Design for Quality and Product Excellence 21
ANSWER – CONTINUED
5. The Importance and Competitive Evaluation of customer requirements can be read
from the survey results in the data tables in spreadsheet Prob07-05.xlsx that are provided,
and placed under their respective columns
Georgio’s Giant Gyros technical requirements must be placed on a more equal basis, which
would best be shown as units/ounce, except for the percent fat value. These are shown
below.
Company
Price/Oz.
Calories/Oz.*
Sodium/Oz.*
Fat (%) *
Georgio’s
$0.545
80.0
159.1
13
Thus, we can see from the competitive evaluation of technical characteristics and Georgio’s
targets, that if Georgio’s is already low in price per ounce, as well as calories, and percent
6. A blueprint specification for the thickness of a refrigerator part at Refrigaria, Inc. is 0.300
± 0.025 centimeters (cm). It costs $25 to scrap a part that is outside the specifications.
Determine the Taguchi loss function for this situation.
Answer
6. The Taguchi Loss Function for refrigerator part at Refrigaria, Inc. is: L(x) = k (x – T)2
7. A team was formed to study the refrigerator part at Refrigaria, Inc. described in Problem
6. While continuing to work to find the root cause of scrap, they found a way to reduce
the scrap cost to $15 per part.
a. Determine the Taguchi loss function for this situation.
$0.567
85.3
124.0
23
Design for Quality and Product Excellence 22
b. If the process deviation from target can be reduced to 0.015 cm, what is the Taguchi
loss?
Answer
7. The Taguchi Loss Function is: L(x) = k (x – T)2
a) $15 = k (0.025)2
8. A specification for the length of an auto part at PartsDimensions, Inc. is 5.0 ± 0.10
centimeters (cm). It costs $40 to scrap a part that is outside the specifications. Determine
the Taguchi loss function for this situation.
Answer
8. The Taguchi Loss Function is: L(x) = k (x – T)2
9. A team was formed to study the auto part at PartsDimensions described in Problem 8.
While continuing to work to find the root cause of scrap, the team found a way to reduce
the scrap cost to $20 per part.
a. Determine the Taguchi loss function for this situation.
b. If the process deviation from target can be reduced to 0.040 cm, what is the Taguchi
loss?
Answer
9. The Taguchi Loss Function is: L(x) = k (x – T)2
Design for Quality and Product Excellence 23
10. Ruido Unlimited makes electronic soundboards for car stereos. Output voltage to a
certain component on the board must be 12 ± 0.5 volts. Exceeding the limits results in an
estimated loss of $60. Determine the Taguchi loss function.
Answer
10. The Taguchi Loss Function is: L(x) = k (x – T)2
11. An electronic component at Eltcomp has a specification of 100 ± 0.4 ohms. Scrapping
the component results in a $81 loss.
a. What is the value of k in the Taguchi loss function?
b. If the process is centered on the target specification with a standard deviation of 0.2
ohm, what is the expected loss per unit?
Answer
11. For Eltcomp’s specification of 100 ± 0.4 ohms:
12. An automatic cookie machine at AutoCM, Inc., must deposit a specified amount of 25 ±
0.3 grams (g) of dough for each cookie on a conveyor belt. It costs $0.03 to scrap a
defective cookie. A sample of 50 cookies was drawn from the production process, which
has been determined to be approximately normally distributed, and the results, in grams,
can be found in worksheet tab Prob.7-12 in the Excel file C07Data file on the Student
Companion Site for this chapter.
a. What is the value of k in the Taguchi loss function?
b. Determine how much the process varies from the target specification, based on the
mean difference and standard deviation of the sample results. What is the expected loss
per unit?
Answer
12. For a specification of 25 ± 0.3 grams and a $0.03 scrap cost:
Design for Quality and Product Excellence 24
Analysis of the dataset for Prob. 7-12 provides the following statistics:
a) L(x) = k (x – T)2
13. A computer chip designed by the MicroKeeb Co. has a specification for the distance
between two adjacent pins of 2.000 ± 0.002 mm. The loss due to a defective chip is $4. A
sample of 25 chips was drawn from the production process and the results, in millimeters,
can be found in the worksheet tab Prob. 7-13 in the Excel file C07Data file.
a. Compute the value of k in the Taguchi loss function.
b. What is the expected loss from this process based on the sample data?
Answer
13. For a specification of 2.000 ± .002 mm and a $4 scrap cost:
Analysis of the dataset for problem 7-13 provides the following statistics:
x
= 2.00008; D = 2.00008 – 2.00 = 0.00008
14. In the production of Raphael Transformers, any output voltage that exceeds 120 ± 10
volts is unacceptable to the customer. Exceeding these limits results in an estimated loss
of $200. However, the manufacturer can adjust the voltage in the plant by changing a
resistor that costs $2.25.
a. Determine the Taguchi loss function.
b. Suppose the nominal specification is 120 volts. At what tolerance should the
transformer be manufactured, assuming that the amount of loss is represented by the cost
of the resistor?
Design for Quality and Product Excellence 25
Answer
14. a) The Taguchi Loss function is: L(x) = k (x – T)2
15. At Elektroparts Manufacturers’ integrated circuit business, managers gathered data from
a customer focus group and found that any output voltage that exceeds 55 ± 0.5 volts was
unacceptable to the customer. Exceeding these limits results in an estimated loss of $75.
However, the manufacturer can still adjust the voltage in the plant by changing a resistor
that costs $2.00.
a. Determine the Taguchi loss function.
b. Suppose the nominal specification remains at 55 volts. At what tolerance should the
integrated circuit be manufactured, assuming that the amount of loss is represented by the
cost of the resistor?
