Page 86 - Six Sigma for electronics design and manufacturing

The Elements of Six Sigma and Their Determination
x – 55
z=

Figure 2.10 z transformation.

b. Nominal = process average
Cpk = Cp = ± SL/± 3 = 3/3 · 2.156 = 0.46
z = 3 · Cp = 1.39
f(z) = f(–1.39) = 0.0823
For two-sided defects, RR = 2 · 0.0823 = 0.1646 or 16.46% or
164,600 PPM
Nominal shifted 1 to the left
Cp = 0.46 (remains the same from above)
Cpk = min(USL – average/3 ) or (average – LSL/3 )
Cpk = (3 – 1)/3 · 2.156 = 0.31
z 1 = 0.93 and z 2 = 1.86
RR = f(–z 1 ) + f(–z 2 ) = 0.1762 + 0.0314 = 0.2076 or 20.76% or
207,600 PPM
Nominal shifted by 0.75 to the right
Cp = 0.46
Cpk = (3 – 0.75)/3 · 2.156 = 0.35
z 1 = 1.04 and z 2 = 1.74
RR = 0.1492 + 0.0409 = 0.1901 or 19.01% or 190,100 PPM

c. For Cp = 1, specification limits are:
12.62 ± 3 · 2.156 = 12.62 ± 6.468 = 19.088 to 6.152
Cp = 1.5, specification limits are:
12.62 ± 4.5 · 2.156 = 12.62 ± 9.702 = 22.322 to 2.918