Homework for Quality Management and Statistical Process Control
Due on Dec. 18th, Friday in Class
PLEASE SHOW DETAILED CALCULATION WORK FOR EACH PROBLEM!
PLEASE WRITE YOUR NAME AND ID NUMBERS CLEARLY ON THE FRONT PAGE!
ALL PAGES SHOULD BE STAPLED!
Problem 1
A manufacturing company wants to use control charts to monitor a continuous process to cut plastic tubes
into standard lengths. Samples of five observations each were taken yesterday, and the results are in the
table below.
1. Using these sample data to construct appropriate control charts to monitor the future cutting process.
Sample
1 2 3 4 5 6
79.1 80.5 79.6 78.9 80.5 79.7
78.9 78.8 79.7 79.4 79.5 80.6
80.5 81.0 80.4 79.8 80.4 80.5
78.4 80.4 80.3 81.3 80.7 79.0
81.0 80.1 80.8 80.6 78.8 80.1
2. Four more samples of the same size have been taken today, and the results are given below. Based on the
control charts you constructed, did you notice any major changes in today’s cutting process?
Sample 1 (today) Sample 2 (today) Sample 3 (today) Sample 4 (today)
78.0 81.0 79.0 79.1
82.5 82.0 82.2 81.0
80.0 81.5 83.1 78.8
81.5 82.2 80.0 79.6
79.0 82.3 79.5 82.0
Problem 2
An automatic screw machine produces hex nuts. If a hex nut does not meet the quality standard, it is
considered as defective. Samples of 200 hex nuts each were taken to monitor the production. The number of
defective hex nuts from the past 13 samples is listed below. Construct an appropriate control chart and
determine whether or not the process is in control. (Hint: The quality here is measured by defective rate)
Sample
1 2 3 4 5 6 7 8 9 10 11 12 13
# of defectives 1 2 2 4 2 4 2 1 2 10 3 2 1
Problem 3
The postmaster of a small western city receives a certain number of complaints about mail delivery each
day. The number of complaints in the past 14 days is given below. Construct a control chart to see if the
quality of mail delivery is in control (stable)?
Day
1 2 3 4 5 6 7 8 9 10 11 12 13 14
# of complaints 4 10 14 8 5 6 3 11 9 7 5 4 2 10
Hint: For Problem 2 and 3, use the data in the table to construct respective control charts and plot the same
data on the charts constructed.
Problem 4
Answer the following questions for a single sampling plan with sample size n = 80 and c = 3
1. Draw the OC curve for the sampling plan, using the Poisson table distributed in class
2. If AQL = 2% and LTPD = 7%, what would be the producer's and consumer's risks associated with the
sampling plan?
3. If the sampling plan is used to inspect a lot of 10,000 products with an average defective rate of 3%,
what would be the average quality after inspection, assuming all the defectives will be replaced if
detected?
Problem 5 (Bonus Question, 10 pts)
Consider the following three-stage production process of glass ceramics, which is operated as a workerpace
line.
Components 6 min/unit 5 min/unit 4 min/unit Finished Units
The process is experiencing severe quality problems related to insufficiently trained workers. Specifically,
20 percent of the parts going through operation 1 are badly processed by the operator. Rather than
scrapping the unit, it is moved to a highly skilled rework operator, who can correct the mistake and finish up
the unit completely within 15 minutes. The same problem occurs at station 2, where 10 percent of the parts
are badly processed, requiring 10 minutes of rework. Station 3 also has a 10 percent ratio of badly
processed parts, each of them requiring 5 minutes by the network operator.
1. What is the process yield? (Remember, process yield is the percentage of good units that are processed
through the overall process.)
2. What is the process yield without hiring the skilled rework operator?
1 2 3
Rework