MGT 3110: Exam 2 Study Guide
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23.
What are the four major categories of cost associated with quality? Explain.
Describe the term Six Sigma in a statistical sense.
How is the term Six Sigma understood in TQM sense?
What are the statistical tools used in TQM?
Describe the four Ms of Cause-and-effect diagram.
What are the values plotted on the two y-axes of a Pareto diagram?
Describe Common Causes and Assignable Causes.
What is the purpose of Statistical Process Control (SPC) charts?
When is a process said to be “in-control”?
Name and describe the five Run test used to determine whether a process is in control or not.
When using SPC charts, what constitutes Type I error and what is the consequence of it?
When using SPC charts, what constitutes Type II error and what is the consequence of it?
Describe the difference between a p-chart and a c-chart.
If a process is capable, does it also mean the process is “in-control”? Explain
For a process to be deemed capable as a 4-sigma process, what is the minimum required value for
Cpk and Cp? What is that value for a 6-sigma process?
Interpret a case where Cpk < 1.333, but Cp > 1.333.
What is Acceptance Sampling?
What is an OC Curve for acceptance sampling plan?
Define the terms (a) Acceptable Quality Level (AQL), (b) Lot Tolerance Percent Defective
(LTPD), (c) Producer’s risk, (d) Consumer’s risk, and (e) Average Outgoing Quality (AOQ).
What is Type I error in acceptance sampling?
What is Type II error in acceptance sampling?
If a bad in-coming lot is accepted based on sampling, what type of error would that be, and what
kind of risk is it known as?
If a good in-coming lot is rejected based on sampling, what type of error would that be, and what
kind of risk is it known as?
24.
25.
26.
27.
What is the objective of ABC analysis?
Describe the thumb rule used in ABC classification.
List the assumptions needed for developing the EOQ formula.
What costs are included in the total cost for the EOQ model?
28.
The EOQ formula consists of three numbers, D, S, and H. Increasing which of these three will
result in increase in the value of EOQ.
If annual demand were to double, would the value of EOQ also double? Why or why not?
29.
30.
31.
32.
Which of the assumptions required for developing the EOQ formula is not necessary for
the Production Lot Size Model?
For the Production Lot Size to be valid, production rate “p” must be greater than the
demand rate “d”. Explain the reasons for this.
What costs are included in the total cost if quantity discount is allowed?
PROBLEMS
1.
A restaurant manager tracks complaints from the diner satisfaction cards that are turned in at each
table. The data collected from the past week’s diners appear in the following table.
Complaint
Food taste
Food temperature
Order mistake
Slow service
Table/utensils dirty
Too expensive
Frequency
80
9
2
16
47
4
Prepare a Pareto chart. To cover 80% of problems which complaints must be address first?
2.
Cartons of Plaster of Paris are supposed to weigh exactly 32 oz. Inspectors want to develop process
control charts. They take ten samples of six boxes and weigh them. Based on the following data,
compute the lower and upper control limits and determine whether the process is in control.
Sample
1
2
3
4
5
Mean
33.8
34.4
34.5
34.1
34.2
Range
1
0.3
0.5
0.7
0.2
Sample
6
7
8
9
10
Mean
34.3
33.9
34.0
33.8
34.0
Range
0.4
0.5
0.8
0.3
0.3
3.
McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They
take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet
is 20' by 100'. Based on the following data, develop limits for the control chart and determine
whether the process is in control.
Sheet
Number of flaws
Sheet
Number of flaws
1
6
6
2
2
1
7
1
3
3
8
0
4
2
9
0
5
1
10
2
4.
Rancho No Tengo Orchards wants to establish control limits for its mangos before they are sent to
the retailers. They randomly take six containers (assume it is enough) of one hundred mangos in an
attribute testing plan and find some mangos with blemishes. What should be the limits on the
control chart? Is the process in control?
Container
Number of mangos with blemishes
1
5
2
3
3
1
4
3
5
4
6
2
5.
