The following data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control.
Day |
Sample Size |
Defects |
1 |
100 |
6 |
2 |
110 |
4 |
3 |
190 |
10 |
4 |
190 |
7 |
5 |
240 |
15 |
6 |
255 |
8 |
7 |
105 |
3 |
8 |
175 |
6 |
9 |
245 |
22 |
10 |
265 |
27 |
b. Find the LCL.
c. Is the process in control? Why/why not?
Day | Sample Size | Defects | Pi | |
1 | 100 | 6 | 0.06 | |
2 | 110 | 4 | 0.036364 | |
3 | 190 | 10 | 0.052632 | |
4 | 190 | 7 | 0.036842 | |
5 | 240 | 15 | 0.0625 | |
6 | 255 | 8 | 0.031373 | |
7 | 105 | 3 | 0.028571 | |
8 | 175 | 6 | 0.034286 | |
9 | 245 | 22 | 0.089796 | |
10 | 265 | 27 | 0.101887 | |
total | 1875 | 108 | 0.53425 |
sample proportion = 0.53425 / 10
=0.053425
STD DEV OF P = √( p(1-p)/n ) = √(0.053425 (1-
0.053425)/ 10 ) = 0.071113
a)
UCL = p + 3 * sd = 0.053425 + 3* 0.071113 = 0.266764
B)
LCL = p - 3 * sd = 0.053425 - 3* 0.071113 =-0.159914 = 0(The proportion cannot be negative)
C)
As, all the proportion are in between UCL and LCL sample process in control.
Please revert back in case of any doubt.
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