Weeks)
Total Crash Cost
A2$25,000
B2$40,000
C4$27,000
D1$9,000
E3$8,500
F2$12,000
G3$11,000
H2$15,000
I3$26,000
J3$13,000
  1. Using the information in completed PERT Network Diagram 2 and Table 5, crash the network in order to reduce the estimated project duration to 20 weeks while minimizing the overall crash cost. Which of the following critical path activities would be the most logical choice for the first activity to crash?
    • Activity D
    • Activity F
    • Activity G
    • Activity J
  2. Which of the following critical path activities would be the most logical choice for the second activity to crash?
    • Activity C
    • Activity D
    • Activity F
    • Activity J
  3. What is the total estimated cost associated with crashing the network to reduce the estimated project duration to 20 weeks at the lowest possible overall crash cost?
    • $3,000
    • $5,000
    • $6,000
    • $8,000
  4. After successfully crashing the network to reduce the estimated project duration to 20 weeks, which of the following paths through the crashed network constitutes the critical path?
    • ABCDG
    • ABEFJG
    • ABCFJG
    • HIJG

Statistical Process Control
A canning company packages canned soup for a major soup manufacturer for distribution to regional wholesalers. The company processes 5,000 cans of soup each day using an automated packaging machine that is programmed to fill each can with 14.0 ± 0.1 ounces net weight of soup. The company’s quality assurance process consists of randomly selecting five cans from the production line each hour and carefully weighing them. Each hour’s sample group is considered acceptable if no less than four out of the five cans examined weigh 14.0 ± 0.1 ounces. Sample observations for a 24-hour production run are reflected in the table below.

HourSample 1Sample 2Sample 3Sample 4Sample 5
113.9813.9314.0114.0614.05
214.0813.8913.9814.0513.94
313.9613.9113.913.9513.96
413.8913.9713.9714.0013.98
513.9813.9814.0613.9913.99
613.9714.0914.0414.1113.96
714.0813.9114.0214.0414.09
813.9913.9714.0313.9814.03
913.9213.9513.9213.9813.99
1014.0013.9814.113.9113.96
1113.8714.0713.9313.9614.03
1214.0214.0414.0213.9313.94
1314.0314.0113.9513.9814.00
1414.0214.0013.9514.0914.02
1514.0014.0414.0413.9613.95
1614.0513.9313.9214.0314.03
1714.1114.0714.0614.0014.00
1814.0213.9913.9413.9114.04
1914.0214.0314.0113.9414.06
2013.9813.9513.9513.9713.97
2113.9714.0414.0213.9614.06
2213.9114.0213.9914.0013.96
2313.9714.0414.0414.0214.03
2414.0814.0114.0214.0913.98

Prepare an x-bar chart and R-chart that reflect a 99.7% confidence level in order to answer questions 15 through 20:

  1. What is the x-bar UCL?
    • 13.65
    • 14.78
    • 14.06
    • 13.25
  2. What is the x-bar LCL?
    • 13.23
    • 13.93
    • 14.07
    • 13.56
  3. What is the range UCL?
    • 0.24
    • 0.39
    • 0.49
    • 0.67
  4. What is the range LCL?
    • 0.00
    • -0.12
    • 0.12
    • -0.20
  5. Does x-bar chart indicate that the process was operating within statistical control during the 24-hour period?
    • Yes
    • No
  6. Does the R-chart indicate that the process was operating within statistical control during the 24-hour period?
    • Yes
    • No

The manager of the customer service hotline for an internet service provider has been approached by the President of the company regarding a perceived increase in the number of customer complaints regarding the lack of timely technical assistance being provided by hotline technicians. In order to evaluate the validity of the President’s concerns he decided to survey customers regarding their satisfaction with the timeliness of the technical assistance they received. Surveys were conducted during a thirty-day period with twenty-five randomly selected customers participating in the survey each day. The number of customers surveyed who expressed dissatisfaction with the timeliness of the technical assistance they received is summarized in the following table.

DayNo. Complaints
10
25
36
40
50
61
73
80
91
102
112
120
130
143
155
161
176
182
190
201
214
223
230
242
251
260
278
289
292
301

Using the preceding data set, prepare a c-chart and p-chart that reflects a 99.7% confidence level in order to answer questions 21 through 25:

  1. What is the UCL for the number of complaints?
    • 5.83
    • 6.78
    • 6.24
    • 4.99
  2. What is the LCL for the number of complaints?
    • 0.00
    • 0.13
    • 0.25
    • -0.16
  3. What is the UCL for the proportion of complaints?
    • 0.45
    • 0.39
    • 0.26
    • 0.15
  4. What is the LCL for the proportion of complaints?
    • -0.18
    • -0.07
    • 0.00
    • 0.08
  5. Do the c-chart and p-chart indicate that the process was operating within statistical control at all points during the thirty day period?
    • Yes
    • No