Applied Statistics and Probability for Engineers

16-7 PROCESS CAPABILITY 621

The process capability ratio(PCR) is

PCR (16-20)

USLLSL

6 

Process Capability

Ratio

The numerator of PCRis the width of the specifications. The limits 3on either side of the

process mean are sometimes called natural tolerance limits,for these represent limits that an

in-control process should meet with most of the units produced. Consequently, 6is often re-

ferred to as the width of the process. For the vane opening, where our sample size is 5, we

could estimate as

Therefore, the PCRis estimated to be

The PCRhas a natural interpretation: (1PCR)100 is just the percentage of the specifica-

tions’ width used by the process. Thus, the vane-opening process uses approximately

(11.55)10064.5% of the specifications’ width.

Figure 16-14(a) shows a process for which the PCRexceeds unity. Since the process

natural tolerance limits lie inside the specifications, very few defective or nonconform-

ing units will be produced. If PCR1, as shown in Fig. 16-14(b), more nonconform-

ing units result. In fact, for a normally distributed process, if PCR1, the fraction

PCR

USLLSL

6 ˆ



40  20

61 2.15 2

1.55

ˆ

r

d 2



5.0

2.326

2.15

5

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

LSL USL

Nominal dimension

Vane opening

10

15

20

Frequency

Figure 16-13

Histogram for vane

opening.

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