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Six Sigma for Electronics Design and Manufacturing
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Figure 2.7 Cp and Cpk sample calculations.

this problem. Several conditions of specification limits are given with
varying average shifts. It can be seen that the Cpk = 1.33 could origi-
nate from many possible conditions. When the process is centered, the
specification limits for Cpk = 1.33 are at ±4 . As the process average
shifts, the specification limits have to increase to compensate for this
shift. For example, if the average shifts by ±1.5 , then the specification
limits have to increase to ±5.5 for the same value of Cpk = 1.33. The
easiest condition to achieve Cpk = 1.33 is to design parts specified at 4
, and with zero shift of process to the nominal, as shown in Table 2.2.

2.2.2 Negative Cpk
Can Cpk be negative? Yes! This is a special condition in which the
process average is greater than one of the specification limits. Though

Table 2.2 Cpk and process average shift
No average shift ±1 Shift ±1.5 Shift
__________________ __________________ __________________
Cp ± SL PPM Cpk PPM Cpk PPM Cpk
1.33 ± 4 64 1.33 1350.0 1.0 6210.0 0.83
1.67 ± 5 0.6 1.67 32.0 1.33 230.0 1.17
1.83 ± 5.5 0.02 1.83 3.4 1.5 32.0 1.33
2.0 ± 6 0.002 2.0 0.3 1.67 3.4 1.5