# Food and Nutrition

1. Five sets of samples were taken every other hour from a fruit juice production line. The following sugar contents were measured:
X1: 5.3, 5.5, 4.0, 4.5, 5.0 g/L
X2: 4.7, 4.7, 6.0, 4.0, 5.3 g/L
X3: 3.9, 5.1, 5.5, 5.7, 3.0 g/L
X4: 4.4, 5.7, 5.4, 5.9, 4.0 g/L
X5: 3.9, 5.8, 5.4, 4.0, 3.2 g/L
i. With the given data, determine the CL, UCL, and the LCL of the quality control chart.
ii. Can we regard the fluctuations in the data as “random process fluctuations”?
iii. Why do we prepare BOTH x bar and R charts when we prepare the statistical control charts for measurements?
iv. The USL for the process is 6.0 g/L, the higher sugar content makes the product unacceptably sweet. There is no LSL. Determine the “process capability index” and discuss your results. (20 pts)

OR

Power-law fluids have apparent viscosity of the form  = Kn-1, where η is the apparent viscosity (Pa s),  is the shear rate (s–1), K is the consistency coefficient (Pa sn), and n is the dimensionless flow behavior index. It is required to have K bar within the limits of 6.40 ± 0.08 and n bar within the limits of 0.550 ± 0.04 for a mayonnaise of acceptable quality. Draw appropriate control charts to determine whether this process with the following K and n values is under control to the given limits. (20 points)

Sample Set K (Pa sn) n
1 6.40, 6.35, 6.45, 6.38, 6.60 0.550, 0.530, 0.551, 0.560, 0.558
2 6.38, 6.37, 6.35, 6.28, 6.50 0.551, 0.532, 0.543, 0.561, 0.547
3 6.40, 6.35, 6.45, 6.38, 6.60 0.550, 0.530, 0.555, 0.560, 0.558
4 6.38, 6.28, 6.35, 6.28, 6.50 0.551, 0.532, 0.549, 0.561, 0.547
5 6.40, 6.43, 6.45, 6.39, 6.60 0.550, 0.530, 0.550, 0.550, 0.558
6 6.38, 6.37, 6.45, 6.55, 6.50 0.531, 0.533, 0.545, 0.571, 0.549
7 6.43, 6.45, 6.47, 6.27, 6.60 0.550, 0.530, 0.565, 0.560, 0.558
8 6.39, 6.27, 6.39, 6.44, 6.50 0.558, 0.539, 0.561, 0.561, 0.547
9 6.68, 6.39, 6.35, 6.46, 6.50 0.551, 0.532, 0.535, 0.572, 0.547
10 6.50, 6.32, 6.55, 6.27, 6.59 0.540, 0.520, 0.562, 0.548, 0.580

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Hint: construct K bar and n bar chart

2. In a confectionery process, 200 bars were sampled after coating for 10 days and the following number (npi) and fraction (pi) of defectives were found:
Day npi pi
1 5 0.025
2 4 0.020
3 4 0.020
4 7 0.035
5 3 0.015
6 2 0.010
7 6 0.030
8 4 0.020
9 6 0.030
10 7 0.035
a. Construct the np chart for maintaining the present level of operation.
b. Construct a p chart with the same data. (20 points)

3. The visual quality control of canned dry beans is done by observing five different groups of defects. One can is opened in every batch and each can contains about 1000 beans. The following data were taken with 15 consecutive batches with an acceptable quality level:
Number of Defects/Can
Batch Number Split Beans Cracked Beans Discolored Beans Wrinkled Beans Pealed Beans Total Defects
1 0 2 0 3 0 5
2 0 1 5 0 8
3 3 3 0 2 0 8
4 3 1 2 1 1 8
5 0 3 2 1 0 6
6 1 0 4 0 1 5
7 1 4 2 1 1 9
8 4 2 1 1 1 9
9 1 3 5 1 1 11
10 1 2 1 2 2 8
11 1 6 0 0 2 9
12 1 4 4 1 1 11
13 0 0 5 1 3 9
14 2 2 2 2 2 10
15 2 1 3 1 3 10

With new batches of beans the following data was obtained
Number of Defects/Can
Batch Number Split Beans Cracked Beans Discolored Beans Wrinkled Beans Pealed Beans Total Defects
1 3 2 1 3 0 9
2 2 7 1 5 0 15
3 0 3 4 2 0 9
4 4 1 4 1 1 11
5 0 0 2 0 3 5
Is the quality of the new beans under control with the standard of the previous ones? (20 points)
Hint: C chart

4. A set of packaging equipment operates with the following CLx and σ at different settings. If USL and the LSL of the packages are 505 and 495 g, respectively, which one of the settings should be preferred? (10 points)

