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Math 329:Quality Control December 2009 Question Paper
Math 329:Quality Control December 2009
Course:Bachelor Of Science In Economics And Mathematics
Institution: Kabarak University question papers
Exam Year:2009
KABARAK
UNIVERSITY
UNIVERSITY EXAMINATIONS
2008/2009 ACADEMIC YEAR
FOR THE DEGREE OF BACHELOR OF SCIENCE IN
ECONOMICS AND MATHEMATICS
COURSE CODE: MATH 329
INSTRUCTIONS:
Attempt question ONE and any other TWO questions
QUESTION ONE (30 MARKS)
(a) Briefly explain the two causes of variations in every manufacturing process. (4 marks)
(b) State the advantages of a process under statistical control.
(2 marks)
(c) Construct the 3 – sigma control limits for
chart.
(4 marks)
(d) A cost accountant is required to set up a system for controlling waste in a certain
department converting rolls of paper into sheets. The pounds of waste are recorded
by shifts for a period of 10 days as shown below.
1.023
0
2.574
1.693
DAYS
1
2
3
4
5
6
7
8
9
10
1
89
112
121
91
75
86
123
98
96
97
T
I
F
2
98
108
106
117
79
105
106
100
83
114
H
S
3
110
132
103
98
81
93
105
114
87
124
(i)
Prepare and R charts.
(6 marks)
(ii)
State whether the process is under control.
(2 marks)
(iii)
What are warning and Action limits for chart.
(2 marks)
(e) Briefly explain the OC- curve for double sampling plan.
(4 marks)
(f) In welding of beams, defects included pin holes, cracks etc. A record was made
of the number of defects formed in one beam each hour for a total of twelve hours.
4, 7, 3, 9, 5, 3, 4, 9, 9, 9, 7, 4
(i)
Set up the 3 – sigma control limits to the number of defects and comment on
your limits.
(3 marks)
(ii) Obtain the Action and warning limits for the C- chart.
(3 marks)
QUESTION TWO (20 MARKS)
(a) Discuss the construction of and R chart when population mean and population
variance are specified.
(8 marks)
(b) (i) Construct a control chart for mean and the range (R) for the following data on
the basic of fuses where samples of five are taken every hour.
(6 marks)
0.58
0
2.11
HOURS
1
2
3
4
5
6
7
8
9
10
11
12
1
56
56 29 41 56 50 61 28 24 69 65
60
S
E
2
66
61
24
53
52
74
61
20
31
109
89
79
L
P
3
76
68 80 70 51 75 72 27 39 112 93
94
M
A
4
77
78 81 78 66 78 94 41 61 119 110 110
S
5
88
91 82 83 77 131 131 61 85 153 111
135
(ii) Comment on whether the production seems to be under control assuming that they
are the first sets of data .
(2 marks)
(c) Explain the double control limits
(4 marks)
QUESTION THREE (20 MARKS)
(a) Construct the P – chart by normal approximation when p is known and unknown
(10 marks)
(b) A table of 10 samples of size are recorded in the table below for the number of
defective items in each sample.
Sample
1
2
3
4
5
6
7
8
9
10
Defectives
4
7
6
12
7
4
3
6
5
9
Sample size
100 200
150
300
120
180
220
350
200
250
(i) Using initial value of p = 5% if the process is under control, set up the p - chart at
a = 0.2% level of significance is the process under control.
(5 marks)
(ii) Set up the 3 – sigma control limits if p is unknown.
(5 marks)
QUESTION FOUR (20 MARKS)
(a) Briefly explain the various types of acceptance inspection procedure.
(8 marks)
(b) From a lot consisting of 2000 items a sample of size 225 is taken. If it contains 14
or less defectives then the lot is accepted, otherwise rejected.
(i)
Plot the OC curve
(ii)
Plot ASN curve
(iii)
Hence obtain AOQL
(12 marks)
QUESTION FIVE (20 MARKS)
(a) Distinguish between single sampling plan and double sampling plan.
(2 marks)
(b) Obtain a sequential sampling plan with the following parameters
0.01
0.02
0.02
0.01
(10 marks)
(d) Determine the control limits for the number of defect per unit (c-chart) for large n
and moderately small p at level of significance.
(8 marks)
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