IE 355 QUALITY AND APPLIED STATISTICS I
LAB ASSIGNMENT 5
PROCESS CONTROL FOR AXLE HOUSINGS
Introduction
A company produces electric motors. One of the parts in the motor is an axle housing into
which an axle must be fit. It has been found at the assembly stage of the axle and axle
housing that some of the axles are not fitting into the housings. In addition, it appears that
some of the housings may simply be too large as indicated by a large number of warranty
claims being made with respect to faulty motors. You have been asked to design a process
control system for the axle housings to monitor the hole drilling process.
Problem
The problem in this assignment is to establish a process control system to monitor the
fraction of axle housings that are not conforming to specifications and to determine an
estimate of this fraction. To do this, you are asked to construct the appropriate control
charts.
Lab Report
Your report should be an engineering report that you would submit in a company given the
assignment to design a process control system for this part. Your report should be written
in paragraphs containing complete sentences. Any graphs or tabular results you show
must be labeled and referred to in the text.
Executive summary
1
This summary, approximately 1/2 page, briefly describes the goal and the result. For
example, “The goal here is to design a process control system to ….” Your result should
be stated using some key numbers; e.g., “I designed such-and-such control charts. I found
that the process is currently producing so-and-so-many fraction defectives which is too
high (or which is just fine or whatever your conclusion is.)”
The executive summary basically reiterates the meat of the report in a few concise
sentences for those busy managers who can only read the first page.
Description of the process control system
Describe how the data was collected. Describe how and with what the measuring was
conducted. Describe the control charts you decided to use to monitor this process and the
theory behind them. Discuss what types of control charts could be used for this process
and why they are appropriate. Describe the steps you used to create them.
Results and recommendations
Present your final control charts and results. Construct at least 3 different control charts.
Give all the control chart parameters such as sample sizes, limits, etc… Give an estimate
of the process fraction nonconforming and any other interesting values. Present the results
such that they tell a coherent and clear story. Present any recommendations you have for
the process.
Procedure

In this lab, each student must work by herself or himself.

A collection of parts is provided that represents the axle housings produced for the
electric motors.

Create appropriate control charts for two different scenarios:
Scenario 1
Imagine that you are observing the drilling process. You decide that every 30 minutes you
2
will select a sample of 5 axle housings and measure them to see if they are conforming.
You decide that you will collect a total of 20 samples.
We simulate this scenario by randomly drawing a sample of 5 from the provided parts,
recording the measurements and then returning the 5 parts back to the collection. Repeat
20 times.
Scenario 2
Again, imagine you are observing the drilling process. This time you decide to measure
all the parts produced in a 10-minute interval. You find that the number of axle housings
that are produced in this interval is variable, that is, the same number of finished housings
is not always produced in the same interval of time. You decide that you will collect 20
samples.
For this scenario, roll a die to simulate the number of housings drilled in each 10-minute
interval. The numbers on the die map to the number of drilled housings as:
Number on die Number of drilled housings
in a 10-minute interval
1 or 4
4
2 or 5
5
3 or 6
6
3
The Measuring Device – The Plug Gage
To measure whether the housing is conforming to specifications, we use a measuring
device called a plug gage. A plug gage typically consists of two sections, a section used to
make the measurement and the handle. The section of the gage that does the measuring is
of two types: one is called the “go” gage and the other is called the “no-go” gage.
Three examples of plug gages are shown in Figure 1. We use type B plug gage shown in
Figure 1. It is called a double-end plug gage. This type has the go and the no-go gages
mounted on a single handle with one gage on each end.
Figure 1. Examples of Plug Gages: Types A, B & C
To evaluate the conformity of the axle housings to specifications, the operator puts the go
end of the gage into the housing. If the go gage can get in, the housing is conforming to
the lower specification limit, otherwise, the hole is undersized. If the go gage did get in,
then the user puts the no-go gage into the housing. If the no-go gage cannot get in the
housing is conforming to the upper specification limit, otherwise, the hole is oversized. In
summary, a conforming axle housing is when the go gage fits inside but the no-go gage
does not.
The specification for the axle housing is 0.370 to 0.385 inches.
4
Worksheet for sample size 5
Sample Number Number conforming
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
5
Worksheet for variable sample size
Sample Number Sample Size Number conforming
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
6