Question

A manufacturing process produces steel rods in batches of 1,700. The firm believes that the percent of defective items generated by this process is 5.4%. a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p⎯⎯ chart. (Round your answers to 3 decimal places.) b. An engineer inspects the next batch of 1,700 steel rods and finds that 6.5% are defective. Is the manufacturing process under control?

Answer #1

**Solution:**

We are given that: A manufacturing process produces steel rods in batches of 1,700.

The percent of defective items generated by this process =

That is:

**Part a)** Calculate the center line, the upper
control limit (UCL), and the lower control limit (LCL) for the p⎯⎯
chart.

Center Line =

The upper control limit (UCL) is:

The lower control limit (LCL) :

**Part b.** An engineer inspects the next batch of
1,700 steel rods and finds that 6.5% are defective. Is the
manufacturing process under control?

Yes , since 6.5% = 0.065 defective are within the control limits and .

A manufacturing process produces steel rods in batches of 2,200.
The firm believes that the percent of defective items generated by
this process is 4.3%.
a. Calculate the centerline, the upper control
limit (UCL), and the lower control limit (LCL) for the p¯p¯ chart.
(Round your answers to 3 decimal places.)
centerline-
Upper control limit-
Lower control limit-
b. An engineer inspects the next batch of 2,200
steel rods and finds that 5.5% are defective. Is the manufacturing
process under...

Twelve samples, each containing five parts, were taken from a
process that produces steel rods at Emmanual Kodzi's factory. The
length of each rod in the samples was determined. The results were
tabulated and sample means and ranges were computed.
Refer to Table S6.1 - Factors for computing control chart limits
(3 sigma) for this problem.
Sample
Size, n
Mean Factor,
A2
Upper Range,
D4
Lower Range,
D3
2
1.880
3.268
0
3
1.023
2.574
0
4
0.729
2.282
0...

An online clothing retailer monitors its order-filling process.
Each week, the quality control manager selects a random sample of
size n = 350 orders that have been filled but have not shipped. The
contents of the shipping container are checked against the items
ordered by the customer (including color and size categories), and
the order is categorized as defective or non-defective. A p chart
is used to identify whether or not the process is in control.
The graph below shows...

Twenty-five samples of 100 items each were inspected when a
process was considered to be operating satisfactorily. In the 25
samples, a total of 185 items were found to be defective.
(a)
What is an estimate of the proportion defective when the process
is in control?
(b)
What is the standard error of the proportion if samples of size
100 will be used for statistical process control? (Round your
answer to four decimal places.)
(c)
Compute the upper and lower...

1. Twelve samples, each
containing five parts, were taken from a process that produces
steel rods. The length of each rod is the sample was determined.
The results were tabulated and sample means and ranges were
computed.
Sample Sample Mean (in.) Range (in.)
Sample
Sample Mean (inches)
Sample Range (inches)
1
10.001
0.011
2
10.003
0.014
3
9.995
0.007
4
10.007
0.022
5
9.997
0.013
6
9.999
0.012
7
10.001
0.008
8
10.006
0.014
9
9.994
0.005
10
10.002
0.010...

The following are quality control data for a manufacturing
process at Kensport Chemical Company. The data show the temperature
in degrees centigrade at five points in time during a manufacturing
cycle.
Sample
x
R
1
95.72
1.0
2
95.24
0.9
3
95.18
0.7
4
95.42
0.4
5
95.46
0.5
6
95.32
1.1
7
95.40
0.9
8
95.44
0.3
9
95.08
0.2
10
95.50
0.6
11
95.80
0.6
12
95.22
0.2
13
95.60
1.3
14
95.22
0.6
15
95.04
0.8
16...

The following are quality control data for a manufacturing
process at Kensport Chemical Company. The data show the temperature
in degrees centigrade at five points in time during a manufacturing
cycle.
Sample
x
R
1
95.72
1.0
2
95.24
0.9
3
95.18
0.7
4
95.42
0.4
5
95.46
0.5
6
95.32
1.1
7
95.40
0.9
8
95.44
0.3
9
95.08
0.2
10
95.50
0.6
11
95.80
0.6
12
95.22
0.2
13
95.58
1.3
14
95.22
0.6
15
95.04
0.8
16...

The following are quality control data for a manufacturing
process at Kensport Chemical Company. The data show the temperature
in degrees centigrade at five points in time during a manufacturing
cycle.
Sample
x
R
1
95.72
1.0
2
95.24
0.9
3
95.18
0.7
4
95.44
0.4
5
95.46
0.5
6
95.32
1.1
7
95.40
0.9
8
95.44
0.3
9
95.08
0.2
10
95.50
0.6
11
95.80
0.6
12
95.22
0.2
13
95.54
1.3
14
95.22
0.6
15
95.04
0.8
16...

A manufacturing company makes runners for cabinet drawers. To
assess the quality of the manufacturing process, the company
collected one sample of 300 consecutively manufactured runners each
day for 20 days and counted the number of defective items. The
resulting sample data are:
Sample: 1 2 3 4 5 6 7 8 9
10
Sample Size: 300 300 300 300 300 300 300 300 300
300
Defectives: 8 6
11 15 12
11 9 6 5 4
The Upper Control Limit, UCL, for a p control chart based on the
above data is

Twenty-five samples of 100 items each were inspected when a
process was considered to be operating satisfactorily. In the 25
samples, a total of 180 items were found to be defective.
(a)What is an estimate of the proportion defective when the
process is in control?
_________________.
(b)What is the standard error of the proportion if samples of
size 100 will be used for statistical process control? (Round your
answer to four decimal places.)
________________.
(c)Compute the upper and lower control...

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