ISYE+512+Exam+2
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School
University of Wisconsin, Madison *
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Course
512
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
docx
Pages
6
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Exam 2: ISYE 512 INSPECTION, QUALITY CONTROL AND
RELIABILITY
NOTES:
1.
Exam is open book, open notes. You can use calculators and/or computer software.
2.
Internet Access is NOT allowed.
3.
You are NOT allowed to communicate with your classmates for the exam questions by any
means during the 48-hour exam window.
4.
The exams will be available only for 48 hours. You must finish and submit your exam
solutions via the course website within this 48-hour window.
5.
Show your steps. Answers with only final result will NOT earn full mark of that problem.
4.
The test is worth 100 points. The assigned points for each question are given beside
it.
There are
7
questions in this
exam. Please show the steps and procedures in your solution in
order to get full points.
Name(print):
1
Honor code: I have neither given nor received unauthorized aid
in this examination.
Signature,
Date:
===============================================================
Question 1: (
12 points
)
A process that produces titanium forgings for automobile turbocharger wheels is to be
controlled through use of a fraction nonconforming chart. Initially, one sample of size 150 is
taken each day for 20 days, and the results shown in the Table.
(a) Establish a control chart to monitor future production. You need to plot the control chart.
(
6 points
)
(b) What is the smallest sample size that could be used for this process and still give a
positive lower control limit on the chart?
(
6 points
)
Question 2: (
14 points
)
2
A control chart is to be established on a process producing televisions.
The inspection unit is
one
television, and a common chart for nonconformities is to be used. As preliminary data, 9
nonconformities were counted in inspecting 50 televisions.
(Samples on the control limits are regarded in-control.)
(a)
Find two-sigma control limits
(
4 points
)
(b)
Find the
α
error for the control chart with two-sigma control limits
(
4 points
)
(c)
Find the
β
error for the chart with two-sigma control limits if the average number
of defects is actually one (i.e., c=1)
(
4 points
)
(d)
Find the ARL if c = 1.0
(
2 points
)
Question 3:
(14 points)
A process is in statistical control with
´
´
x
=
39.5,
´
R
=
2.5
. The control chart uses a sample
size of
n
=
2
. Specifications are at
40
±
5
. The quality characteristic is normally
distributed.
(a) Estimate the potential capability of the process. (
2 points
)
(b) Estimate the actual process capability. (
2 points
)
(c) Calculate
C
pkm
and compare the
C
p
,
C
pkm
and
C
pk
. (
4 points
)
(d) How much improvement could be made in process performance if the mean could be
centered at the nominal value? (Hint: compare the probabilities of the unit being out of
the specification limits) (
6 points
)
Question 4: (
14 points
)
In a gauge R&R study, 2 inspectors use the same gauge to measure 10 different batches of
parts 3 times each. For each inspector, the averages and ranges of the 3 measurements on
each batch are given below (units are in mm):
Batch
Number
Inspector 1
Inspector 2
¯
x
R
¯
x
R
1
149/3
1
149/3
3
2
155/3
1
153/3
0
3
153/3
3
157/3
3
4
150/3
2
149/3
3
5
145/3
1
145/3
1
6
152/3
2
152/3
2
3
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7
153/3
0
151/3
1
8
151/3
3
151/3
5
9
151/3
1
148/3
3
10
142/3
3
141/3
2
Average
150.1/3
1.7
149.6/3
2.3
(a)
Please estimate
gauge
. (
6 points
)
(b) Suppose the total observed variance (
total
) is 5.60mm
2
. Estimate the variability of
product. (
4 points
)
(c)
Suppose the USL and LSL are 50
10mm, respectively. Assess the capability of the
measurement system (
4 points
)
Question 5: (
18 points
)
The following data represent individual observations on bath concentration from a chemical
process. The target value is 50 and the process standard deviation is given as
= 1.8.
4
(1) Use k = 0.5 and h =5, build a tabular CUSUM to quickly detect a shift of about 1
in the
process mean. Based on the tabular CUSUM, please fill in the three blanks. (
4 points
)
(2) Please conclude whether the process has a mean shift using k = 0.5 and h =5.
If the
process has a mean shift, please indicate at which sample this mean shift started. (
8 points
)
(3) Estimate the magnitude of the mean shift and calculate the
=
|
μ
1
−
μ
0
|/
σ
.
(
6 points
)
Question 6: (
16 points
)
.
Consider a process with µ
0
= 10, σ = 1 and n=1. Compute the steady-state control limits for
the following EWMA control charts:
(a) λ = 0.1, L = 3 (
4 points
)
(b) λ = 0.2, L = 3 (
4 points
)
(c) λ = 0.4, L = 3 (
4 points
)
(d) What is the effect of λ on the behavior of the control limits? (
4 points
)
Question 7: (
12 points
)
.
Show that if
λ
=
2
(
w
+
1
)
for the EWMA control chart, then this chart is equivalent to a w-
period moving average control chart in the sense that the control limits are identical in the
steady state.
5
6
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