Setting CLx (g) σ (g)
I 498 1.2
II 500 2.0
III 501 0.5
Hint: Process capability

5. Compare and contrast different food safety certifications- BRC, SQF, ISO, Kosher, and IFS (15 points)

Food and Nutrition
Final Study case

1. Five sets of samples were taken every other hour from a fruit juice production line. The following sugar contents were measured:
X1: 5.3, 5.5, 4.0, 4.5, 5.0 g/L
X2: 4.7, 4.7, 6.0, 4.0, 5.3 g/L
X3: 3.9, 5.1, 5.5, 5.7, 3.0 g/L
X4: 4.4, 5.7, 5.4, 5.9, 4.0 g/L
X5: 3.9, 5.8, 5.4, 4.0, 3.2 g/L
i. With the given data, determine the CL, UCL, and the LCL of the quality control chart.
ii. Can we regard the fluctuations in the data as “random process fluctuations”?
iii. Why do we prepare BOTH x bar and R charts when we prepare the statistical control charts for measurements?
iv. The USL for the process is 6.0 g/L, the higher sugar content makes the product unacceptably sweet. There is no LSL. Determine the “process capability index” and discuss your results. (20 pts)

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OR

Power-law fluids have apparent viscosity of the form  = Kn-1, where η is the apparent viscosity (Pa s),  is the shear rate (s–1), K is the consistency coefficient (Pa sn), and n is the dimensionless flow behavior index. It is required to have K barwithin the limits of 6.40 ± 0.08 and n bar within the limits of 0.550 ± 0.04 for a mayonnaise of acceptable quality. Draw appropriate control charts to determine whether this process with the following K and n values is under control to the given limits. (20 points)

Sample Set K (Pa sn) n
1 6.40, 6.35, 6.45, 6.38, 6.60 0.550, 0.530, 0.551, 0.560, 0.558
2 6.38, 6.37, 6.35, 6.28, 6.50 0.551, 0.532, 0.543, 0.561, 0.547
3 6.40, 6.35, 6.45, 6.38, 6.60 0.550, 0.530, 0.555, 0.560, 0.558
4 6.38, 6.28, 6.35, 6.28, 6.50 0.551, 0.532, 0.549, 0.561, 0.547
5 6.40, 6.43, 6.45, 6.39, 6.60 0.550, 0.530, 0.550, 0.550, 0.558
6 6.38, 6.37, 6.45, 6.55, 6.50 0.531, 0.533, 0.545, 0.571, 0.549
7 6.43, 6.45, 6.47, 6.27, 6.60 0.550, 0.530, 0.565, 0.560, 0.558
8 6.39, 6.27, 6.39, 6.44, 6.50 0.558, 0.539, 0.561, 0.561, 0.547
9 6.68, 6.39, 6.35, 6.46, 6.50 0.551, 0.532, 0.535, 0.572, 0.547
10 6.50, 6.32, 6.55, 6.27, 6.59 0.540, 0.520, 0.562, 0.548, 0.580

Hint: construct K bar and n bar chart

2. In a confectionery process, 200 bars were sampled after coating for 10 days and the followingnumber (npi) and fraction (pi) of defectives were found:
Day npi pi
1 5 0.025
2 4 0.020
3 4 0.020
4 7 0.035
5 3 0.015
6 2 0.010
7 6 0.030
8 4 0.020
9 6 0.030
10 7 0.035
a. Construct the np chart for maintaining the present level of operation.
b. Construct a p chart with the same data. (20 points)

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3. The visual quality control of canned dry beans is done by observing five different groups of defects. One can is opened in every batch and each can contains about 1000 beans. The following data were taken with 15 consecutive batches with an acceptable quality level:
Number of Defects/Can
Batch Number Split Beans Cracked Beans Discolored Beans Wrinkled Beans Pealed Beans Total Defects
1 0 2 0 3 0 5
2 0 1 5 0 8
3 3 3 0 2 0 8
4 3 1 2 1 1 8
5 0 3 2 1 0 6
6 1 0 4 0 1 5
7 1 4 2 1 1 9
8 4 2 1 1 1 9
9 1 3 5 1 1 11
10 1 2 1 2 2 8
11 1 6 0 0 2 9
12 1 4 4 1 1 11
13 0 0 5 1 3 9
14 2 2 2 2 2 10
15 2 1 3 1 3 10

With new batches of beans the following data was obtained
Number of Defects/Can
Batch Number Split Beans Cracked Beans Discolored Beans Wrinkled Beans Pealed Beans Total Defects
1 3 2 1 3 0 9
2 2 7 1 5 0 15
3 0 3 4 2 0 9
4 4 1 4 1 1 11
5 0 0 2 0 3 5
Is the quality of the new beans under control with the standard of the previous ones? (20 points)
Hint: C chart

4. A set of packaging equipment operates with the following CLx and σ at different settings. If USL and the LSL of the packages are 505 and 495 g, respectively, which one of the settings should be preferred? (10 points)

Setting CLx (g) σ (g)
I 498 1.2
II 500 2.0
III 501 0.5
Hint: Process capability

5. Compare and contrast different food safety certifications- BRC, SQF, ISO, Kosher, and IFS (15 points)

6. What did you learn from other groups HACCP presentations (15 points)