Applied Statistics and Probability for Engineers

622 CHAPTER 16 STATISTICAL QUALITY CONTROL

nonconforming is 0.27%, or 2700 parts per million. Finally, when the PCRis less than

unity, as in Fig. 16-14(c), the process is very yield-sensitive and a large number of non-

conforming units will be produced.

The definition of the PCRgiven in Equation 16-19 implicitly assumes that the process

is centered at the nominal dimension. If the process is running off-center, its actual capa-

bilitywill be less than indicated by the PCR. It is convenient to think of PCRas a meas-

ure of potential capability,that is, capability with a centered process. If the process is not

centered, a measure of actual capability is often used. This ratio, called PCRk, is defined

below.

LSL μ USL

Nonconforming

units

Nonconforming

units

(^3) σ (^3) σ
(c)
PCR < 1
LSL USL
μ
Nonconforming
units
Nonconforming
units
3 σ 3 σ
(b)
PCR = 1
LSL μ USL
3 σ 3 σ
(a)
PCR > 1
Figure 16-14
Process fallout and the
process capability ratio
(PCR).
PCRkmin c (16-21)
USL
3 
,
LSL
3 
d
PCRk
In effect, PCRkis a one-sided process capability ratio that is calculated relative to the specifi-
cation limit nearest to the process mean. For the vane-opening process, we find that the
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