Page 115 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
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Given the LSL = 16 MH, the specification nominal N is 16 + 18 = 34
MH. Therefore, Cp = 2; Cpk = 1.5; reject rate from previous tables
(±1.5 shift) = 3.4 PPM.
Assuming that the shift is toward the lower specification, then the
process average could be +4.5 from the LSL or –1.5 from the nom-
inal: 34 – 1.5 · 3 = 29.5 MH; or 16 + 4.5 · 3 = 29.5 MH.
The R chart remains the same as Example 3.4a, since the process
variability did not change. If the X chart is centered on X = 29.5,
then LCL x = 29.5 – 3 s = 26.5 MH and UCL x = 32.5 MH.
Example 3.2c – –
A new contract was written with a supplier to deliver parts with the
following stipulation: Cpk = 0.85 and part specifications = 10 ± 2 mils.
The supplier found that part process average was 11 mils. The suppli-
er kept control of their process by using a variable control chart with
sample size n = 4. Calculate the Cp and the variable chart limits.
Example 3.2c solution
Cpk is the minimum of [(USL – )/3 ] or [( – LSL)/3 ]
Cpk = Min (12 – 11)/3 vs. (11 – 8)/3
The first alternative is chosen because it is the minimum of the two:
Cpk = 0.85 = (USL – )/3 = 1/3
= 0.392 and s = / n = 0.196
Cp = ±SL/±3 = ±2/(3 · 0.392) = 1.7
z = (SL – )/
z 2 = 1/0.392 = 2.55; f(–z 2 ) = 0.0054
z 1 = 3/0.392 = 7.65; f(–z 1 ) = 0
Total reject rate = 0.0054 = 5400 PPM
UCL x = process average + 3 s = 11 + 3 · 0.196 = 11.588 and LCL x =
11 – 3 · 0.196 = 10.412
R = d 2 · = 2.059 · 0.392 = 0.807
UCL R = 2.28 · 0.807 = 0.84
LCL R = 0

3.3 Attribute Charts and Their Relationship with
Six Sigma
Attribute charts directly measure the rejects in the production opera-
tion, as opposed to measuring a particular value of the quality charac-