A woodworker is concerned about the quality of the finished appearance of her work. In sampling
units of a split-willow hand-woven basket, she has found the following number of finish defects in
ten units sampled: 4, 0, 3, 0, 1, 0, 1, 1, 0, 2.
a. Calculate the average number of defects per basket
b. If 3-sigma control limits are used, calculate the lower control limit, centerline, and upper
control limit.
6.
The specifications for a plastic liner for concrete highway projects call for a thickness of 6.0 mm ±
0.1 mm. The standard deviation of the process is estimated to be 0.02 mm. What are the upper and
lower specification limits for this product? The process is known to operate at a mean thickness of
6.04 mm. Determine the values of Cpk and Cp for this process. Is the process capable? Explain.
7.
A medical supplies company buys its supplies in bulk and redistributes them to doctor’s offices and
clinics. The receive thermometers in lots of 500 from the vendor. They are considering a sampling
plan of n = 50 and c = 1.
a. Develop a OC curve for this sampling plan. (Use Poisson Tables)
b. Determine the producer’s risk if the AQL is 2%.
c. Determine the consumer’s risk if the LTPD is 14%.
d. Develop a curve for AOQ and determine the value of AOQL.
8.
An acceptance sampling plan has lots of 5000 units, a sample size of 200 and c is 5. Suppose that
the incoming lots have percentage defective of 3%. What is AOQ?
9.
A company has 12 items in its inventory. Using the data given below classify the items into A, B,
and C classes.
SKU
D120
E111
C140
E151
B180
B120
E149
A180
E110
A155
F120
B150
10.
Annual usage (units)
6850
371
1292
62
12667
9625
7010
5100
258
862
1940
967
Unit $ value
1.20
8.60
13.18
91.80
3.20
10.18
1.27
0.88
62.25
18.10
0.38
2.20
Montegut Manufacturing produces a product for which the annual demand is 10,000.
Production averages 100 per day, while demand is 40 per day. Holding costs are $1.50 per
unit per year; set-up costs $200.00. If they wish to produce this product in economic
batches, what size batch should be used? What is the maximum inventory level? What is
the time between orders? What is the time to producing a lot? How many order cycles are
there per year? Determine the total annual inventory cost?
11.
The annual demand, ordering cost, and the inventory carrying cost rate for a certain item
are D = 600 units, S = $10/order and holding cost is 30% of item price. Price is established
by the following quantity discount schedule. What should the order quantity be in order to
minimize the total annual cost?
Quantity
Unit price
12.
1 to 49
$5.00
50 to 249
$4.50
250 and up
$4.10
Herbert Adams sells bicycles. One particular model is highly popular with annual sales of
2,000 units per year. The cost of one such bicycle is $800.00. Annual holding costs are
25% of the item's cost, and the ordering cost is $40. The store is open 250 days a year.
a.
b.
c.
d.
What is the economic order quantity?
What is the optimal number of orders?
What is the optimal number of days between orders?
What are the annual total costs?
Answers
1.
Complaint
Food taste
Table/utensils dirty
Slow service
Food temperature
Too expensive
Order mistake
Frequency
80
47
16
9
4
2
158
%
Cum %
50.6%
29.7%
10.1%
5.7%
2.5%
1.3%
100.0%
50.6%
80.4%
90.5%
96.2%
98.7%
100.0%
Frequency
Pareto Chart: Complaints
90
80
70
60
50
40
30
20
10
0
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
To cover 80% of complaints, Food Taste and dirty utensils must be addressed first.
2
Sample
1
2
3
4
5
6
7
8
9
10
33.8
34.4
34.5
34.1
34.2
34.3
33.9
34.0
33.8
34.0
𝑋̿ = 34.1
R
1.0
0.3
0.5
0.7
0.2
0.4
0.5
0.8
0.3
0.3
= 0.5
n=6
0.483
A2 =
A2
=
0.2415
LCL = 𝑋̿ - A2 =
UCL = 𝑋̿ + A2 =
33.86
34.34
D2 =
0
D3 =
2.004
LCLR =
0
UCLR =
1.002
The process is not in control, since the values for samples 1, 2, 3, and 9 fall outside the
control limits. Although all the sample ranges fall within 0 and 1.002, the assignable causes
should be investigated and eliminated.
