Statistical Quality ControlControl Charts (ISS (Statistical Services) Statistics Paper IV): Questions 21  22 of 31
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Question number: 21
» Statistical Quality Control » Control Charts » Variable
Describe in Detail
a) The number of customer complaints are recorded at a television manufacturing company. Complaints have been recorded over the past 20 weeks. Construct 3σ control limits for the cchart.
Week  No. of complaints  Week  No. of complaints 
1  0  11  4 
2  3  12  3 
3  4  13  1 
4  1  14  1 
5  0  15  1 
6  0  16  0 
7  3  17  2 
8  1  18  1 
9  1  19  2 
10  0  20  2 
b) A machine is manufacturing mica discs. samples of size 5 are drawn every hour and their thickness in units are recorded as follows. From this data construct 3σ control limits for chart.
Sample No.  Observstions  
1  8  9  15  4  11 
2  7  10  7  6  8 
3  11  12  10  9  10 
4  12  8  6  9  12 
5  11  10  6  14  11 
6  7  7  10  4  11 
7  10  7  4  10  10 
8  8  11  11  7  7 
9  8  11  8  14  12 
10  12  9  12  17  11 
11  7  7  9  17  13 
12  9  9  4  4  11 
13  10  12  12  12  12 
14  8  11  9  6  8 
15  10  13  9  4  9 
16  9  11  8  5  11 
Explanation
a) Average number of defects per sample is
=1.5+ =1.5 + 3 (1.22) =5.174
= →0
Since number of defects cannot be negative, can be considered as zero. (rounded up to zero)
b) Second question:
Question number: 22
» Statistical Quality Control » Control Charts » Variable
Describe in Detail
When should RChart be Analyzed? Six samples which contain 20 observations per sample have been collected and the sample means and sample ranges are computed as shown below. Test whether the sample means are within control limits of ?
Sample  Mean  Range 
1  3.06  0.42 
2  3.15  0.5 
3  3.11  0.41 
4  3.13  0.46 
5  3.06  0.46 
6  3.09  0.45 
Explanation

Range chart should be analyzed before the mean chart since variability of the process must be in control before the mean chart can be analyzed.

If the R chart indicates that the dispersion of the quality by the process is out of control, generally it is better not to construct