Answer
15. a) The Taguchi Loss function is: L(x) = k (x – T) 2
75 = k (0.5)2
Design for Quality and Product Excellence 26
16. Two processes, P and Q, are used by a supplier to produce the same component, Z, which
is a critical part in the engine of the BearingPort 778 airplane. The specification for Z
calls for a dimension of 0.24 mm ± 0.03. The probabilities of achieving the dimensions
for each process based on their inherent variability are shown in the table found in the
C07Data file for Prob.7-16 on the Student Companion Site for this chapter. If k =
60,000, what is the expected loss for each process? Which would be the best process to
use, based on minimizing the expected loss?
Answer
16. For the BearingPort 778 plane parts (see spreadsheet Prob07-16.xlsx for detailed
calculations):
Specifications are 24 ± 3 mm
BearingPort Airplane Co.
Calculation of Taguchi Loss Values
Value
Loss ($)
Process P
Probability
Weighted
Loss ($)
Process Q
Probability
Weighted
Loss ($)
0.20
96.00
0
0.00
0.02
1.92
0.21
54.00
0.12
6.48
0.03
1.62
0.25
0.12
0.72
0.15
0.90
Design for Quality and Product Excellence 27
17. The average time to handle a call in a the Call-Nowait call processing center has a
specification of 6 ±1.25 minutes. The loss due to a mishandled call is $12. A sample of
25 calls was drawn from the process and the results, in minutes, can be found in the
C07Data file for Prob.7-17 on the Student Companion Site for this chapter.
a. Compute the value of k in the Taguchi loss function.
b. What is the expected loss from this process based on the sample data?
Answer
17. For a specification of 6 1.25 minutes and a $12 call mishandling cost:
a) L(x) = k (x – T)2
18. Massive Corporation’s tested five motors in a 900-hour test. Compute the failure rate if,
three failed after 200, 475, and 750 hours and the other two ran for the full 900 hours
each.
Answer
18. Massive Corporation’s motors have a failure rate of:
19. The life of a Supercellular phone battery is normally distributed with a mean of 950 days
and standard deviation of 40 days. Using the Excel functions (see Chapter 6), determine
the following:
a. What fraction of batteries is expected to survive beyond 1010 days?
b. What fraction will survive fewer than 900 days?
c. Draw a chart of the reliability function using Excel.
d. What length of warranty is needed so that no more than 10 percent of the batteries will
be expected to fail during the warranty period?
Answer
Design for Quality and Product Excellence 28
19. a) P(x > 1010) = 1 – P(x < 1010)
c) The reliability function looks approximately as follows (see spreadsheet Prob07–18.xlsx
for details):
c) Let xw be the limit of the warranty period.
0.000
0.100
0.800
0.900
1.000
775 800 825 850 875 900 925 950 975 1000 1025 1050
Battery Life – Hours
Reliability Curve
Design for Quality and Product Excellence 29
20. Widetred, Inc. makes automobile tires that have a mean life of 60,000 miles with a
standard deviation of 2,000 miles. Using Excel functions (see Chapter 6), determine the
following:
a. What fraction of tires is expected to survive beyond 63,250 miles?
b. What fraction will survive fewer than 56,600 miles?
c. Draw a chart of the reliability function using Excel.
d. What length of warranty is needed so that no more than 5 percent of the tires will be
expected to fail during the warranty period?
Answer
20. a) P(x > 63250) = 1 – P(x < 63250)
c) The reliability function looks approximately as follows (see spreadsheet Prob07–20.xlsx
for details):
Design for Quality and Product Excellence 30
d) Let xw be the limit of the warranty period.
21. Livelong, Inc.’s computer monitors have a failure rate of 0.00095 units per hour. What is
the reliability function? Assuming an exponential distribution, what is the probability of
failure within 5,000 hours? Calculate your answer using the appropriate mathematical
formula and verify your result using Excel.
Answer
21. The reliability function for Livelong, Inc.’s monitors is R(T) = 1 – F(T) = e–T
22. An electronic component in a satellite radio has failure rate of = .000015. Find the mean
time to failure (MTTF). What is the probability (assuming an exponential probability
distribution) that the component will not have failed after 12,000 hours of operation?
Calculate your answer using the appropriate mathematical formula and verify your result
using Excel.
Answer
22. The MTTF for the component is 𝜃 = 1
𝜆= 1
0.000015; so, = 66666.67
23. The MTBF of an integrated circuit made by Outer Limits, Inc.is 18,000 hours. Calculate
the failure rate.
Design for Quality and Product Excellence 31
Answer
24. A manufacturer of MP3 players, purchases major electronic components as modules. The
reliabilities of components differ by supplier (see diagram, below). Suppose that the
configuration of the major components is given by:
The components that can be purchased from three different suppliers. The reliabilities of
the components are as follows:
Component Supplier 1 Supplier 2 Supplier 3
A 0.98 0.96 0.95
B 0.95 0.97 0.98
C 0.99 0.96 0.94
Transportation and purchasing considerations require that only one supplier be chosen.
Which one should be selected if the radio is to have the highest possible reliability?
Answer
24. Supplier 1: RaRbc = (0.98) [1 – (1 – 0.95)(1 – 0.99)] = 0.980
25. An electronic missile guidance system consists of: Components A, B, C, and D which
have reliabilities of 0.98, 0.97, 0.91, and 0.99, respectively (see the following diagram).
What is the reliability of the entire system?
a. What is the reliability of the entire system?
b. Suppose the customer requires a reliability of at least 0.98. Try to find a configuration
that meets this requirement using the minimum number of components.
Answer
25. a) The reliability of the parallel Rcc shown in the diagram from the problem above, is
calculated as: