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Quality Control HW Solutions
Problem 1:
The management of the Diners Delight restaurant chain is in the process of establishing quality control charts for the time that its service people give to each customer. Management thinks the length of time that each customer is given should remain within certain limits to enhance service quality.
For simplicity, the data from four samples are displayed below. In each sample, six service people were randomly selected, and the customer service they provided was observed. The activities that the service people were performing were identified, and the time to service each customer was recorded as below.
Service time (in seconds)
Service person
Sample 1
Sample 2
Sample 3
Sample 4
1
200
150
175
90
2
120
85
105
75
3
83
93
130
150
4
68
150
145
175
5
110
90
75
105
6
115
65
115
125
116
105.5
124.17
120
R
200-68=132
150-65=85
175-75=100
175-75=100
Use the given information, please (a)
Find the 99.73% (3-sigma) upper and lower control limits for X-bar chart and R-chart. (b) After the control chart was established, a sample of six service personnel was observed, and
the following customer service times in seconds were recorded: 180, 125, 110, 98, 156 and 190. Is the process in control? Any corrective action needed?
Solution:
(a)
X
=(
116
+
105.5
+
124.17
+
120
)/
4
=
116.42
R
=(
132
+
85
+
100
+
100
)/
4
=
104.25
Sample size n = 6
A2 = 0.48, D3=0, and D4=2.0
Control limits for mean:
UCL
=
¯
¯
X
+
A
2
¯
R
=
116 .42
+(
.48
)(
104.25
)=
166.46
1
LCL
=
¯
¯
X
−
A
2
¯
R
=
116 .42
−(
.48
)(
104.25
)=
66.38
Control limits for range:
UCL
=
D
4
¯
R
=(
2.0
)(
104.25
)=
208.5
LCL
=
D
3
¯
R
=(
0
)(
104.25
)=
0
(b)
Sample mean:
= (180 + 125 + 110 + 98 + 156 + 190)/6 = 143.17
Sample range: R = 190 - 98 = 92
and R are both within the control limits. Process is in control, no action is needed.
Problem 2: Several complaints recently have been sent to the Logan police department regarding the increasing
incidence of congestion on the city’s streets. The complaints attribute the cause of these traffic tie-
ups to a lack of synchronization of the traffic lights. The lights are controlled by a main computer system, and adjusting this program is costly. Therefore, the controllers are reluctant to change the situation unless a clear need is shown.
During the past year, the police department has collected 1,000 data each month at major intersections. The data were as shown below.
Month
Congestion incidence
January
14
February
18
March
14
April
12
May
16
June
8
July
19
August
12
September
14
October
7
November
10
December
18
(a)
Construct a control chart with 3-sigma quality standard based on the above data.
2
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Related Questions
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Sample Number of Defectives Sample Number of Defectives
1 12 16 6
2 14 17 3
3 10 18 7
4…
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Problem 1:
Auto pistons at Wemming Chung’s plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must
be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
Day
Mean (mm)
Range (mm)
1
156.9
4.2
2
153.2
4.6
3
153.6
4.1
4
155.5
5.0
5
156.6
4.5
a) What are the UCL x (line on top of x, counldn't find the button to do it) and LCL x (line on top of x) , using 3σ? Plot the data.
b) What are the UCL R and LCL R , using 3σ? Plot the data.
c) Is the Process in Control?
(Please screen shot the EXCEl if its in excel)
Note:-
Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism.
Answer completely.
You will get up vote for sure.
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Problem 5
Madras Medical College is trying to improve its image providing a positive experience for its patients and
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he or she is satisfied or unsatisfied with the meal. A 100-patient sample of the survey results over the past
7 days yielded the following data:
June through December and the MAD and
January. The initial
the end of December. What can you say about the performance or
Day
1
Sample size
100
100
100
100
100
100
100
Construct p-chart that plots the percentage of patients unsatisfied with their meals. Set the control limits
to include 99.73% of the random variation in meal satisfaction. Comment on your results.
2
3
4
5
6
7
No. of unsatisfied patients
24
22
8
15
10
26
17
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Costs (in thousands)
Last Year
This Year
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$ 720
$ 909
Quality engineering
$ 450
$ 765
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$ 270
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$ 1,530
Statistical process control
$ 0
$ 225
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$ 1,350
$ 1,260
Supplies used in testing
$ 45
$ 81
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$ 720
$ 900
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$ 1,620
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Total
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23
21
5
18
4
6
2
1
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850
Scrapped units (number)
3,400
850
Inspection (hours)
3,400
1,700
Quality training (hours)
85
85
Activities:
Performing warranty work
$816,000
Scrapping units
612,000
Inspecting
306,000
Quality training
85,000
Required:
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Generator B
Unit cost
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$fill in the blank 2
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Number Defective
Percent defective
9
18
7
14
4
8
9
18
1
2
9
18
11
22
5
10
5
10
8
16
7
14
15
30
a. Insert the mean proportion defective, UCL, and LCL. (Leave no cells blank - be certain to enter "0" wherever required. Round your intermediate calculations and final answers to 2 decimal places.)
Mean proportion defective
UCL
LCL
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Sample
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14
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18
2
12
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10
3
9
13
19
4
10
14
20
5
11
15
17
6
7
16
18
7
8
17
18
8
14
18
22
9
16
19
24
10
17
20
23
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Note:-
Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism.
Answer completely.
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2
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1
6
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10
Sample
Number
Irregularities 11
2
3
4
5
7
9
8
12
4
16
5
8
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Sample
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[8 marks]
[2 marks]
9,
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13 5
2
23
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14 5
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