What Is Six Sigma and the 1.5
shift?
The Original Concepts And Theories
To quote a Motorola hand out from
about 1987 ...
'The performance
of a product is determined by how much margin exists between the
design requirement of its characteristics (and those of its
parts/steps), and the actual value of those characteristics. These
characteristics are produced by processes in the factory, and at the
suppliers.
Each process
attempts to reproduce its characteristics identically from unit to
unit, but within each process some variation occurs. For more
processes, such as those which use real time feedback to control
outcome, the variation is
quite small, and for others it may be quite large.
A variation of
the process is measured in Std.
Dev, (Sigma) from the Mean.
The normal variation, defined as process width, is +/-3 Sigma about
the mean.
Approximately
2700 parts per million parts/steps will fall outside the normal
variation of +/- 3 Sigma. (see
chart #2) This, by
itself, does not appear disconcerting. However, when we build a
product containing 1200 parts/steps, we can expect 3.24 defects per
unit (1200 x .0027), on average. This would result in a rolled yield
of less than 4%, which means fewer than 4 units out of every 100 would
go through the entire manufacturing process without a defect. (see
chart #3)Thus,
we can see that for a product to be built virtually defect-free, it
must be designed to accept characteristics which are significantly
more than +/- 3 sigma away from the mean.
It can be shown
that a design which can accept TWICE THE NORMAL VARIATION of
the process, or +/- 6 sigma, can be expected to have no more than 3.4
parts per million defective for each characteristic, even if the
process mean were to shift by as much as +/- 1.5 sigma (see
chart #2) In the same
case of a product containing 1200 parts/steps, we would now expect
only only 0.0041 defects per unit (1200 x 0.0000034). This would mean
that 996 units out of 1000 would go through the entire manufacturing
process without a defect. To quantify this, Capability Index (Cp) is
used; where:
|
Design
Specification Width |
| Capability Index Cp = |
|
|
Process Width |
A design
specification width of +/- 6 Sigma and a process width of +/- 3 Sigma
yields a Cp of 12/6 = 2. However, as shown in (see
chart #4), the process
mean can shift. When the process mean is shifted with respect to
design mean, the Capability Index is adjusted with a factor k, and
becomes Cpk. Cpk = Cp(1-k), where:
|
Process Shift |
| k Factor = |
|
|
Design
Specification Width |
The k factor for
a +/- 6 Sigma design with a 1.5 Sigma process shift ...
1.5/(12/2) or
1.5/6 = 0.25
and the
Cpk = 2(1-
0.25)=1.5
...'
Also see RTY
- Rolled throughput yield.
NOTE: Our
software always calculates sigma. It only estimates sigma when
calculating control limits for the X Bar and Range control
charts.
These concepts are what our
software was designed around. And
our software allows you to grow from 3 to 6 sigma in .5 sigma steps.
You need to see how to Interpret
the Histogram and Capability Indices and
how Cpk
compares to PPM in order to
understand what Six Sigma is all about. And remember, Six Sigma
depends on one's process being in statistical control according to WECO,
(Western Electric Company), rules.
