Question

19,Suppose that you monitor the fraction defectives in ounces of a process that fills beer cans. The data given below were collected in the production process. Each day, 20 cans are inspected. What control chart would be the best for process monitoring? Calculate UCL and LCL of the relevant chart.

Days # of defectives

1 2

2 3

3 5

4 1

5 2

x-bar chart, UCL = 0.042 and LCL = 0 |
||

c chart, UCL = 0.1462 and LCL = 0 |
||

p chart, UCL = 0.1462 and LCL = 0 |
||

p chart, UCL = 0.3556 and LCL = 0 |
||

p chart, UCL = 0.3556 and LCL = -0.0956 |

21.

In a process, cycle time is the critical-to-quality characteristic being monitored. The data given below were collected from 15 cycle times in the process. Using histogram, identify what time interval has the highest frequency in cycle time? (# of columns = K = 6)

13 minutes 13 minutes 12 minutes

14 minutes 11 minutes 10 minutes

2 minutes. 11 minutes 11 minutes

7 minutes 7 minutes 9 minutes

9 minutes 6 minutes 7 minutes

10-12 minutes |
||

2-4 minutes |
||

12-14 minutes |
||

4-6 minutes |
||

none of the above |

Answer #1

19) For the process monitoring the p-chart would be best as we are monitoring the fraction defectives

Sample size(n) = 20

Number of samples = 5

Total number of observation (n ) = Sample size x number of samples = 20 x 5 = 100

Sum of number of defectives(np)= 2+3+5+1+2 = 13

P-bar = np/ n = 13/100 = **0.13**

Sp = √{[P-bar(1-P-bar)] / n}

= √ {[0.13(1-0.13)] / 20}

= √ [(0.13 x 0.87) /20]

= √(0.1131/20)

= √0.005655

= **0.075199734**

UCL = P-bar + 3(Sp) = 0.13 + (3x0.075199734) = 0.13 + 0.2256 =
**0.3556**

**LCL =** P-bar - 3(Sp) = 0.13 - (3x0.075199734) =
0.13 - 0.2256 = **-0.0956 = 0 (**when the LCL value is
negative it is taken as 0)

A process produces parts that are determined to be usable or
unusable. The process average defective rate is 1%. You plan to
monitor this process by taking samples of 400 parts.
Sample: 1 2 3 4 5 6 7 8 9 10
Defectives: 6 2 5 6 0 4 8 0 2 8
(A.) What is your p chart UCL?
(B.) What is your p chart LCL?
(C.) Is this process in control or not?

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
2
2
15
2
3
15
2
4
15
0
5
15
2
6
15
1
7
15
3
8
15
2
9
15
1
10
15
3
a. Determine the p−p− , Sp,
UCL and...

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...

Based on your recommendations, Mr. Miller improved shop
operations and successfully reduced the number of customer
complaints. To maintain good service, Mr. Miller asked you to keep
monitoring the wait times of oil change customers
at the shop.
First, you decide to create an x-bar chart to
monitor the central tendency (i.e., mean). But you know that we
sometimes overlook a problem if we use only an x-bar chart.
Therefore, you decide to create an R-chart to
monitor the process...

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...

Edit question
The results of inspection of samples of a product taken over the
past 5 days are given below. Sample size for each day has been
100:
Day 1
2
3
4
5
Defectives
2
6
14 3
7
Determine the UCL for this chart
Determine the LCL for this chart
Is this process in control?

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

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
1
2
15
1
3
15
3
4
15
1
5
15
0
6
15
0
7
15
2
8
15
1
9
15
2
10
15
1
a. Determine the p−p− , Sp,
UCL and...

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