Quality Control 5th Edition Montgomery Solutions Manual

Chapter 2 Exercise Solutions
Several exercises in this chapter differ from those in the 4th edition. An “*” following the
exercise number indicates that the description has changed (e.g., new values). A second
exercise number in parentheses indicates that the exercise number has changed. For
example, “2-16* (2-9)” means that exercise 2-16 was 2-9 in the 4th edition, and that the
description also differs from the 4th edition (in this case, asking for a time series plot
instead of a digidot plot). New exercises are denoted with an “ ”.

2-1*.
(a)
n
x n 16.05 16.03 ⋯ 16.07 16.029 oz
xi 12
i 1




(b)
n n
 xi2 −  xi n
s i=1 i=1
2
(16.052 +⋯+16.072 ) − (16.05 +⋯+16.07)2 12 0.0202 oz
n −1 12 −1

MTB > Stat > Basic Statistics > Display Descriptive Statistics
Descriptive Statistics: Ex2-1
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Ex2-1 12 0 16.029 0.00583 0.0202 16.000 16.013 16.025 16.048
Variable Maximum
Ex2-1 16.070



2-2.
(a) n

x n 50.001 49.998 ⋯ 8 50.002 mm
xi 50.004
i 1




(b)
n n
 xi2 −  xi n
s i=1 i=1
2
(50.0012 +⋯+ 50.0042 ) − (50.001+⋯ + 50.004)2 8 0.003 mm
n −1 8 −1

MTB > Stat > Basic Statistics > Display Descriptive Statistics
Descriptive Statistics: Ex2-2
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Ex2-2 8 0 50.002 0.00122 0.00344 49.996 49.999 50.003 50.005
Variable Maximum
Ex2-2 50.006


2-1

,Chapter 2 Exercise Solutions

2-3.
(a) n

x n 953 955 ⋯ 9 952.9 °F
xi 959
i 1




(b)

x − x n
(9532 +⋯+ 9592 ) − (953 +⋯+ 959)2 9
s 3.7 °F
n −1 9 −1




MTB > Stat > Basic Statistics > Display Descriptive Statistics
Descriptive Statistics: Ex2-3
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Ex2-3 9 0 952.89 1.24 3.72 948.00 949.50 953.00 956.00
Variable Maximum
Ex2-3 959.00



2-4.
(a)
In ranked order, the data are {948, 949, 950, 951, 953, 954, 955, 957, 959}. The sample
median is the middle value.

(b)
Since the median is the value dividing the ranked sample observations in half, it remains
the same regardless of the size of the largest measurement.


2-5.
MTB > Stat > Basic Statistics > Display Descriptive Statistics
Descriptive Statistics: Ex2-5
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Ex2-5 8 0 121.25 8.00 22.63 96.00 102.50 117.00 144.50
Variable Maximum
Ex2-5 156.00




2-2

,Chapter 2 Exercise Solutions

2-6.
(a), (d)
MTB > Stat > Basic Statistics > Display Descriptive Statistics
Descriptive Statistics: Ex2-6
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Ex2-6 40 0 129.98 1.41 8.91 118.00 124.00 128.00 135.25
Variable Maximum
Ex2-6 160.00


(b)
Use n= 40 7 bins
MTB > Graph > Histogram > Simple

Histogram of Time to Failure (Ex2-6)

20




15
Frequency




10




112 120 128 136 144 152 160
Hours



(c)
MTB > Graph > Stem-and-Leaf
Stem-and-Leaf Display: Ex2-6
Stem-and-leaf of Ex2-6 N = 40
Leaf Unit = 1.0
2 11 89
5 12 011
8 12 233
17 12 444455555
19 12 67
(5) 12 88999
16 13 0111
12 13 33
10 13
10 13 677
7 13
7 14 001
4 14 22
HI 151, 160




2-3

, Chapter 2 Exercise Solutions

2-7.
Use n 9 bins
90

MTB > Graph > Histogram > Simple

Histogram of Process Yield (Ex2-7)
18

16

14

12
Frequency




10




84 88 92 96
Yield




2-4