Chapter 8: Quality Management
Review Questions
1.
What is the role of quality in strategic planning within any company?
Answer: Quality affects every aspect of an organization. High quality products and
processes allow a company to gain a competitive advantage through higher customer
satisfaction and lower scrap and rework costs. In addition, as the text mentions, higher
quality also affects worker morale positively. It is not just the quality products that count.
It is the quality ethic that relates to integrity and is a source of pride in workmanship for
all employees. One of Deming’s 14 points is “remove barriers to pride of workmanship.”
2.
What is the competitive role of quality externally (in the marketplace)?
Answer: There are several areas where quality is an important agent to gaining
competitive advantage. Products having better quality have a marketplace advantage.
Better quality protects against competitors that compete on price. Better quality saves
money by decreasing defectives that must be scrapped or reworked. Better quality
increases customer loyalty. Better product quality obtained at a reasonable price generally
leads to growth in market shares and increases in revenues. The function of price-elasticity
is well-known but equally important is the quality-price-elasticity relationship which
(among other effects) depicts the impact of quality on substitutability. Low quality
products are not substitutable for high quality products when a consumer can afford to pay
more. Quality differentials change the price-elasticity relationship. As an example, a Coach
purse sells at a high price because Coach –aficionados do not believe that there is anything
that can substitute for it. Other examples are Apple iPhones and Tiffany bracelets.
3.
Since quality is important in different ways to different providers of services, why do we
need to teach what is so obvious?
Answer: Surprisingly consumers are far more sensitive to quality of services rendered than
are the providers of those services. There are many good reasons for this. In particular note
the answer to Review Question 6. We will offer a different interpretation of the same cause
here. Providers of services have many things to consider beside quality. For example, they
must take into account costs and reasonable charges for services provided. For reasons that
psychologists can probably explain, as consumers we wear one hat; as producers selling out
services we wear a different hat. We must teach producers to listen to the voice of the
customer and to learn to walk in the customer’s shoes. When we say that something about
quality is obvious—we must be very careful. Steak lovers and vegetarians will not have the
same opinion about restaurants.
4.
What is TQM and why is it important for attaining better quality?
Answer: TQM was never directly addressed in this chapter because some teachers like the
concept but others do not. We did give a number of References for further reading. For
those of us who like it, TQM stands for Total Quality Management. There was a decade of
adoration of the TQM concept. It was supposed to solve all existing problems. The time
has now come to define and explain the idea behind total quality management. TQM is a
management strategy that requires a company-wide systems approach to quality. If
quality management is company-wide, then, everyone who works in any capacity is part of
the team responsible for achieving the best quality results. TQM is the procedure of choice.
The attainment of TQM is the critical precursor to excellence in quality. TQM enables the
systems approach to operate effectively. TQM could have been called SMQ, for Systems
Management of Quality, because the systems approach is so important to TQM success.
5.
Friends have said that TQM means the quickest method. Is that correct?
Answer: It is not correct. Criticism of TQM could be based on there being better ways to
develop a quality culture but not on its being a quick and dirty approach. Far from that, it
may seem to be too sweeping an effort to instill quality goals.
6.
What are the differences between consumer and producer definitions for quality?
Sometimes the consumer is called the buyer and the producer is called the supplier. What
are the differences between them?
Answer: The producer’s definition of quality is about the properties of goods and
services without distinctions about being good or bad. It is based on the commitment to
deliver according to specifications. Many of these properties are tangible and measurable.
The producer is primarily dedicated to achieving conformance to specifications. If specs
are met, then there are no defectives and quality is acceptable. The producer ships to the
buyer (aka consumer, customer, purchasing agent). Producers are aka suppliers and
vendors. The consumer’s view is that quality relates to the degree of excellence of things
that matter to that consumer’s market segment. Comparisons are relative being based on
experience of the user with the product-class. Value for money paid is conditioned by
opinions of friends and family as well as by the utility derived from use. The consumer’s
view is quite likely to be intrinsic, innate and subjective.
7.
