operation management
OM 305
Dr. Robert Aboolian
Assignment # 3
Problem 1: (10 points) Auto pistons at Wemming Chung’s plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must
be controlled. From sample sizes of 10 pistons produced each day, the mean and
the range of this diameter have been as follows:
Day Mean (mm) Range (mm) 1 156.9 4.2 2 153.2 4.6 3 153.6 4.1 4 155.5 5.0 5 156.6 4.5
a) What are the UCL x and LCL x , using 3σ? Plot the data.
b) What are the UCLR and LCLR , using 3σ? Plot the data.
c) Is the Process in Control?
Problem 2: (5 points) The school board is trying to evaluate a new math
program introduced to second- graders in five elementary schools across the
county this year. A sample of the student scores on standardized math tests in
each elementary school yielded the following data:
School No. of Test Errors A 52 B 27 C 35 D 44 E 55
a) Construct a c- chart for test errors, and set the control limits to contain
99.73% of the random variation in test scores.
b) What does the chart tell you?
Problem 3: (10 points) One of New England Air’s top competitive priorities is on time arrivals. Quality VP Clair Bond decided to person-ally monitor New
England Air’s performance. Each week for the past 30 weeks, Bond checked a
random sample of 100 flight arrivals for on- time performance. The table that
follows contains the number of flights that did not meet New England Air’s
definition of “on time”:
Sample
(week)
Late
Flights
Sample
(week)
Late
Flights
1 2 16 2 2 4 17 3 3 10 18 7 4 4 19 3 5 1 20 2 6 1 21 3 7 13 22 7 8 9 23 4 9 11 24 3 10 0 25 2 11 3 26 2 12 4 27 0 13 2 28 1 14 2 29 3 15 8 30 4
a) Using a 95% confidence level, plot the overall percentage of late flights ( p ) and the upper and lower control limits on a control chart.
b) Assume that the airline industry’s upper and lower control limits for flights that are not on time are .1000 and .0400, respectively. Draw them
on your control chart.
c) Plot the percentage of late flights in each sample. Do all samples fall within New England Air’s control limits? When one falls out-side the
control limits, what should be done?
d) What can Clair Bond report about the quality of service?
Problem 4: (25 points: a to g) A production line is to be designed to produce modems. The production tasks, their times, and their precedence
requirements are shown in the table below.
Task Time(min) Predecessor(s) a b c d e f g h i j
0.6 0.3 0.8 0.7 0.4 0.8 0.5 0.9 0.2 0.1
a
c, d b, e f f g h, i
a. (3 points) Develop the precedence diagram.
b. (3 points) If the production line operates 8 hours per day, what is the
maximum production rate and what is the minimum production rate?
c. (3 points) Calculate the number of followers for each task (show your
answer on the precedence diagram).
d. (2 points) If the production line is targeted to produce 300 modems per
day, what is the cycle time?
e. (2 points) What is the theoretical minimum number of stations for
producing 300 modems per day?
f. (8 points) Form work stations using the most number of followers rule.
Break ties with the longest processing time rule. Use a cycle time of 1.6
minutes.
g. (4 points) Calculate the efficiency and the production rate of the assembly
line balanced in part f.