Question

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 |

5 |
0.577 |
2.115 |
0 |

6 |
0.483 |
2.004 |
0 |

7 |
0.419 |
1.924 |
0.076 |

8 |
0.373 |
1.864 |
0.136 |

9 |
0.337 |
1.816 |
0.184 |

10 |
0.308 |
1.777 |
0.223 |

12 |
0.266 |
1.716 |
0.284 |

Sample Sample Mean (in.) Range
(in.) Sample Sample Mean (in.)
Range (in.)

1 12.602 0.044 7
12.603 0.021

2 12.600 0.051 8
12.607 0.058

3 12.591 0.042 9
12.597 0.039

4 12.604 0.037 10
12.601 0.038

5 12.599 0.048 11
12.601 0.054

6 12.601 0.053 12
12.606 0.061

- For the given data, **the x-double bar = ?
inches** (round you response to four decimal places).

- Based on the sampling done, *the control limits for 3 sigma
x-bar chart are*:

**Upper Control Limit (UCL) = ? inches** (round
your response to four decimal places).

**Lower Control Limit (LCL) = ? inches** (round
your response to four decimal places).

*Based on the x-bar chart,* is one or more samples beyond
the control limits? **yes?/no?**

**For the given data, the R-bar = ? inches** (round
your response to four decimal places).

- The control limits for the 3-sigma R-Chart are:

**Upper Control Limit (UCL) = ?
inches** (round your response to four decimal places).

**Lower Control Limit (LCL) = ? inches** (round
your response to four decimal places).

*Based on the R-chart,* is one or more samples beyond the
control limits? **Yes?/No?**

Answer #1

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...

Twelve samples, each containing five parts, were taken
from a process that produces steel rods. The length of each rod
in the
samples was determined. The results were tabulated and
sample
means and ranges were computed. The results were:
Sample Sample Mean (in.) Range (in.)
1 10.002 0.011
2 10.002 0.014
3 9.991 0.007
4 10.006 0.022
5 9.997 0.013
6 9.999 0.012
7 10.001 0.008
8 10.005 0.013
9 9.995 0.004
10 10.001 0.011
11 10.001 0.014
12 10.006...

Random samples of size n = 410 are taken from a
population with p = 0.09.
Calculate the centerline, the upper control limit (UCL), and the
lower control limit (LCL) for the p¯p¯ chart.
(Round the value for the centerline to 2 decimal places and
the values for the UCL and LCL to 3 decimal places.)
Calculate the centerline, the upper control limit (UCL), and the
lower control limit (LCL) for the p¯p¯ chart if samples of
290 are used....

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...

Random samples of size n = 200 are taken from a population with
p = 0.08.
a. Calculate the centerline, the upper control limit (UCL), and
the lower control limit (LCL) for the p¯chart
b. Calculate the centerline, the upper control limit (UCL), and
the lower control limit (LCL) for the p¯ chart if samples of 120
are used.
c. Discuss the effect of the sample size on the control limits.
The control limits have a ___ spread with smaller...

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...

A process sampled 20 times with a sample of size 8 resulted
in = 23.5 and R = 1.8.
Compute the upper and lower control limits for the x chart for
this process. (Round your answers to two decimal places.)
UCL=________.
LCL=________.
Compute the upper and lower control limits for the R
chart for this process. (Round your answers to two decimal
places.)
UCL=_________.
LCL=___________.

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...

Ten samples of 15 parts each were taken from an ongoing process
to establish a p-chart for control. The samples and the
number of defectives in each are shown in the following table:
SAMPLE
n
NUMBER OF
DEFECTIVE ITEMS IN THE SAMPLE
1
15
0
2
15
0
3
15
0
4
15
2
5
15
0
6
15
3
7
15
1
8
15
0
9
15
3
10
15
1
a.
Determine the p−p−, Sp, UCL and LCL...

Ten samples of 15 parts each were taken from an ongoing process
to establish a p-chart for control. The samples and the
number of defectives in each are shown in the following table:
SAMPLE
n
NUMBER OF
DEFECTIVE ITEMS IN THE SAMPLE
1
15
0
2
15
2
3
15
0
4
15
3
5
15
1
6
15
3
7
15
1
8
15
0
9
15
0
10
15
0
a.
Determine the p−p−, Sp, UCL and LCL...

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