How does the systems approach apply to the following statement: Quality—like a
chain—is betrayed by its weakest link.
Answer: Like the orchestra that must play in synchronization to achieve quality music,
the company needs to synchronize its elements to achieve company-wide quality. One
musician that cannot or will not play in sync with the others will surely spoil the overall
musical effect. To mix metaphors, that one musician is the orchestra’s weak link. In the
organization, omit any one of its elements from participation and the systems concept
fails. Let one element, person, or department exclude itself from participation, and the
systems concept fails. The quality chain from an operations viewpoint is vulnerable when
any element that fails produces a defective product. The systems approach spots the
problem and corrects the weakness. Organizational weak links may show up only for
certain production items.
8.
Discuss the statement “Although the name TQM may be viewed by some as faddish, the
fundamental concept is not.”
Answer: Some people do not like the name TQM, and they think that it has been
overblown or overused. However, everyone agrees that what TQM stands for is here to
stay. While the label TQM is cosmetic, and assures no one of anything, the ingredients of
TQM, what TQM stands for, are both individually--and as a systems approach—relevant.
An alternative label that is more recent is Six Sigma. Both labels include statistical
methods but the latter uses probability to a more intense degree.
9.
What quality dimensions apply to the software industry?
Answer: The eight quality dimensions noted by Garvin apply to services, as well as to
manufactured goods. Treating a piece of computer software as a service (as compared to
hardware), and dropping the conformance item (not consumer-oriented), the dimensions
apply as follows. Appropriate quality dimensions for the software industry:
Performance: Does the program do what it is designed to do? How well, how fast does it
perform its basic task? How easy is the program to use? Is there network support and links
to other types of software? How steep is the learning curve?
Features: What does this product do that is beyond the standard for this class of software?
Is the product customizable? Is context-sensitive help provided? Does the program perform
additional classes of tasks, etc.?
Reliability: Is the program free of bugs, glitches, and General Protection Faults?
Durability: Holding up under stress of use may be an important software issue. Protection
against hacker’s malware creating a computer overload is sometimes necessary.
Serviceability: How easy is it to do software maintenance? Are upgrades frequent? Can
upgrades be accomplished while other programs are running? How good and how available
is customer support?
Aesthetics: How are the sensory communications accomplished? Are voice and touch part
of the control system? Are the visuals and sounds pleasing or disturbing?
Perceived quality: Is management satisfied with the cost, quality, and delivery time of the
software programs? Are users content with the operations of the programs?
10.
Set down appropriate quality dimensions for buying or designing a hybrid automobile.
a. Explain the differences in the systems approach.
Answer: Appropriate quality dimensions for a hybrid automobile:
Power
Safety features
Capacities
Fuel economy
Reliability
Durability
Resale value
Serviceability
Other features (accessories)
Design (ergonomics)
Design (style)
Perceived quality
a. The designer and the buyer use different criteria in their systems approach to the
qualities of the auto. From the company’s point of view it would be best if the two
perspectives are as aligned as possible. However, in actuality there are likely to be
differences. The designer will consider how to make the car look as elegant as
possible because the fuel economy issue is paramount in the marketing of this
auto. It must not look as though the owner is being frugal—rather it should send a
signal of a good citizen with a green conscience. Elegance of design style often
trumps comfort (design ergonomics). The buyer will check on the believability of
stated fuel economy and if satisfied will read in consumer magazines about
possible weaknesses including safety features (often overlooked by designers).
Ultimately the comfort of the auto will play a major role in the buyer’s decision.
11.
What problem exists because quality standards can age?
Answer: Standards change over time. What is an acceptable level of product quality one year
is not sufficient the next year. What is an appropriate quality program at one time, if not
dynamic, becomes unacceptable by staying the same. Companies that fail to keep up with
new standards may be barred from participating in markets that adhere to those standards.
This has been true with ISO 9000 criteria and Japanese national quality standards. It is clear
that market dynamics demand tracking results and that good market research is essential.
