Applied Statistics and Probability for Engineers

612 CHAPTER 16 STATISTICAL QUALITY CONTROL

and this result is nearly the same as from. The Schart is shown in Fig. 16-9. Because the con-

trol limits for the chart calculated from are nearly the same as from , the chart is not shown.

Suppose that all of these assignable causes can be traced to a defective tool in the wax-

molding area. We should discard these five samples and recompute the limits for the and R

charts. These new revised limits are, for the chart,

and for the Rchart,

LCLD 3 r 1021 5.0 2  0

UCLD 4 r 1 2.115 21 5.0 2 10.57

LCLxA 2 r33.21 1 0.577 21 5.0 2 30.33

UCLxA 2 r33.21 1 0.577 21 5.0 2 36.10

X

X

X s r

r

0

0

1

1

2

3

4

5

6

Sample standard

deviation

5 10 15 20

Subgroup

UCL = 4.899

LCL = 0.00

S = 2.345

Figure 16-9. The Scontrol chart for vane opening.

1

1

1

1

1

1

30

2 3 4 5 6 7 8 9 1011121314151617181920

Subgroup

10

Subgroup

Means

Ranges

32

34

36

38

40

42

28

26

LCL = 29.97

UCL = 36.67

x =

33.32

1

4

2 3 4 5 6 7 8 9 11121314151617181920

6

8

10

12

14

16

2

0

UCL = 12.27

r = 5.80

LCL = 0.00

Figure 16-8 The and X Rcontrol charts for vane opening.

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