3.
c = total defects/number of sheets = 1.8
Use c-chart
UCLc = 1.8 + 3 1.8 = 1.8 + 4.02 = 5.825
LCLc = 1.8 - 3 1.8 = 1.8-4.02 = converts to zero
Sheet number 1 has too many flaws; investigate the cause.
4.
UCLp
0.03 (1−0.03)
= 0. 03 + 3√
100
0.03 (1−0.03)
LCLp = 0. 03 − 3√
100
= 0.03 + (3 * 0.017) = .081
= 0.03 - (3 * 0.017) = -0.021 converts to 0
Limits are LCL = 0 and UCL = 0.081. All six points are in control; there is no pattern or
trend in the data.
= 1.2; (b) LCLc = 1.2 – 3 √1.2 = -2.0862, or zero
UCLc = 1.2 + 3 √1.2 = 4.49.
5.
(a)
6.
LSL = 5.9 mm, USL = 6.1 mm.
Cpk = min{(6.1-6.04)/(3*0.02), (6.04 - 5.9)/(3*0.02) = min{1.00, 2.33} = 1.
Cp = (6.1 – 5.9)/(6*.02) = 1.67
Since Cpk is < 1.333 the process is not capable. Since Cp = 1.67, the process variability is small
enough to be within the desired specification range. Therefore, the process needs to be centered to
achieve a Cpk of at least 1.33.
7.
Pd
0.00
nPd
0.00
Pa
1.000
0.01
0.02
0.03
0.04
0.05
0.50
1.00
1.50
2.00
2.50
0.910
0.736
0.558
0.406
0.288
0.06
0.07
0.08
0.09
0.10
3.00
3.50
4.00
4.50
5.00
0.199
0.137
0.092
0.061
0.040
For AQL = 2%, Pa= 0.736
i.e., Producer’s risk = 1 – 0.736 = 0.264
For LTPD = 14%, nPd = 50 x 0.14 = 7.0,
Pa from Poisson table = 0.007
i.e. Consumer’s risk = 0.007
Pd
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Pa
1.000
0.910
0.736
0.558
0.406
0.288
0.199
0.137
0.092
0.061
AOQ
0.00000
0.00819
0.01325
0.01507
0.01462
0.01294
0.01075
0.00860
0.00662
0.00494
0.10
0.040
0.00360
Percent defective accepted
(d)
AOQ
0.02000
0.01500
0.01000
0.00500
0.00000
0.00
0.05
0.10
0.15
Pd
AOQL = 0.01507
OC-Curve for the sampling plan, n=50, C = 1
1.0
0.9
P(Accepting lot)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Pd (% of defectives in the lot)
8.
N=
n=
c=
Pd =
5000
200
5
3%
nPd =
Pa =
AOQ =
AOQ =
6
0.446
<-- from Poisson table
.03(.446)(5000-200)/5000
0.0128448 i.e. = 1.28%
9.
No. SKU
1 B120
2 B180
3 C140
4 E110
5 A155
6 E149
7 D120
8 E151
9 A180
10 E111
11 B150
12 F120
Annual
usage
(units) Unit $ value
10.18
9625
3.20
12667
13.18
1292
62.25
258
18.10
862
1.27
7010
1.20
6850
91.80
62
0.88
5100
8.60
371
2.20
967
0.38
1940
Annual Dollar
volume
Dollar %
97,982.50
40,534.40
17,028.56
16,060.50
15,602.20
8,902.70
8,220.00
5,691.60
4,488.00
3,190.60
2,127.40
737.20
220565.66
44.4%
18.4%
7.7%
7.3%
7.1%
4.0%
3.7%
2.6%
2.0%
1.4%
1.0%
0.3%
100%
Cum. % Cum. % for
for $ no. of items
44.4%
8.3%
62.8%
16.7%
70.5%
25.0%
77.8%
33.3%
84.9%
41.7%
88.9%
50.0%
92.6%
58.3%
95.2%
66.7%
97.3%
75.0%
98.7%
83.3%
99.7%
91.7%
100.0%
100.0%
10.