Products and processes must be altered to match changed expectations. The change agents
are P/OM and marketing. The information is provide my IT and market researchers.
12.
Explain P/OM’s relationship with market research.
Answer: Market research is the direct connection to the customer and how he/she uses the
product and perceives its quality. Market research is needed to explore alternative uses for a
product. This relates to “purpose utilities,” which may require reconsideration of the quality
standards for product performance. Frequently, there are regional differences in quality
perceptions, which may lead P/OM to have different standards for different regions. Market
research is important for determining the extent of choice or variety desired by customers.
Operations must produce the variety level demanded by the marketing strategy. Additional
variety in the product mix generally introduces additional production costs. To summarize,
P/OM needs to hear the voice of the customer. Marketing and market research provide the
channel but there needs to be a listener before anyone can hear.
13.
Explain how consistency of conformity translates into low reject rates.
Answer: Conformance is the degree to which measured product attributes correspond to
the design specifications. If there is consistency in conformance, then there is consistency
in meeting design specifications. That is, the product as manufactured meets the design
established for the product; such an item is acceptable under quality control standards.
Consistency of conformance removes or reduces a source of rejected items. The possible
disconnect lies between design specifications and customer satisfaction with them.
14.
Discuss the strengths and weaknesses of quality circles. Are they similar to student cohort
work groups?
Answer: We expect the students to look up Quality Circles (QC). Wikipedia has a very good
entry. Using a systems point of view, the strengths of Quality Circles include: (1) Teamwork
for productivity is enhanced; (2) Absenteeism and turnover are diminished; (3) Pride in work
is real, not fictional. The weaknesses of quality circles include: (1) QCs can fail in their
mission if top management is not sincere; (2) QCs may impair quality achievement when the
team is improperly chosen and the program not well-designed; (3) Poor training dooms QCs.
Excellent training is required for QC success.
15.
What are the ways to reduce the cost of detailing?
Answer: Detailing involves removing defective items from a lot rejected by acceptance
sampling. Then, every item in this detailed lot conforms to specifications. Some methods of
reducing the cost of detailing are: (1) Reduce the percent defective so that there are fewer
defectives to begin with and a lower chance the lot will be rejected; (2) Raise the rejection
number so that fewer lots are rejected; (3) Redefine defective more liberally to allow more
items to pass inspection; (4) Reduce the wage of detailers; (5) Stop performing acceptance
sampling. Although all of these methods decrease the cost of detailing, not all of these are
compatible with a systems approach. Number 1 is the only cost reduction method that treats
the problems and not the symptoms. That is what the systems approach advocates.
Explain what the House of Quality does and how it works. (Look up House of Quality in
Wikipedia. Follow up on Quality Function Deployment before answering this question.)
16.
Answer: The House of Quality (HOQ) is a model for mapping the relationships that exist
between customers—and those that supply them (i.e., producers of goods and services). By
using the HOQ model there is a graphical picture that maps the interactive and mutual
concerns of sales and marketing with those of design, production/operations, engineering,
and the voice of the customer. As such, HOQ is a combination of description and analysis.
Customer needs are identified by marketing. Operations identifies process capabilities and
design factors that are supposed to satisfy those needs. HOQ includes means to identify
differential needs of market segments and the comparison of the current product to its
competition. This results in a set of interrelated matrices that form a TQM scoring model.
The end result is a graphic “house” that attempts to show how well the product meets the
needs of customers. This is often referred to as listening to the voice of the customer.
17.
What prize competitions exist for quality and why are these prizes given?
Answer: Prize competitions for quality include the Deming Prize and the Malcolm
Baldrige National Quality Award*. The Deming Prize emphasizes success with Statistical
Process Control and with Quality Function Deployment. This prize results from Deming’s
profound influence on Japanese manufacturing practices. The Malcolm Baldrige National
Quality Award was conceived as a program to trigger competition among U.S. companies
with respect to their adherence to management principles that resulted in quality products.
This award was created in 1987 in reaction to the outstanding success of Japanese export
firms, and was undertaken to spur improvement in the quality of American products.
