Page 85 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
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2.3.1 Relationship between z and Cpk
Since the formulas for z and Cpk are somewhat similar, the two can
be derived from each other, especially if the process is centered (no av-
erage shift from nominal):
Cpk = [min of {z 1 , z 2 }]/3
SL
(2.13)
Cpk = ±
when process is centered (z 1 = z 2 )
= z/3;
3
2.3.2 Example calculations of defects and Cpk (2.12)
Example 2.1
A check on parts made by a factory indicated that they are made with
normal distribution with average = 12.62 and standard deviation of
2.156.
a. What is the probability that parts of the following lengths (L) will
be made in that factory: L > 18 , L < 8 , and 10
L
12 ?
b. If the specifications for the length of the part were 12.62 ± 3 , and
the factory made parts with a = 12.62 and = 2.156, what are Cp
and Cpk and the predicted defect or reject rate (RR)? Repeat the
above if the process average is shifted with respect to specification
nominal by 1 to the left and 0.75 to the right.
c. What should the specifications be if the factory decided on the fol-
lowing: Cp = 1, Cp = 1.5, and Cp = 2 (six sigma), assuming the av-
erage is 12.62 and the = 2.156?
Solutions to Example 2.1
a. From the standard normal distribution (Table 2.3), the area under
the curve is used to determine the answers:
L > 18 : z 2 = (18 – 12.62)/2.156 = 2.5
f(z 2 ) = f(–2.5) = 0.0062 or 0.62% or 6,200 PPM
L < 8
z 1 = (8 – 12.62)/2.156 = –2.14
f(z 1 ) = f(–2.14) = 0.0162 or 1.62% or 16,200 PPM
10
L
12
z 2 = (12 – 12.62)/2.156 = –0.29
z 1 = (10 – 12.62)/2.156 = –1.22
f(z 2 ) – f(z 1 ) = f(–0.29) – f(–1.22) = 0.3859 – 0.1112 = 0.2747

or 27.47% or 274,700 PPM