Nontechnical
Definition
Of Six Sigma
Six
Sigma
management is the relentless and rigorous pursuit of
the reduction of variation in all critical processes
to achieve continuous and breakthrough improvements
that impact the bottomline and / or topline of the
organization and increase customer satisfaction.
Another common definition of Six Sigma management is
that it is an organizational initiative designed to
create manufacturing, service and administrative
processes that produce a high rate of sustained
improvement in both defect reduction and cycle time
(e.g., when Motorola began their effort the rate
they chose was a 10fold reduction in defects in two
years along with a 50% reduction in cycle). For
example, a bank takes 60 days on average to process
a loan with a 10% rework rate in 2000.
In a “Six Sigma” organization, the bank
should take no longer than 30 days on average to
process a loan with a 1% error rate in 2002, and no
more than 15 days on average to process a loan with
a 0.10% error rate by 2004.
Clearly, this requires a dramatically
improved/innovated loan process.

Technical
Definition of “Six Sigma” Management
The
Normal Distribution.
The
term “Six Sigma” is derived from the normal
distribution used in statistics.
Many observable phenomena can be graphically
represented as a bellshaped curve or a normal
distribution. Figure 1 shows a theoretical normal
distribution (smooth blue line) with a mean (center of
distribution) of zero and a standard deviation (spread
of distribution) of one, as well as a random sample of
10,000 normally distributed data points (histogram)
with a mean of zero and a standard deviation of one.
Figure
1: Normal Distribution with Mean (µ =
0)
and Standard Deviation
(σ
=1)
In a normal distribution, the interval created by the
mean plus or minus 2 standard deviations contains
95.44% of the data points, or 45,600 data points per
million are outside of the area created by the mean
plus or minus 2 standard deviations [(1.00  .9544 =
.0456) x 1,000,000 = 45,600].
In a normal distribution the interval created
by the mean plus or minus 3 standard deviations
contains 99.73% of the data, or 2, 700 data points per
million are outside of the area created by the mean
plus or minus 3 standard deviations [(1.00  .9973 =
.0027) x 1,000,000 = 2,700].
In a normal distribution the interval created
by the mean plus or minus 6 standard deviations
contains 99.9999998% of the data, or 2 data points per
billion data points outside of the area created by the
mean plus or minus 6 standard deviations.

Relationship
Between Voice of the Process and Voice of the
Customer. Six
Sigma promotes the idea that the distribution of
output for a stable normally distributed process
(Voice of the Process) should be designed to takeup
no more than half of the tolerance allowed by the
specification limits (Voice of the Customer).
Although processes may be designed to be at
their best, it is assumed that over time the
variation may increase in the processes.
This increase in variation may be due to
small variation with process inputs, the way the
process is monitored, changing conditions, etc.
The increase in process variation is often
assumed for sake of descriptive simplicity to be
similar to temporary shifts in the underlying
process mean. The
increase in process variation has been shown in
practice to be equivalent to an average shift of 1.5
standard deviations in the mean of the originally
designed and monitored process.
If a process is originally designed to be
twice as good as a customer demands (i.e., the
specifications representing the customer
requirements are 6 standard deviations from the
process target), then even with a shift in the
distribution of output the customer
demands are likely to be met.
In fact, even if the process shifted off
target by 1.5 standard deviations there are 4.5
standard deviations between the process mean (µ
+ 1.50σ)
and closest specification
(µ + 6.00σ).
This results in at worst 3.4 defects per million
opportunities (DPMO) at the time the process has
shifted or the variation has increased to have
similar impact as a 1.5 standard deviation shift.
Figure
4: Six Sigma Process with a 0.0 Shift in the Mean
Six
Sigma Process with 1.5 Sigma Shift in the Mean.
Figure 5 shows the same scenario as figure 4, but the
process average shifts by 1.5 standard deviations (the
process average is shifted down or up by 1.5 standard
deviations [or 0.75 days = 1.5 x 0.5 days] from 7.0
days to 6.25 days or 7.75 days) over time.
The 1.5 standard deviation shift in the mean
results in 3.4 defects per million opportunities, or
one early or late monthly report in 24,510 years
[(1/.0000034/12].
This is the definition of 6 Sigma level of
quality.
Figure
5: “Six Sigma” Process with 1.5 Sigma Shift in the
Mean
The
difference between a 3 sigma process (66,807 defects
per million opportunities) and a 6 sigma process (3.4
defects per million opportunities) can be seen in a
service with 20 component steps.
If each of the 20 component steps has a quality
level of 66,807 defects per million opportunities,
assuming each step does not allow rework, then the
likelihood of a defect at each step is 0.066807
(66,807/1,000,000).
By subtraction, the likelihood of a defect free
step is 0.933193 (1.0  0.066807).
Consequently, the likelihood of
delivering a defect free final service is 25.08
percent.
This is computed by multiplying 0.933193 by
itself 20 times ([1.0  0.066807]^{20 }=
0.2508 = 25.08%).
However, if each of the 20 component parts has
a quality level of 3.4 defects per million
opportunities (0.0000034), then the likelihood of
delivering a defect free final service is 99.99932%
([1.0  0.0000034]^{20} = 0.99999966^{20 }=
0.9999932 = 99.99932%).
A 3 sigma process generates 25.08% defectfree
services, while a 6 sigma process generates 99.99932%
defectfree services.
The difference between the three sigma process
and the “Six Sigma” process is dramatic enough to
certainly believe that 6 Sigma level of performance
matters, especially with more complex processes with a
greater number of steps or activities.