*Established by Congress for manufacturers, service businesses and small businesses, the Baldrige Award was designed
to raise awareness of quality management and recognize U.S. companies that have implemented successful qualitymanagement systems.
Problems
1. After setup in the job shop, the first items made are likely to be defectives. If the order size (X)
calls for 125 units, and the expected percent defective (p) for start-up is 7 percent, how many
units should be made?
Solution: This problem (i.e., one like it) is repeated in Chapter 11 where it is used to reveal
the potential for innovation to cut down on waste. Brainstorming to cut 7 percent in half is a
smart goal. In this case, we want to show the fundamental costs of producing defective items.
After removing the defectives, more items must be produced to fill this order for X units.
The defective’s cost is usually large enough to warrant rework. If not it might be sold as
scrap. A lot of time and effort has gone into non-value-adding activities. This is the very
essence of a non-lean system. Time is lost. Rather than adding value, defectives subtract
value. Inventory is wasted. Now, let us turn to the calculation (the derivation of β will be
found in Problem 8 of Chapter 11:
ORDER SIZE (X) = (RUN QUANTITY; X + β) = X + X(p/(1 – p)) = 125 + (125)(p/(1-p)) =
125[1+(0.07)/(0.93)] = 125(1.075) = 134.4086. A simpler alternative formulation is:
RUN QUANTITY = ORDER SIZE (X)/(1-p) = 125/(1 – p) = 125/(0.93) = 125(1.075) =
134.4086. The number of defectives is 134.4086 x 0.07 = 9.4086 units (on average).
2. A subassembly of electronic components, called M1, consists of 5 parts that can fail. Three
parts have failure probabilities of 0.03. The other two parts have failure probabilities of 0.02.
Each M1 can only be tested after assembly into the parent DVR. It takes a week to get M1
units (the lead time is one week), and the company has orders for the next five days of 32, 44,
36, 54, and 41. How many M1 units should be on hand right now so that all orders can be
filled?
Solution:
This is a generalization of the second solution method used in Problem 1:
BATCH SIZE = ORDER QUANTITY/
in
i0
(1 – pi).
Here, the order quantity = 32 + 44 + 36 + 54 + 41 = 207 and p1 = p2 = p3 = 0.03 and
p4 = p5 = 0.02:
BATCH SIZE = 207(1 – 0.03)3(1 – 0.02)2 = 236.16.
3. Use SPC with the following table of data to advise this airline about its on-time arrival and
departure performance. These are service qualities highly valued by their customers. The
average total number of flights flown by this airline is 660 per day. This represents three
weeks of data. It is suggested that a late flight be considered as a defective. Draw up a p-chart
and analyze the results. Discuss the approach.
The Number of Late Flights (NLF) Each Day
Day
NLF
1
31
2
56
3
65
4
49
5
52
6
38
7
47
8
43
9
39
10
41
11
37
12
48
13
45
14
33
15
22
16
34
17
29
18
31
19
35
20
44
21
37
Assuming that days 1, 8, and 15 are Mondays; 2, 9, and 16 are Tuesdays, etc., Use the
concepts from chapter on forecasting to determine if there is any correlation between day
of the week and the number of late flights.
Solution:
This problem is covered in Section 8.9 of the text.
See Excel file SMCh08 (worksheet P3) for calculations and p chart.
First, chart the p-values for the NLF per day as a percent of total flights per day (660).
Day
NLF
p
Day
1
NLF
31
0.047
8
43
2
56
0.085
9
3
65
0.098
4
49
5
p
Day
NLF
p
0.065
15
22
0.033
39
0.059
16
34
0.052
10
41
0.062
17
29
0.044
0.074
11
37
0.056
18
31
0.047
52
0.079
12
48
0.073
19
35
0.053
6
38
0.058
13
45
0.068
20
44
0.067
7
47
0.071
14
33
0.050
21
37
0.056
Sample calculation: for day 1, p = 31/660 = 0.0469. Second, determine the p-chart parameters.
p = Total NLF/(21*660) = 856/13,860 = 0.06176 or 0.0618.
