**The term
Six Sigma**
Sigma (the lower-case Greek
letter σ) is used to represent standard
deviation (a measure of variation) of a
population (lower-case 's', is an estimate, based
on a sample). The term "six sigma
process" comes from the notion that if one
has six standard deviations between the mean of a
process and the nearest specification limit,
there will be practically no items that fail to
meet the specifications. This is the basis of the
Process Capability Study, often used by quality
professionals. The term "Six Sigma" has
its roots in this tool, rather than in simple
process standard deviation, which is also
measured in sigmas. Criticism of the tool itself,
and the way that the term was derived from the
tool, often sparks criticism of Six Sigma.
The widely accepted definition of
a six sigma process is one that produces 3.4
defective parts per million opportunities (DPMO).
A process that is normally distributed will have
3.4 parts per million beyond a point that is 4.5
standard deviations above or below the mean
(one-sided Capability Study). This implies that
3.4 DPMO corresponds to 4.5 sigmas, not six as
the process name would imply. This can be
confirmed by running on QuikSigma or Minitab a
Capability Study on data with a mean of 0, a
standard deviation of 1, and an upper
specification limit of 4.5. The 1.5 sigmas added
to the name Six Sigma are arbitrary and they are
called "1.5 sigma shift" (SBTI Black
Belt material, ca 1998). Dr. Donald Wheeler
dismisses the 1.5 sigma shift as
"goofy".
In a Capability Study, sigma
refers to the number of standard deviations
between the process mean and the nearest
specification limit, rather than the standard
deviation of the process, which is also measured
in "sigmas". As process standard
deviation goes up, or the mean of the process
moves away from the center of the tolerance, the
Process Capability sigma number goes down,
because fewer standard deviations will then fit
between the mean and the nearest specification
limit (see Cpk Index). The notion that, in the
long term, processes usually do not perform as
well as they do in the short term is correct.
That requires that Process Capability sigma based
on long term data is less than or equal to an
estimate based on short term sigma. However, the
original use of the 1.5 sigma shift is as shown
above, and implicitly assumes the opposite.
As sample size increases, the
error in the estimate of standard deviation
converges much more slowly than the estimate of
the mean (see confidence interval). Even with a
few dozen samples, the estimate of standard
deviation often drags an alarming amount of
uncertainty into the Capability Study
calculations. It follows that estimates of defect
rates can be very greatly influenced by
uncertainty in the estimate of standard
deviation, and that the defective parts per
million estimates produced by Capability Studies
often ought not to be taken too literally.
Estimates for the number of
defective parts per million produced also depends
on knowing something about the shape of the
distribution from which the samples are drawn.
Unfortunately, there are no means for proving
that data belong to any particular distribution.
One can only assume normality, based on finding
no evidence to the contrary. Estimating defective
parts per million down into the 100s or 10s of
units based on such an assumption is wishful
thinking, since actual defects are often
deviations from normality, which have been
assumed not to exist.
While the particulars of the
methodology were originally formulated by Bill
Smith at Motorola in 1986, Six Sigma was heavily
inspired by six preceding decades of quality
improvement methodologies such as quality
control, TQM, and Zero Defects. Like its
predecessors, Six Sigma asserts the following:
·Continuous efforts to reduce
variation in process outputs is key to business
success
·Manufacturing and business processes can be
measured, analyzed, improved and controlled
·Succeeding at achieving sustained quality
improvement requires commitment from the entire
organization, particularly from top-level
management
In addition to Motorola,
companies that adopted Six Sigma methodologies
early on and continue to practice it today
include Honeywell International (previously known
as Allied Signal) and General Electric
(introduced by Jack Welch).
Recently some practitioners have
used the TRIZ methodology for problem solving and
product design as part of a Six sigma approach
**Origin**
Bill Smith did not really
"invent" Six Sigma in the 1980s;
rather, he applied methodologies that had been
available since the 1920s developed by luminaries
like Shewhart, Deming, Juran, