Applied Statistics and Probability for Engineers

16-5XAND ROR SCONTROL CHARTS 613

1

30

2 3 4 5 6 7 8 9 1011121314151617181920 Sample number

X Chart

32

34

36

38

40

42

28

x

Revised LCL = 30.33

Revised UCL = 36.10

CL = 33.21

1

4

2 3 4 5 6 7 8 9 1011121314151617181920 Sample number

R Chart

6

8

10

12

14

16

2

r

Revised UCL = 10.57

CL = 5.0

Estimation of limits

= not used in computing

control limits

Estimation of limits

= not used in computing

control limits

Figure 16-10 The and X Rcontrol charts for vane opening, revised limits.

The revised control charts are shown in Fig. 16-10. Notice that we have treated the first

20 preliminary samples as estimation datawith which to establish control limits. These lim-

its can now be used to judge the statistical control of future production. As each new sample

becomes available, the values of and rshould be computed and plotted on the control charts.

It may be desirable to revise the limits periodically, even if the process remains stable. The

limits should always be revised when process improvements are made.

Computer Construction of and RControl Charts

Many computer programs construct and Rcontrol charts. Figures 16-8 and 16-10 show

charts similar to those produced by Minitab for the vane-opening data. This program will

allow the user to select any multiple of sigma as the width of the control limits and use the

Western Electric rules to detect out-of-control points. The program will also prepare a

summary report as in Table 16-2 and exclude subgroups from the calculation of the control

limits.

X

X

x

Table 16-2 Summary Report from Minitab for the Vane-Opening Data

Test Results for Xbar Chart

TEST 1. One point more than 3.00 sigmas from center line.

Test Failed at points: 6 8 11 19

Test Results for R Chart

TEST 1. One point more than 3.00 sigmas from center line.

Test Failed at points: 9

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