Sample Exam II KEY 2016 (3)
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EXAM II
FDSCTE 5310 – Food Quality Assurance
Please, read the questions carefully before answering. The test should be completed in 1
hr. Copies of probability tables have been attached to the test, in case you need them.
1.
You work for a company that produces applesauce. Four trucks of apples are received
every Tuesday and Thursday, while 6 trucks are received on Saturday. Each truck
contains about 30,000 apples (ranging from 25,000 to 35,000). Management designs
a double sampling plan like this: n
1
= 15, acceptance number c
1
=2.
If the sample has
6
defectives or more, the lot would be rejected on the first sampling. If the first
sample had between 3-5 defectives, a second sample would be taken.
a)
What would be the probability of accepting a lot with 5% defectives?
n = 15
np =
15 x 0.05 = 0.75
p = 0.05
c = 2
From the table, for np = 0.75 and c = 2
P (2 or less) = P (c=2)
= 0.959
b) What would be the probability of having to take a second sample?
n = 15, p = 0.05, np = 0.75
P (take 2
nd
sample) = P (3, 4, 5) = P (5 or less) – P ( 2 or less) = P (c=5) – P (c=2)
= 1 – 0.959
= 0.041
c) What would be the probability of rejecting the lot with the first sample?
n = 15, p = 0.05, np = 0.75
P (reject with first sample) = P (higher than 5) = 1 – P (5 or less) = 1 – P (c=5)
= 1 – 1
= 0
2.
In a packing plant, incoming asparagus are washed, cut to an 8 inches length and
sorted by size according to diameter of stalks:
No. 1:
0.75-1 inch diameter, No. 2:
0.6-0.75, No. 3: 0.35-0.6 inches diameter. Any asparagus with a stalk diameter higher
than 1 inch or lower than 0.35 inches are discarded. A truck containing 100,000
asparagus arrives to the plant. The mean diameter of the stalks is 0.65 inches, with a
standard deviation of 0.1inch. Assume that the diameters are normally distributed and
determine the following:
µ= 0.65,
= 0.1
a)
What is the percent of asparagus No 1.
P (0.75-1) = P (>0.75) – P (>1)
Z.75 = 0.75-0.65/0.1 = 1, P(>0.75) = 0.159
Z 1 = 1-0.65/0.1 = 3.5, P (>1) ~ 0
(or more
accurately 0.000233)
P (0.75-1) ~ 0.159
About 15.9% of asparagus will be No 1.
b)
What is the percent of asparagus No. 3
P (0.35-0.6) = P (<0.6) – P (<0.35)
Z .35 = 0.36-0.65/0.1 = 3; P (<0.35) = 0.00135 ~ 0
Z .6 = 0.6-0.65/0.1 = 0.5; P (<0.6) 0.309
P (0.35-0.6) ~ 0.309
(or more accurately 0.309 – 0.00135 = 0.30765)
About 30.9% or asparagus will be No. 3
(or more accurately, 30.8%)
c)
How many asparagus will be discarded ?
P (less than 0.35) + P (more than 1) ~ 0
~ 0 … then we could say no asparagus will be discarded.
More accurately:
If you use the accurate numbers from the table, the probability is
P (less than 0.35) + P (more than 1) = 0.00135 + 0.000233 = 0.001583
To calculate how many will be discarded, we need to multiply the probability by the total
number of asparagus:
Discarded asparagus = 0.001583 x 100,000 = ~158 asparagus
Note: if you round up or down, your answers may vary a bit.
3.
You are the QC manager at a company that produces cheese. The product
development team is working on a new formulation of reduced-fat cheese that should
have also an extended shelf life, since its water activity is expected to fall between
0.8 and 0.85. You proceed to take samples under 3 different processing conditions,
and collect the data summarized in table 1. You have been asked to determine if the
process is actually capable of producing the product under the specifications
established, and to determine the process capability indexes. Please, complete the
data on the table and make recommendations to the Product development team:
a)
Are the specifications realistic?