σ = p 1 p / n =
0.0618(0.9382) / 660 = 0.00937.
Using the conservative 1.96 sigma limits means that if the process is under control, about 95
percent of the observations will be within the limits, which are
UCL = p + 1.96σ = 0.0618 + 1.96(0.00937) = 0.080, and
LCL = p – 1.96 σ = 0.0618 – 1.96(0.00937) = 0.043.
The above p-chart has 3 out of 21 (0.143) observations (on days 2, 3 and 15) out of bounds,
which is a little high (you would expect about 5 out of 100 = 0.05). Two extreme
observations are at the beginning of the first week, which possibly indicates that there
was some reason (such as start-up effects) for the clustering at that particular time.
Neglecting the first two observations, it appears that the lateness rate is 1:19 or 0.0526
which is close enough to 5 percent (which is what you expect for 1.96-sigma). That does
not mean it is acceptable to the airlines or its customers.
We ran a correlation between day of the week and number of late flights (NLF). There
are many ways to do that. We chose to rank order days by their total number of late
flights. Mondays were assigned 1 because they had the lowest total NLF (96). Thursdays
and Sundays with 117 were tied for number 2. Saturdays were assigned number 3, etc.
The correlation coefficients (under two different schemes) were very high. See Excel file
SMCh08 (worksheet P3). They ranged from 0.925 to 0.929. Result: We found a strong
correlation exists between day of the week and the number of late flights. Mondays had
the best record with the least number of late flights. Wednesdays and Fridays had the
worst records.
Now, look at the p-chart. The highest NLF value (above the UCL) occurred on a
Wednesday (Day 3). The next highest NLF value (also above the UCL) occurred on a
Tuesday (Day 2). The lowest NLF value (below the LCL) occurred on a Monday (Day
15). All of these observations align with the correlational results that we just determined.
4. New data have been collected for the BCTF. It is given in the following table. Start your
analysis by creating an x-bar chart and then create the R-chart. Provide interpretation of the
results.
Weight of Chocolate Truffles (in Grams)
Subgroup

Time-
1
2
3
4
I
II
III
IV
V
10 A.M.
30.00
30.50
29.95
30.60
11 A.M.
30.25
31.05
30.00
29.70
1 P.M.
29.75
29.80
30.05
29.80
3 P.M.
29.90
29.00
29.95
29.65
4 P.M.
30.05
29.60
29.90
29.85
Using Linear Regression, analyze the effect of the time of day on the truffle weights of
samples.
Solution:
For purposes of correlation and regression we have numbered subgroups I, II, III, IV and
V as 1, 2, 3, 4 and 5 respectively.
See Excel file SMCh08 (worksheet P4) for calculations.
Subgroup j =
1
2
3
4
5
Time
10:00
A.M.
11:00
A.M.
1;00
P.M.
3:00
P.M.
4;00
P.M.
1
30.00
30.25
29.75
29.90
30.05
2
30.50
31.05
29.80
29.00
29.60
3
29.95
30.00
30.05
29.95
29.90
4
30.60
29.70
29.80
29.65
29.85
Sum
SUM
Rj
121.05
121.00
119.40
118.50
119.4
599.35
30.26
30.25
29.85
29.63
29.85
149.8375
0.65
1.35
0.30
0.95
0.45
3.70
Quality Control Models (Statistical Quality Control [SQC]) will help create the x -chart and the
R-chart.
x = 149.84/5 = 29.9675, R = 3.70/5 = 0.74
Conversion factors are in Table 8.2 in the text.
To develop the 3-sigma control limits for the x -chart, A2 = 0.73 when n = 4,
So UCL = x + A2 R = 29.97 + 0.73(0.74) = 30.51 and
LCLx = x – A2 R = 29.97 – 0.73(0.74) = 29.43.
To develop the 3-sigma control limits for the R-chart, D3 = 0 and D4 = 2.28 when n = 4,
So UCLR = D4 R = 2.28(0.74) = 1.69 and
LCLR = D3 R = 0(0.74) = 0
The x-bar and the R-charts are drawn
below.
