562 Chapter 13:Quality Control
Cars Defects Cars Defects Cars Defects Cars Defects
1141 67411 631668
2162 78512 741795
3 150 8 95 13 103 18 81
4 111 9 76 14 81 19 102
5 92106815 942073
Does it appear that the production process was in control throughout?
SOLUTION SinceX=94.4, it follows that the trial control limits are
LCL=94.4− 3
√
94.4=65.25
UCL=94.4+ 3
√
94.4=123.55
Since the first three data values are larger than UCL, they are removed and the sample
mean recomputed. This yields
X=
(94.4)20−(141+ 162 +150)
17
=84.41
and so the new trial control limits are
LCL=84.41− 3
√
84.41=56.85
UCL=84.41+ 3
√
84.41=111.97
At this point since all remaining 17 data values fall within the limits, we could declare that
the process is now in control with a mean value of 84.41. However, because it seems that
the mean number of defects was initially high before settling into control, it seems quite
plausible that the data valueX 4 also originated before the process was in control. Thus, it
would seem prudent in this situation to also eliminateX 4 and recompute. Based on the
remaining 16 data values, we obtain that
X=82.56
LCL=82.56− 3
√
82.56=55.30
UCL=82.56+ 3
√
82.56=109.82
and so it appears that the process is now in control with a mean value of 82.56. ■