A manufacturer of automobile headlamps tests 400 samples each day. The non-confo
ID: 452133 • Letter: A
Question
A manufacturer of automobile headlamps tests 400 samples each day. The non-conformities are counted as scratches, circuit breaks etc. These defects are corrected before sending the headlamps to customers. The data are then used to aid process engineers in their problem solving activities. Given the following information, create and graph the chart. How is their performance? What is the process capability?
Subgroup
Sample size
Non-conformities
1
400
50
2
400
23
3
400
27
4
400
32
5
400
26
6
400
38
7
400
57
8
400
31
9
400
48
10
400
34
11
400
37
12
400
44
13
400
34
14
400
32
15
400
50
16
400
49
17
400
54
18
400
38
19
400
29
20
400
47
Sum
8000
780
Subgroup
Sample size
Non-conformities
1
400
50
2
400
23
3
400
27
4
400
32
5
400
26
6
400
38
7
400
57
8
400
31
9
400
48
10
400
34
11
400
37
12
400
44
13
400
34
14
400
32
15
400
50
16
400
49
17
400
54
18
400
38
19
400
29
20
400
47
Sum
8000
780
Explanation / Answer
Subgroup Non-conformities Sample size Non-conformities rate 1 50 400 0.125 2 23 400 0.058 3 27 400 0.068 4 32 400 0.080 5 26 400 0.065 6 38 400 0.095 7 57 400 0.143 8 31 400 0.078 9 48 400 0.120 10 34 400 0.085 11 37 400 0.093 12 44 400 0.110 13 34 400 0.085 14 32 400 0.080 15 50 400 0.125 16 49 400 0.123 17 54 400 0.135 18 38 400 0.095 19 29 400 0.073 20 47 400 0.118 Total 780 8000 P bar (total Number of incorrect analysis/ total sample) 0.0975 Sp (sqrt (P bar*(1- p bar)/400) 0.0148 z (assumed at 95%) 1.96 UCL (p bar + z* Sp) 0.1266 LCL (p bar - z* Sp 0.0684 Cp = (upper specification - lower specification)/ 6 0.653333 Cpk = min of { (mean - lower specification)/3, (upper specification - mean)/3)} 0.653333 Because the values of Cp and Cpk are less than 1, the process is not capable of meeting specifications
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