Applied Statistics and Probability for Engineers

620 CHAPTER 16 STATISTICAL QUALITY CONTROL

The tolerance chart for all 20 samples from the vane-manufacturing process is shown in

Fig. 16-12. The specifications on vane opening are in. In terms of the

coded data, the upper specification limit is USL40 and the lower specification limit is

LSL20, and these limits are shown on the chart in Fig. 16-12. Each measurement is plot-

ted on the tolerance chart. Measurements from the same subgroup are connected with

lines. The tolerance chart is useful in revealing patterns over time in the individual meas-

urements, or it may show that a particular value of or rwas produced by one or two un-

usual observations in the sample. For example, note the two unusual observations in sam-

ple 9 and the single unusual observation in sample 8. Note also that it is appropriate to plot

the specification limits on the tolerance chart, since it is a chart of individual measure-

ments. It is never appropriate to plot specification limits on a control chart or to use

the specifications in determining the control limits.Specification limits and control lim-

its are unrelated. Finally, note from Fig. 16-12 that the process is running off-center from

the nominal dimension of 30 (or 0.5030 inch).

The histogram for the vane-opening measurements is shown in Fig. 16-13. The observa-

tions from samples 6, 8, 9, 11, and 19 (corresponding to out of-control points on either the

or Rchart) have been deleted from this histogram. The general impression from examining

this histogram is that the process is capable of meeting the specification but that it is running

off-center.

Another way to express process capability is in terms of an index that is defined as

follows.

X

x

0.5030 0.0010

(^155101520)
20
25
30
35
40
45
Nominal
dimension = 30
Sample number
LSL = 20
USL = 40
Vane opening
Figure 16-12
Tolerance diagram of
vane openings.
c 16 .qxd 5/8/02 9:58 PM Page 620 RK UL 6 RK UL 6:Desktop Folder: