Introduction to Probability and Statistics for Engineers and Scientists

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. ■