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.