Lowell D. Outland
Quality Control (IET 319)
Department of Industrial and Engineering Technology
College of Science and Technology
Morehead State University
Exam 2
SPRING 2010
Note: The exam is open book. There are five questions. Please answer all the five
questions. You have two hours to complete the exam.
IMPORTANT NOTE: SHOW YOUR WORK INCLUDING THE FORMULAS
YOU USE.
1. CHAPTER 5: Control Charts for Variables [20 points]
Control charts for X and R are kept on the weight in pounds of a color pigment
for a batch process. After 25 subgroups with a subgroup size of 4,  X  52.08
lb and
(i) X
 R  11.82 lb. Assuming the process is in a state of control, compute:
0
𝑔
̅̅̅ / 𝑔 = 52.08 / 25 = 2.0832
= 𝑋 = ∑𝑖=1 𝑋𝑖
𝑔
(ii) R0 = R = ∑𝑖=1 𝑅̅ 𝑖 / 𝑔 = 11.82/ 25 = 0.4728
0.4728
(iii)  0 = 𝑅0 ⁄𝑑2 =
(iv) UCLR
=
𝐷2 𝜎0
=
2.059
= 0.2296
(4.698)(. 2296) = 1.078
(v) LCLR = D1σ0 = (0)(.2298) = 0
2. Control Charts for Variables [20 points]
A new process is started and the sum of the sample standard deviation for 25
subgroups of size 4 is 750. Compute:
𝑔
∑𝑖=1 𝑠𝑖
s =
(ii)
 0 = ∑ 𝑠 /𝑔 =
𝑔
=
750
(i)
25
= 30
30
0.9213
= 32.56
If the specifications are 800  50 , what is the
820?
Min(USL-𝑋 )/ 3𝜎
= 0.12
C pk
value when the process average is
Lowell D. Outland
3. Chapter 8: Control Charts for Attributes [20 points]
An electronics parts manufacturer samples 100 parts each day from a batch of
6,000. The standard value for the fractions non-conforming is 0.15.
Compute:
np0 = 100(0.15) = 15
(i)
the UCL = np0 + 3 √np0(1-p0) = 15 + 3√15(1-0.15) = 25.712
(ii)
the LCL = np0 - 3 √np0(1-p0) = 15 - 3√15(1-0.15) = 4.288
4. CHAPTER 7: Fundamentals of Probability [20 points]
A census official examines 3 data entries to determine if they are acceptable. It is
known that the probability of finding no conforming data sets in a sample of 3
entries is 0.850, the probability of finding 1 nonconforming entry in the sample of 3
is 0.005, the probability of finding 3 nonconforming entries in the sample of 3 is
0.065. What is the probability of finding 2 nonconforming entries in the sample of
3?
P(0) + P(1) +P(2) +P(3) = 1.000
0.850 + 0.005 + P(2) + 0.065 = 1.000
P(2) = 0.008
5. CHAPTER 7: Fundamentals of Probability [20 points]
A construction company produces 6 different colored bricks of which 4 will be used
in designing a retaining wall. How many combinations are possible?
n!/r!(n-r)! = 6!/ 4!(6-4) = 360