D=
p=
d=
H=
S=
ELS = √
10000
100
40
$1.50
$200
2𝐷𝑆
𝑑
𝑝
𝐻(1− )
per day
per day
2(10000)200
=√
1.50(1−
40
)
100
= 2108
Imax = (Q/p)(p-d) = (2108/100)(100-40) = 1264.80
N = No. of orders per year = D/Q = 10000/2108 = 4.74
T = Time between orders = Q/d = 2108/40 = 52.7 days
Production time = Q/p = 2108/100 = 21.08 days
Annual holding cost = (Imax/2) x H = (1264.80/2) x 1.50 = $948.60
Annual setup cost = (D/Q) x S = (10000/2108) x 200 = $948.77
Total cost = 948.60 + 948.77 = $1,897.37
Class
A
A
B
B
B
B
C
C
C
C
C
C
11.
D=
Q
600
Price
S=
10
Holding
cost
Holding cost =
Formula Q
1 - 49
5.00
1.50
89
50 - 249
250 &
above
4.50
1.35
94
4.10
1.23
99
Q
1 – 49
50 - 249
>= 250
EOQ =
Candidate
Price
Q
5.00
4.50
94
4.10
250
250 @ P = $4.10
30%
Candidate Q
Formula Q > upper limit -not a candidate
Formula Q is within range, =
Candidate Q = Formula Q
Formula Q < lower limit,
Candidate Q = lower limit
Ordering cost
Holding cost
63.83
24.00
63.45
153.75
250
Total cost
2700
2460
2827.28
2637.75
2000
250
$200
$40
b.
2(2000)40
 28
200
N = D/Q = 2000/28 = 70.7
c.
d = D/No. of days per year = 2000/250 = 8, T = Q/d = 28/8 = 3.5 days
d.
TC = (D/Q)S + (Q/2)H = (2000/28)40 + (28/2)200 = $5,657
a.
94
Item cost
12.
D=
No. of days =
H = 25% x $800 =
S=
-
EOQ =
Answers to questions:
1.
What are the four major categories of cost associated with quality? Explain.
 Prevention costs - reducing the potential for defects
 Appraisal costs - evaluating products, parts, and services
 Internal failure - producing defective parts or service before delivery
 External costs - defects discovered after delivery
2.
Describe the term Six Sigma in a statistical sense.
A six-sigmaPlus is one for which plus or minus 6 times the process standard deviation fits
within the specification limits. In other words, Cpk >= 2.
3.
How is the term Six Sigma understood in TQM sense?
Six-sigma is a management philosophy of continuous improvement with the objective of
eliminating defectives.
4.
What are the statistical tools used in TQM?
Pareto diagram, Cause-and-effect diagram, check sheet, scatter plot.
5.
Describe the four Ms of Cause-and-effect diagram.
Man, material, machine, method
6.
What are the values plotted on the two y-axes of a Pareto diagram?
Frequency and Cumulative relative frequency.
7.
Describe Common Causes and Assignable Causes.
Common causes result in natural variations in a process that cannot be eliminated. Assignable
causes of a process produce variations that can be eliminated by eliminating the assignable
causes.
8.
What is the purpose of Statistical Process Control (SPC) charts?
SPC charts are used to detect the presence of assignable causes.
9.
When is a process said to be “in-control”?
When a process is free of assignable causes, it is said to be in control.
10.
Name and describe the five Run test used to determine whether a process is in control or not.
 One point outside the control limits
 Trend of five or more consecutive points
 Run of five
 Two consecutive points at or near either control limit
 Erratic behavior
11.
When using SPC charts, what constitutes Type I error and what is the consequence of it?
Concluding a process is not in control even though it is in control is Type I error. When this
happens, the process would be shut down unnecessarily that will result in lost production.
12.
When using SPC charts, what constitutes Type II error and what is the consequence of it?
This error is caused when we conclude a process is in control even though it is not. In this
case, bad parts will get produced and sent down the line.
13.
