558 Chapter 13:Quality Control
SincenFiis equal to the number of defectives in subgroupi, we see thatFkcan also be
expressed as
F=nF 1 +···+nFk
nk=total number of defectives in all the subgroups
number of items in the subgroupsIn other words, the estimate ofpis just the proportion of items inspected that are defective.
The upper and lower control limits are now given by
LCL=F− 3√
F(1−F)
n, UCL=F+ 3√
F(1−F)
nWe should now check whether the subgroup fractionsF 1 ,F 2 ,...,Fkfall within these
control limits. If some of them fall outside, then the corresponding subgroups should be
eliminated andFrecomputed.
EXAMPLE 13.4a Successive samples of 50 screws are drawn from the hourly production of
an automatic screw machine, with each screw being rated as either acceptable or defective.
This is done for 20 such samples with the following data resulting.
Subgroup Defectives F Subgroup Defectives F
1 6 .12 11 1 .02
2 5 .10 12 3 .06
3 3 .06 13 2 .04
4 0 .00 14 0 .00
5 1 .02 15 1 .02
6 2 .04 16 1 .02
7 1 .02 17 0 .00
8 0 .00 18 2 .04
9 2 .04 19 1 .02
10 1 .02 20 2 .04We can compute the trial control limits as follows:
F=total number defectives
total number items=34
1,000=.034