Week 4 Homework
Name
Bryant Devine____
1. An American company is beating the odds against foreign competition. During the
past 8 years, the company has averaged 8% compounded growth. The company
chairman and CEO credits their competitiveness with their focus on providing zero
defect quality.
Though the company relies primarily on preventive quality measures such as nonfaulty systems, employee training, and design for quality, they do inspect a randomly
selected group of axles each day as a quality measure.
They ship 4.600 axles a day ($1,175 worth of components in each vehicle). This
steady stream of production has a defect rate of 0.01 %. Calculate the probability
that 0 defects will be found in a sample of 160.
160
0!160!
(.01)0 (.99)160 = .20 or 20 %
2. As container ships get ready to leave to begin their careers on the high
seas, a final inspection is held in order to create a list containing
defects that need to be corrected before the ship can put to sea. The
following information and chart is data for these final inspections. Each
sample represents one ship (n = 1). Create a c chart.
135
30



= 4.5 𝑟𝑜𝑢𝑛𝑑𝑒𝑑 𝑢𝑝 𝑡𝑜 5
What is the UCL? c = 5 + 3√5 = 12
What is the LCL? c = 5 - 3√5 = -1.708203932 𝑟𝑜𝑢𝑛𝑑𝑒𝑑 𝑢𝑝 𝑡𝑜 0
What is c bar? 5
The process capability is 5, an upward trend
3. Describe a situation where you, as the customer, did not receive the
product or service you expected. What costs of quality did you, as the
customer, incur? What costs of quality did the provider of the product
or service incur?
I bought windows a year ago from American Exteriors, which would
help me save on my energy costs. The company was very
professional; including the installers, yet the product I received has
saved me little in the way of energy costs. Nonetheless, since they
were installed in September of last year, I have seen no decrease in
my energy bills. I have wasted time and money on these windows,
which were supposed to save me money. The company has incurred intangible
costs because the windows are not performing to my expectations. When I say
intangible, I mean that I have dissatisfaction, the company image is discredited, and
they have lost me as a customer and wasted my time. In order to overcome this they
will need to go back and fix their internal failures.
Summers, D. C. S. (2010). Quality. (5th ed., pp. 411). Upper Saddle, NJ: Prentice
Hall.
4. According to studies by VHA Inc., an alliance of community hospitals, on average, it
takes 49 minutes before a doctor sees a patient in a U.S. emergency room.
One hospital, Oakwood Medical Center in Dearbom, Michigan, promises that anybody
taken to the emergency department would be seen by a doctor within 30 minutes - or
they would get a written apology and two free movie passes.
To reduce emergency room waiting times, the hospital improved patient check-in
procedures, billing, record keeping, and laboratory processes. Acute-care beds are set
aside for the real emergencies and an adjacent "fast track" section is designed to treat
lesser emergencies to get patients treated and released quickly.
One of the performance measures tracked by the hospital revealed that only 0.9% of
the 191,000 emergency room patients (about 1,700 people) were eligible for free
tickets. Given this level of performance, what is the probability that l or fewer customers
in the next 20 (n = 20) will have to wait longer than 30 minutes? In other words, what is
the probability that l or fewer customers will receive free tickets?
n=20
P(1 or fewer) = P(0) + P(1)
p=.09
q=.91
20
1!19!
20
0!20!
(.09)1 (.91)19 = .015
(.09)0 (.91)20 = .15
= .015+.15
= .17 or 17 %
5. On a pipeline, a device known affectionately as a pig, checks the pipeline seams for
leaks. The hundreds of thousands of seams along the 500 mile pipeline can be
considered a steady stream of product.
At any given moment, the pipeline managers estimate that 1% of the seams will need
repair. What is the probability that in the next sample of 25 seams, 2 or fewer of the
seams will need repair?
n=25
P (2 or fewer) = P(0) + P(1) + P(2)
p=.01
q=.99
25
0!25!
20
1!24!
(.01)0 (.99)25 = .778
(.01)1 (.99)24 = .079
20
2!23!
(.01)2 (.99)23 = ?
= .778+.079+?
=?
6. The average number of oil tanker ships arriving at a particular port each day is ten.
The facilities at the port can dock and load/unload at most, 15 tanker ships per day.
What is the probability that the port will need to turn a ship away? In other words, what
is the probability that the number of ships arriving per day will be greater than 15?
p=0.33
n=15
15!
P (1) = 1!14! (0.333)1 (0.667)14= .01 or 1%
7. An environmental engineer places monitors in a large number of streams to measure
the amount of pollutants in the water. If the amount of pollutants exceeds a certain level,
the water is considered non-conforming.
In the past, the proportion non-conforming has been 0.04. What is the probability that
one of the fifteen samples taken today will contain an excessive amount of pollutants?
p=0.04
n=15
15!
P (1) = 1!14! (0.03)1 (0.97)14= .34 or 34%
8. At a major airport, over 1000 planes land each day on their runways. This steady
stream of air traffic has created complexities and delays in landing and departing
planes. At any given moment, the airport managers estimate that there is a 1% chance
of a runway incursion (near miss). What is the probability that in the next sample of 25
flights, 1 or fewer runway incursions will occur?
n=25
P(1 or fewer) = P(0) + P(1)
p=.01
q=.99
25
1!24!
25
0!25!
(.01)1 (.99)24 = .008
(.01)0 (.99)25 = .778
= .778+.008
= .79 or 79 %
9. What does the upper control limit of either a p, np, c, or u chart tell us about the
process? What does the lower control limit tell us?
There should be no pattern in the data, such as trends, runs, cycles, points
above the upper control limits. The number of points of each side of the
centerline should be balanced with most of the points close to the centerline. All
the points should fall between the upper and lower control limits, points beyond
this indicates instability on the process. In all these charts, it is desirable for the
points to approach the lower control limits. This marks an improvement in quality
and should be studied to determine their causes and to ensure that it is repeated
in the future.
10. What are intangible costs? Why should a company be concerned about the
intangible costs associated with not providing a product or service that the consumer
expected?
Intangible costs are the hidden costs associated with providing a nonconforming
product or service to a customer; involve the company’s image, i.e., customer
dissatisfaction, lost sales, loss of customer goodwill, time loss, and offsetting
customer dissatisfaction. Nonetheless, Intangible costs are important for a
company to be concerned about because they can be “three to four times as
great as the tangible costs of quality” (Summers, pp. 411). The companies must
ensure that they understand that they exist in order correct them in the future.
11. Describe the difference between an internal failure cost and an external failure cost.
Give an example of each.
Internal failure costs are costs that are incurred because of identifying defective
products before they are shipped to customers, e.g., rework, scrap, repair,
material-failure reviews, design changes, corrective actions, making up lost time,
rewriting a proposal, stocking extra arts, engineering change notices. External
Failure costs represent a category in the total cost of quality where the quality
costs are related to defects found after delivery of the product to the customer,
e.g. returned goods, corrective actions, warranty costs, customer complaints,
liability costs, penalties, replacement parts, and investigating complaints.
12. Describe the difference between a prevention cost and an appraisal cost. Give an
example of each.
Prevention cost is an expense incurred as part of the quality control efforts of a
business performed in order to avoid having defective products reach
consumers, e.g., quality planning, quality program administration, supplier-rating
program, customer requirements/expectations market research, product
design/development, equipment and preventive maintenance, and quality
education programs. Appraisal costs is an expense incurred in inspection and
test activities aimed at ensuring consistent quality and conformance to
established requirements or specifications, e.g., in-process inspection, incoming
inspection, testing/inspection equipment audits, and product evaluations.