Describe the difference between a p-chart and a c-chart.
p-chart is for proportion of defectives in the sample. C-chart is for count of defects in one unit
of the product.
14.
If a process is capable, does it also mean the process is “in-control”? Explain
Yes. Process capability can be assessed only if the process is in control.
15.
For a process to be deemed capable as a 4-sigma process, what is the minimum required value for
Cpk and Cp? What is that value for a 6-sigma process?
For 4-sigma process both factors must be at least 1 and 1/3. For 6-sigma process, this value
must be at least 2.
16.
Interpret a case where Cpk < 1.333, but Cp > 1.333.
Cpk < 1.333 means, this process is not capable. However, Cp > 1.333 tell us that the process
variance is small enough to meet the requirements of a 4-Sigma process.
17.
What is Acceptance Sampling?
The process of taking a random sample from a lot of products, inspecting the items in the
sample and based on the number of defectives in the sample accepting or rejection the, lot is
called Acceptance Sampling.
18.
What is an OC Curve for acceptance sampling plan?
OC Curve is a graph with probability of defectives (Pd) in the lot on the x-axis, and the
corresponding probability of acceptance (Pa) of the lot for a given sampling plan on the y-axis.
19.
Define the terms (a) Acceptable Quality Level (AQL), (b) Lot Tolerance Percent Defective
(LTPD), (c) Producer’s risk, (d) Consumer’s risk, and (e) Average Outgoing Quality (AOQ).
 AQL = The probability of defectives (Pd) up to which a lot is considered good.
 LTPD = Probability of defectives (Pd) in the lot at which the lot will be considered bad.
 Producer's risk = Probability of rejecting a lot that is considered good, i.e. Pd <= AQL
 Consumer's risk = Probability of accepting a bad lot, i.e. Pd >= LTPD.
 AOQ = The proportion of defectives that will be taken into stock for a given sampling
plan, over the long run.
20.
What is Type I error in acceptance sampling?
Type I error is the probability of rejecting a good lot, aka, producer's risk.
21.
What is Type II error in acceptance sampling?
Type II error is the probability of accepting a bad lot, aka, consumer's risk.
22.
If a bad in-coming lot is accepted based on sampling, what type of error would that be, and what
kind of risk is it known as?
Type II error, consumer's risk.
23.
If a good in-coming lot is rejected based on sampling, what type of error would that be, and what
kind of risk is it known as?
Type I error, producer's risk.
24.
What is the objective of ABC analysis?
The objective of ABC analysis is to identify the inventory items with (i) the largest
annual dollar expenditure (class A), (ii) least annual dollar investment (class C), and
(iii) all other items that fall in between (class B).
25.
Describe the thumb rule used in ABC classification.
 Class A: ~15% of items, 70-80% annual $ usage
 Class B: ~30% of items, 15-25% annual $ usage
 Class C: ~55% of items, 5% annual $ usage
26.
List the assumptions needed for developing the EOQ formula.
 Demand is known, constant, and independent
 Lead time is known and constant
 Receipt of inventory is instantaneous and complete
 Quantity discounts are not possible
 Only variable costs are setup and holding
 Stockouts can be completely avoided
27.
What costs are included in the total cost for the EOQ model?
Annual holding cost and annual ordering cost
28.
The EOQ formula consists of three numbers, D, S, and H. Increasing which of these three will
result in increase in the value of EOQ.
D and S.
29.
If annual demand were to double, would the value of EOQ also double? Why or why not?
No. The annual demand is inside square-root.
30.
Which of the assumptions required for developing the EOQ formula is not necessary for
the Production Lot Size Model?
The assumption of instantaneous delivery is not necessary.
31.
For the Production Lot Size to be valid, production rate “p” must be greater than the
demand rate “d”. Explain the reasons for this.
If p < d, a negative number will result inside the square-root. If p = d, a zero will
result in the denominator. These two cases represent situations where the production
needs to be continuous without a stop, i.e. there is no determinable batch size.
32.
What costs are included in the total cost if quantity discount is allowed?
Annual holding cost, annual ordering cost, and annual item cost