Page 88 - Six Sigma for electronics design and manufacturing

item, the specification limits are 10.00 ± 0.04 . The process is charac-
terized by = 10.00 and = 0.015.
Cpk = Cp = ± SL/± 3 = 0.04/3 · 0.015 = 0.89
z = 3 · Cp = 2.67; f(–z) = .0038; RR = 0.38%; for each side above the
USL and below the LSL. Percent OK = 1 – total RR = 99.24%.
Note that in this case, the Cp was less than 1, therefore it is expect-
ed that the reject rate would be higher than 3 design defect rates of
2700 PPM or 0.27%. The Elements of Six Sigma and Their Determination 57
For the second item, the specification limits remain the same at
10.00 ± 0.04 . The process is shifted from the first item by 0.01 and
characterized by = 9.99 and = 0.015.
Cp = 0.89 (remains the same from the first item)
Cpk = min(USL – average/3 ) or (average – LSL/3 )
Cpk = 0.67 = minimum of (10.04 – 9.99/3 · 0.015) = 1.11
or (9.99 – 9.96/3 · 0.015) = 0.67
z 1 = 3 · Cpk (low) = 3 · 0.67 = 2.00; f(–2) = 0.0228 or 2.28%
z 2 = 3 · Cpk (high) 3 · 1.11 = 3.33; f(–3.33) = 0.00043 or 0.43%
Total RR = f(–z 1 ) + f(–z 2 ) = 0.00228 + 0.00043 = 0.02323
Percent OK = 1 – total RR = 1 – 0.2323 = 0.97677 or 97.68%.
It is apparent that if the manufacturing process is not centered
with the specification nominal (second case in the table), the total de-
fect rate increases, even if the manufacturing process standard devia-
tion remains the same. Similar increases in the defect rate occur if the
manufacturing process standard deviation increases or there is a com-
parable decrease in the tolerance limits of the design. The table also
illustrates the use of Cp or Cpk as indicators of quality, depending on
whether the manufacturing process average is equal to the design
specification nominal.

2.3.3 Attribute processes and reject analysis
for six sigma
For attribute processes (those with quality measured in terms of de-
fects in a sample or number defective), an implied Cpk will have to be
calculated in the quality assessment of design and manufacturing. It
is assumed that defects are occurring because of violation of a particu-
lar or a composite specification(s). The composite specification can be
one-sided or two-sided, depending on the interpretation of the defects.
For example, a wire bond defect could be the result of one-sided speci-