output of a production line is checked by an inspector for one or more of the three different types of defects

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

QUESTION ONE

The output of a production line is checked by an inspector for one or more of the three different types of defects: A, B, and C. If defect A occurs, the item is scrapped. If defect B or C occurs, the item must be reworked. The time required to rework a B defect is 15 minutes and the time required to rework a C defect is 30 minutes. The probability of an A, B and C defect are 0.15, 0.20 and 0.10 respectively.  For 20 items coming off the assembly line, determine, using Monte Carlo simulation, the number of items without any defects, the number of items scrapped and the total rework time.

Using the following sets of random numbers:

Defect A Defect B Defect C

48 47 82

55 36 95

91 57 18

40 04 96

93 79 20

01 18 08

83 10 56

63 13 11

47 57 52

52 09 03

82 48 47

95 55 36

18 91 57

96 40 04

20 93 79

08 01 18

56 83 10

11 63 13

52 47 57

03 52 09

 

 

QUESTION TWO

At the start of football season, the ticket office gets busy the day before the first game.

Customers arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes. Traditionally, there are two ticket sellers working. The university is considering an automated ticket machine similar to the airlines’ e-ticket system. The automated ticket machine can service a customer in 2 minutes.

(a) What is the average length of the queue for the in-person model?

(b) What is the average length of the queue for the automated system model?

(c) What is the average time in the system for the in-person model?

(d) What is the average time in the system for the automated system model?

(e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5 years). The wait time is only $4 per hour because students are patient. What is the total cost of each model?

 

Question Three

The time estimate (in weeks) for the activities of a PERT network are given below:

 

(a) Draw the project network and identify all the paths through it.

(b) Determine the expected project length.

(c) Calculate the standard deviation and variance of the project length.

(d) What is the probability that the project will be completed.

I. at least 4 weeks earlier than expected time

II. no more than 4 weeks later than expected time?

(e) If the project due date is 19 weeks, what is the probability of not meeting the due date?

(f) The probability than the project will be completed on schedule if the scheduled completion time is 20 weeks.

(g) What should be the scheduled completion time for the probability of completion to be 90%?

 

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