Studying the two graphs (above) reveals that this process appears to be under control. However, there is a
run of decreasing x-bar values starting at 11:00 A.M. and ceasing at 3:00 P.M. That may reflect
management’s urging supervisors to get as close to the ideal of 28.35 grams. It is worth analyzing so we
will perform a regression analysis using the average candy weights for each time period. Let us employ an
Excel spreadsheet for linear regression. There is a line (y = mx + b) which has a negative slope -0.145.
The correlation coefficient for these data is high with a negative value. This is apparent from the graph as
well as the slope of the regression line. That correlation coefficient is – 0.82123.
The following data were used for regression analysis.
Time (X)
X-bar (Y)
1
30.26
2
30.25
3
29.85
4
29.63
5
29.85
5. Analyze the following data to calculate the parameters for the x-bar chart and draw the
revised chart. Discuss the results. Using Linear Regression, analyze the effect of the time
of day on the revised truffle weights of samples. Also calculate the R-chart parameters and
discuss the results.
Subgroup
I
II
III
IV
V
Time-
10 A.M.
11 A.M.
1 P.M.
3 P.M.
4 P.M.
1
30.50
30.30
30.15
30.15
30.15
2
29.75
31.00
29.50
29.95
30.25
3
29.90
30.20
29.75
29.80
30.50
4
30.25
30.50
30.00
30.05
29.70

Solution:
See Excel file SMCh08 (worksheet P5) for calculations.
The difference between this table and Table 8.3 is in column IV. The 3:00 pm data in Table 8.3
have been removed and in their place we have substituted the following four values of xi:
(30.15), (29.95), (29.80), and (30.05). Since the 3 P.M. data of Table 8.3 are the four items that
are changed, only revised calculations are given here. Recalculating parameters for the x -chart:
For 3 pm: x = (30.15 + 29.95 + 29.80 + 30.05)/4 = 29.99 and R = 0.35.
Thus, x = 150.59/5 = 30.12 and R = 3.35/5 = 0.67.
To develop the 3-sigma control limits for the x -chart, A2 = 0.73 when n = 4, so
UCL x = x + A2 R = 30.12 + 0.73(0.67) = 30.61 and
LCL x = x – A2 R = 30.12 – 0.73(0.67) = 29.63
The old 3 pm data in Table 8.3 had the highest data point (32), the largest mean (30.9), and the
largest range 2.0); in short, the noisiest and highest data set. From the information and graph
above, the new 3 P.M. data set was much less noisy and had an average in the overall center. The
overall effect is a process more in control and desirable.
Changing time as we did in Problem 4 to 1, 2, 3, 4 and 5 we performed a regression analysis using the
average candy weights for each time period. Employing an Excel spreadsheet, there is a line (y = mx + b)
which has a minimal negative slope (- 0.0413). That negative slope is not very meaningful because the
correlation coefficient for these data is low enough (minus – 0.2684) to let us state that the data pattern is
fairly random around the mean. This would indicate that there is no pattern of changing p values from
early morning till late afternoon.
The following data were used for regression analysis.
Time (X)
X-bar (Y)
1
30.10
2
30.50
3
29.85
4
29.99
5
30.15
6. For the following tabulated data, draw the p-chart. NR = number of rejects and n = sample
size. Also analyze the effect of the day on the number of rejects in each sample using
regression analysis
Subgroup No.
1 - Monday
2 - Tuesday
3 - Wednesday
4 - Thursday
5 - Friday
NR
1
2
1
3
1
n
9
9
9
16
9
Solution:
This is similar to the bottom of Table 8.4 in the text.
See Excel file SMCh08 (worksheet P6) for calculations.
Subgroup
No.