They do not seem realistic as none of the
processes can meet the specifications.
b)
Calculate the process capability indexes (Cp and Cpk)
see in table
c)
Determine which processing conditions should be used to better fit the
specifications of water activity?
Process II is the one that has higher Cp AND
Cpk, so is closest to be centered and is capable but marginal.
d)
What would you recommend to management based on the data obtained? Do you
have any recommendations for the improvement of the process?
The best
approach would be to start from Process II. Based on that, improvements on the
process could be implemented, or the specifications would have to be adjusted.
USL = 0.85, LSL = 0.8,
Cp = 0.05 / 6
;
Cpu = (0.85 - µ) / 3
;
Cpl = (µ - 0.8) / 3
Table 1. Water activity of the new reduced-fat
cheese formulation manufactured with 3
different processing conditions.
Process I
Process II Process III
1
0.81
0.85
0.84
2
0.83
0.84
0.82
3
0.83
0.83
0.85
4
0.82
0.83
0.79
5
0.81
0.83
0.81
6
0.8
0.84
0.84
7
0.79
0.83
0.82
8
0.81
0.85
0.82
9
0.83
0.84
0.83
10
0.84
0.83
0.80
Mean
0.817
0.837
0.822
SD
0.0157
0.0082
0.0187
Cp
Cpk
0.53
0.36
1.02
0.53
0.44
0.39
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4.
A company selects a sampling plan that gives the following Standard Operating
Curve.
a)
Label the axis
Y axis: Probability of acceptance, x axis: % defectives
.
b)
Using the curve, determine what would be the chance to reject a good lot, if a
good lot is defined as 1% defectives or less, and what would be the chance to
accept bad lots, if a bad lot is defined as having 3% defectives or more.
From the figure, P (accept) lots with 1% is about 0.85.
P(reject good lot) = 0.15
From the figure, P (accept) lots with 3% is about 0.2.
c)
The producer is ok with his risk, however, the buyer does not like his. He
thinks the probability of accepting a bad lot under this sampling plan is too
high. What could be modified and how in order to decrease the risk of
You can change n or c or both: either increase n with the same c, OR decrease c,
keeping n the same.
5.
Your company makes bakery products. They have been making bagels for many
years and their product has a good acceptance with comsumers. For cost reasons, they
are looking into replacing their typical leavening agent with a lower cost one, but do
not want to consumers to notice a difference. You need to design a sensory
experiment to determine if consumers will be able to detect a difference in the
product.
Note: There could be more than one correct answer, but here I present the most
typical scenario and best anwer, based on QA practices.
a)
What type of sensory test would you recommend
Discrimination test (triangle most typically) – they are best suited to test for
differences.
b)
Who should test the samples (type of panel and size of the panel that you
recommend)
Consumer panel
c)
Name 3 conditions you would need to control to get valuable data
1.
Who will try the samples, preferably the target consumer
2.
Sample presentation, equal size (small), same temperature / freshness
3.
The place, free of distractions, comfortable.
(some other answers may also work, based on class notes and discussions).
d)
How the results would be interpreted.
If we use a triangle test, there is a 1/3 probability to choose the different sample just by
chance. We would need large number of panelists (100-300). If most panelists can pick
the different sample, then the different ingredient is causing a change in the final product:
consumers will notice the difference. If ~ 1/3 or less picked the sample with the new
ingredient, that would mean we can make the change, and consumers will not notice.
6.
The company wants to expand their line of muffins with a new flavor. They came up
3 different prototypes: a) grape chocolate, b) apple raspberry and c) banana
strawberry. However, only one of those will be introduced into the market. Desing a
sensory test that would help you choose which one should be chosen:
a)
What test would you choose
Could use ranking, or hedonic
b)
Who would test the samples (type and size of panel)
Should be consumer panel
c)
What type of scale would you use?
Ranking: rank the samples. Hedonic: 9-point hedonic scale.
d)
How would you know which sample should make it into the market?
The sample that ranked highest or the sample that was liked the most would make
it into the market.