Applied Statistics and Probability for Engineers

606 CHAPTER 16 STATISTICAL QUALITY CONTROL

a particular pattern in terms of assignable causes requires experience and knowledge of the

process. That is, we must not only know the statistical principles of control charts, but we

must also have a good understanding of the process.

The Western Electric Handbook (1956) suggests a set of decision rules for detecting non-

random patterns on control charts. Specifically, the Western Electric ruleswould conclude

that the process is out of control if either

1. One point plots outside 3-sigma control limits.


2. Two out of three consecutive points plot beyond a 2-sigma limit.


3. Four out of five consecutive points plot at a distance of 1-sigma or beyond from the
   center line.


4. Eight consecutive points plot on one side of the center line.
   We have found these rules very effective in practice for enhancing the sensitivity of control
   charts. Rules 2 and 3 apply to one side of the center line at a time. That is, a point above the
   upper2-sigma limit followed immediately by a point below the lower2-sigma limit would not
   signal an out-of-control alarm.
   Figure 16-7 shows an control chart for the piston ring process with the 1-sigma,
   2-sigma, and 3-sigma limits used in the Western Electric procedure. Notice that these inner

X

Figure 16-7 The

Western Electric zone

rules.

1

73.9820

2 3 4 5 6 7 8 9 10 11 12

73.9865

73.9910

73.9955

74.0000

74.0045

74.0090

74.0135

74.0180

Zone A

σ

Zone B

Zone C

Zone C

Zone B

Zone A

(^3) X
2 σX
1 σX
1 σX
2 σX
3 σX
LCL = 73.9865
UCL = 74.0135
Sample number
Figure 16-6 (a)
Variability with the
cyclic pattern.
(b) Variability with
the cyclic pattern elim-
inated.
LSL μ USL
(a)
LSL μ USL
(b)
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