NR
n
p
1
1
9
0.111
2
2
9
0.222
3
1
9
0.111
4
3
16
0.187
5
1
9
0.111
SUM
8
52
p = 8/52 = 0.15; now addressing the standard deviation for subgroups with n = 9:
z=
p(1  p) / n =
0.15(0.85) / 9 = 0.12
Using the conservative 1.96 sigma limits means that if the process is under control, about 95
percent of the observations will be within the limits, which are
UCL = p + 1.96σ = 0.15 + 1.96(0.12) = 0.39 and
LCL = p – 1.96σ = 0.15 – 1.96(0.12) = – 0.08 (so use 0.00).
Change the UCL for subgroup 4 because it does not have a sample size of 9, as follows:
σ=
p(1  p) /16 = 0.09
UCL = 0.15 + 1.96(0.09) = 0.33
LCL = – 0.03 (so use 0.00).
These data are better than those of Table 8.4 and the process looks in control for the information
that we have, but the value of p is uncomfortably high. We arranged the data so that days with
the lowest p value (0.111) were called 1; next highest p value days (0.187) were called 2; the
highest p value day (0.222) was called 3. Monday, Wednesday and Friday were each labeled 1.
Thursday was labeled 2 and Tuesday was labeled 3. The regression line has a minimal positive
slope of 0.05816, which means that variations by day are not large. However, the correlation
coefficient is 0.98529 indicating that the variations that exist may not be large but they are very
significant. Mondays, Wednesdays and Fridays have low p values; Tuesdays bring high values.
However, this amount of data is not enough to draw sound conclusions. We need many more
Mondays, Tuesdays, etc.
See Excel file SMCh08 (worksheet P6) for calculations.
The following data were used for rank correlation.
Rank
p-values
1
0.11111
Coefficient of
Correlation
1
1
0.11111 0.11111
Slope
2
0.1875
3
0.22222
0.98529
0.05816
7. A food processor specified that the contents of a jar of salsa should weigh 14 ± 0.10
ounces net. A statistical quality control operation is set up, and the following data are
obtained for one week:
Sample No
1 - Monday
2 - Tuesday
3 - Wednesday
14.10
13.90
14.40
14.06
13.85
14.30
14.25
13.80
14.10
14.06
14.00
14.20
4 - Thursday
5 - Friday
13.95
14.05
14.10
13.90
14.00
13.95
14.15
14.60
Using regression analysis, analyze the effect of the day on the sample means for the
weight of the contents of the salsa jars.
a.
b.
c.
d.
Construct an x- bar chart based on these 5 samples.
Construct an R-chart based on these 5 samples.
What points, if any, have gone out of control?
Discuss the results.
Solution:
This is similar in approach to the analysis of Table 8.3.
See Excel file SMCh08 (see worksheet P7) for calculations.
In the table below, we have rearranged the data so that days are shown as columns. First, we are
looking for any effect related to which day of the week is considered.
Day
Total
Weights
x
R
1
14.10
14.06
14.25
14.06
56.47
2
13.90
13.85
13.80
14.00
55.55
14.12
0.19
13.89
0.20
3
14.40
14.30
14.10
14.20
57.00
14.25
0.30
4
13.95
14.10
14.00
14.15
56.20
5
14.05
13.90
13.95
14.60
56.50
14.05
0.20
14.13
0.70
x = 14.09, R = 0.32.
a. For the 3-sigma x -chart,
A2 = 0.73 for n = 4, so UCL = x + A2 R = 14.09 + 0.73(0.32) = 14.32 and
LCL = x – A2 R = 14.09 – 0.73(0.32) = 13.85.
b. For the 3-sigma R-chart,
D3 = 0 and D4 = 2.28 for n = 4, so UCL = D4R = 2.28(0.32) = 0.73 and LCL = D3R = 0(0.67) = 0.
c. There are no points out of control.
d. Even though there are no points out of control, we have only 5 data points and would expect
about 5 out of 100 to be out of bounds. So far, so good, but we need more data.
The linear regression can take various forms. In this case, we will arrange the daily sample
averages of the contents of a jar of salsa for each day of the week in rank order. We were asked
to look for “the effect of the day on the sample means.” Day 2 (Tues.) with rank order 1 has the
lowest total weight at 55.55. Day 3 (Wed.) with rank order 5 has the highest total weight at 57.0.
When we run our linear regression against the rank order values we get a line with a positive
slope of 0.32. The correlation coefficient is high at 0.955. There is a day effect in these data, but
too little data exists to bank on it. We should ask the company’s managers if it makes sense to
them that Tuesday has the lowest averages and Wednesday the highest.
8. Use a data check sheet to track the Dow Jones average, regularly reported on the financial
pages of most newspapers. Record the Dow Jones closing index value on a data check
sheet every day for one week. Do an Ishikawa analysis, trying to develop hypotheses
concerning what causes the Dow Jones index to move the way it does. Draw scatter
diagrams to see if the hypothesized causal factors are related to the Dow Jones.
Solution:
The solution to this problem will vary based upon the days used and how well the student
understands the factors affecting the Dow. Note that explanations often can be found for any
series of numbers after the fact. These explanations have no predictive value.
9. In developing control lines for a “p” chart the total number of defective items from all
samples is 3,000, the number of samples is 150, and the sample size is 50. What would be
the standard deviation used in developing the control lines?
Solution:
The number of defectives divided by the number of samples (3000/150 = 20) gives us the
average number of defectives in a sample. Since the sample size is 50, the p-bar value is 20
divided by 50 which equals 40 percent and that is the grand mean value of p in this example.
The standard deviation is then the square root of (0.4)(0.6)/50 = 0.069. Three sigma is
almost 0.21 which indicates too much variability in this process.
10. What are the values of UCL and LCL for the following data? Sample size = 100. The
fraction defective is 0.06 and the standard deviation is 0.01. The desired confidence level
is 95.00 percent. Give your answer and we will compare your answer with those of our
friends and colleagues down under.
Solution:
UCL = p + 1.96s = 0.06 + 1.96(0.01) = 0.0796 and
LCL = p – 1.96s = 0.06 – 1.96(0.01) = 0.0404.
Note: Ignore the following part of this question. “Give your answer and we will compare
your answer with those of our friends and colleagues down under.”
11. In a double sampling plan the two acceptance numbers are: c1 = 4 and c2 = 7. The number
of defectives found in the first sample is 5. Therefore, a second sample is taken. What is
the maximum number of defectives allowed in the second sample for the lot to be
accepted?
Solution:
The maximum number of defectives allowed is 7 so only two more defectives can be
permitted.
12. A manufacturing process is being monitored using a sample of size 50. The upper and
lower control limits on percentage defectives p are 6.30 % (.063) and 4.80 % (.048)
respectively. On a given day 6 defective items were found in the sample of 50. Is the
process in control?
Solution:
Six defectives divided by the sample size of 50 (6/50 = 0.12) gives us the p value. It is very
high (way above the maximum acceptable value of (0.063) which indicates that something
bad has happened to the process. Investigators better get going.
13. In a single sampling plan, the manufacturer will prefer to have a large acceptance number
c. Explain why you agree or disagree.
Solution:
The classical (greedy) manufacturer would like to have an acceptance number so high that
nothing is ever rejected. The manufacturer (aware of sustainability) would prefer to catch an
unexpected number of defectives as early as possible to protect the customers from misery.
Thus, the smart manufacturer wants to find out when there are problems while avoiding costs
incurred by statistical errors. That c number is not too high and not too low. P/OM is ideally
able to derive what it should be set at.
14. Buyers prefer to have lower values of c. Is this statement True or False? Explain.
Solution: In general, buyers will prefer lower values of c. However, the answer to this
question requires more discussion. We will be direct and transparent in our response. On the
face of it, the buyer would like to reject any lot that has some defectives. However, this buyer
wants to be able to produce and ship without disruptions. Too low values of c will reject lots
that are quite acceptable. Rejection will disrupt production for the buyer. The purchasing
agent will be held accountable. The systems approach says that the buyers and producers
should have the same goals in setting values of c. Therefore, they will agree on the selection
of c.