ISE235-HW2 - Solutions
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School
San Jose State University *
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Course
235
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
3
Uploaded by NickTian
1
ISE 235 Homework Assignment #2
–
Solutions
Problem #1: Exercise 6.19 (Exercise 6.41 of the 7
th
Edition; Exercise 6.33 of the 6
th
Edition; Exercise 5-33 of the 5
th
Edition; 5-26 of the 4
th
Edition).
The exercise
statement starts with,
“
Control charts on
X
and
R
for samples of size n=5 are to be
maintained on the tensile strength in pounds of a yarn. …..”.
Note:
For Part (b), treat the estimated mean and standard deviation as the true mean and
true standard deviation.
Then, use the technique of Standardization for Normal
Distributions.
Problem #2: Exercise 6.17 (Exercise 6.39 of the 7
th
Edition; Exercise 6.31 of the 6
th
Edition; Exercise 5-31 of the 5
th
Edition; 5-24 of the 4
th
Edition).
The exercise
statement starts with, “An
X
char has a center line of 100, uses three-sigma control
limits, and is based on a sample size of four. …..”
Note: We derived the formula –
Equation (6.19)
–
in the class.
The textbook has the same derivation (in section 6.2.6 and
on page 238 of the 8
th
Edition), although it has less detail.
The derivation process
requires the use of a common technique of Standardization of a Normal Random
Variable. This technique can be found in all textbook on a first course on probability and
statistics.
This same technique is required for solving some of the other problems
assigned in this HW and some future homework problems. Please review and master the
technique.)
2
Problem #3: Exercise 6.30. (Exercise 6.55 of the 7
th
Edition; Exercise 6.47 of the 6
th
Edition; Exercise 5-47 of the 5
th
Edition; 5-40 of the 4
th
Edition).
The exercise
statement starts with,
“
X
and
R
charts with n = 4 are used to monitor a normally
distributed quality characteristic.
The control chart parameters are …..”.
(This exercise
illustrates the numerical process for developing the Operating Characteristic (OC) Curve
of a control chart. An OC
curve is simply a “Probability of Acceptance curve.”)
Problem #4: and Exercise 6.31. (Exercise 6.56 of 7
th
Edition; Exercise 6.48 of 6
th
Edition; Exercise 5-48 of 5
th
Edition; 5-41 of 4
th
Edition).
The exercise statement is,
“
Consider the
𝑋
̅
chart i
n Exercise 6.55.
Find the average run length for the chart.” Note:
A more precise way of phrasing the question is the following: “What is the average run
length for the chart to detect the shift to 790.”
3
Problem #5: Part (a) and Part (b) of Exercise 6.5
(Exercise 6.9 of the 7
th
Edition;
Exercise 6.3 of the 6
th
Edition; Exercise 5-3 of the 5
th
Edition; 5-3 of the 4
th
Edition).
The exercise statement starts with,
“The data shown in table
are the deviations from
nominal diameter for holes drilled in the carbon-fiber composite material used in
aerospace manufacturing. …..”
Use the mathematical functions of Microsoft Excel to help you solve this problem, whose
solution involves a large amount of computation; do not attempt a completely manual
solution.
The data shown in table have been entered into a companion Excel worksheet.
Use it for
your convenience and to avoid typos in your data entry.
Solution:
Your Excel answers should be the same or approximately equal to those shown
on the following two control charts, which are produced by Minitab.
(b)
𝜎
̂ =
𝑅
̅
𝑑
2
= 27.30
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