Quality control engineers at Advanced Electronics (AE) are monitoring the quality level of AE's main production line. The engineers took 20 samples with each sample containing 40 units of the same products. After careful inspection, they found some of the products are defective. The results of inspection with a total of 28 defective units are shown in the following table. The engineers decided to use p chart to further analyze the quality of the production. Table: Quality Level Data Defective Rate Sample # Defective Units (D¡) Sample # Defective Units (D¡) Defective Rate (D¡/40) 0.025 (Di/40) 0.050 1 11 2 2 1 0.025 12 1 0.025 0.050 0.025 3 1 0.025 13 4 3 0.075 14 1 5 2 0.050 15 1 0.025 1 0.025 16 1 0.025 7 0.050 17 1 0.025 8 1 0.025 18 2 0.050 1 0.025 19 1 0.025 10 1 0.025 20 2 0.050 Total 28 Formulas to determine the center line and control limits of a p chart are p E1 Di and p+3× px(1-p) respectively. nxm n 1) Based on the given data, calculate the center line, upper and lower control limits of the p chart 2) Based on the results calculated in 1) and data in the above table, draw the corresponding p chart in your answer paper. The chart may not be precise but should reflect in general the production quality. 3) Briefly explain if the quality of the production is "in control" or “out of control".
Quality control engineers at Advanced Electronics (AE) are monitoring the quality level of AE's main production line. The engineers took 20 samples with each sample containing 40 units of the same products. After careful inspection, they found some of the products are defective. The results of inspection with a total of 28 defective units are shown in the following table. The engineers decided to use p chart to further analyze the quality of the production. Table: Quality Level Data Defective Rate Sample # Defective Units (D¡) Sample # Defective Units (D¡) Defective Rate (D¡/40) 0.025 (Di/40) 0.050 1 11 2 2 1 0.025 12 1 0.025 0.050 0.025 3 1 0.025 13 4 3 0.075 14 1 5 2 0.050 15 1 0.025 1 0.025 16 1 0.025 7 0.050 17 1 0.025 8 1 0.025 18 2 0.050 1 0.025 19 1 0.025 10 1 0.025 20 2 0.050 Total 28 Formulas to determine the center line and control limits of a p chart are p E1 Di and p+3× px(1-p) respectively. nxm n 1) Based on the given data, calculate the center line, upper and lower control limits of the p chart 2) Based on the results calculated in 1) and data in the above table, draw the corresponding p chart in your answer paper. The chart may not be precise but should reflect in general the production quality. 3) Briefly explain if the quality of the production is "in control" or “out of control".
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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ISBN:9780079039897
Author:Carter
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Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 11PPS
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Transcribed Image Text:Quality control engineers at Advanced Electronics (AE) are monitoring the quality level of AE's main production line.
The engineers took 20 samples with each sample containing 40 units of the same products. After careful inspection, they
found some of the products are defective. The results of inspection with a total of 28 defective units are shown in the
following table. The engineers decided to use p chart to further analyze the quality of the production.
Table: Quality Level Data
Defective Rate
Sample #
Defective Units (D¡)
Sample #
Defective Units (D¿)
Defective Rate
(D¡/40)
0.025
(D¡/40)
0.050
1
1
11
2
1
0.025
12
1
0.025
3
1
0.025
13
2
0.050
4
3
0.075
14
1
0.025
2
0.050
15
1
0.025
6
1
0.025
16
1
0.025
7
0.050
17
1
0.025
8
1
0.025
18
2
0.050
9
1
0.025
19
1
0.025
1
0.025
20
0.050
Total
28
Formulas to determine the center line and control limits of a p chart are p
E1 Di
and p ±3 ×
px(1-p)
respectively.
nxm
n
1) Based on the given data, calculate the center line, upper and lower control limits of the p chart
2) Based on the results calculated in 1) and data in the above table, draw the corresponding p chart in your answer
paper. The chart may not be precise but should reflect in general the production quality.
3) Briefly explain if the quality of the production is “in control" or "out of control".
4) If AE management decides that the defective rate of the production should not exceed 2%,
(In answering 4.1) and 4.2) below, you do NOT need to draw a new p chart)
4.1) indicate if the production process is "in control" or "out of control".
4.2) briefly explain why it is "in control" or "out of control" as you indicated in 4.1) above.
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