Question

In: Statistics and Probability

The following data represent samples that were taken on 10 separate days. Each day has a...

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?

Solutions

Expert Solution

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


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