Page 90 - Six Sigma for electronics design and manufacturing

The Elements of Six Sigma and Their Determination
the 100 PPM error rate is significant because it is larger than the tar-
get of 3.4 PPM. If a quality team has to report on their progress to-
ward six sigma using 100 PPM current defect rate, then they can
present the following arguments:
1. For two-sided specifications, f(z) = 0.00005 or z = 3.89. If a shift of
±1.5 is assumed, then all of the failures result from one side of
the distribution, whereas the other side is much lower in defects,
and therefore contributes no defects. The design is 3.89 + 1.5 = 5.39
or 5.39 in the classical six sigma definition. 59
2. For one-sided specifications, f(z) = 0.0001 or z = 3.72. If we assume
a shift of ±1.5 , then the design is 3.72 + 1.5 = 5.22 or 5.22
in the classical six sigma definition.
Attribute processes present more difficulty in calculating and visu-
alizing the reject rates; more on that in upcoming chapters.
2.4 Are Manufacturing Processes and Supply Parts
Always Normally Distributed?
A very common question regarding the reject rate calculations is
whether the normal distribution is always applicable in every part
manufacturing or supply case. The answer is a definite no! In some
cases, such as high-accuracy resistors, parts are made, then tested
and segregated according to the measured accuracy, so that a distri-
bution of supply of low-accuracy parts would look like a disjointed
normal curve with the middle of the curve missing. For high-accuracy
parts, the distribution is narrow with no trailing edges. Obviously,
neither set of parts are normally distributed, since the manufacturing
processes have been interfered with.
Several tools are available to design and manufacturing teams to
manage this condition. Verifying that the manufacturing process or
the supply parts are normally distributed can be accomplished by us-
ing simple graphical techniques and, if needed, more complex statisti-
cal analysis. If the distribution is not normal, parts can be described in
other statistical distributions. Then their data can be transformed into
an equivalent normal distribution. All the six sigma calculations can be
made, then data can be transformed back to the original distribution.

2.4.1 Quick visual check for normality
Using graph paper, spreadsheets, or statistically based software,
measurement data from randomly selected samples of parts can be
quickly checked for normality as follows: