In: Statistics and Probability
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 |
110 |
6 |
2 |
112 |
3 |
3 |
195 |
8 |
4 |
185 |
6 |
5 |
245 |
10 |
6 |
250 |
7 |
7 |
100 |
5 |
8 |
170 |
7 |
9 |
250 |
20 |
10 |
270 |
25 |
a. Find the UCL.
b. Find the LCL.
c. Is the process in control? Why/why not?
From the given data
Size (ni) | Number of defects (ui) | ||||
Day | ui = ci/ni | LCL | UCL | ||
1 | 110 | 6 | 0.0545 | -0.01345 | 0.116257 |
2 | 112 | 3 | 0.0268 | -0.01287 | 0.115675 |
3 | 195 | 8 | 0.041 | 0.002696 | 0.100113 |
4 | 185 | 6 | 0.0324 | 0.001397 | 0.101412 |
5 | 245 | 10 | 0.0408 | 0.00795 | 0.094859 |
6 | 250 | 7 | 0.028 | 0.008386 | 0.094422 |
7 | 100 | 5 | 0.05 | -0.01661 | 0.119422 |
8 | 170 | 7 | 0.0412 | -0.00076 | 0.103571 |
9 | 250 | 20 | 0.08 | 0.008386 | 0.094422 |
10 | 270 | 25 | 0.0926 | 0.01001 | 0.092799 |
Total : | 1887 | 97 |
c) NControl Chart:
Interpretation: The process is under control since all points lies between LCL and UCL.
The number of defects per unit is stable. No subgroups are out of control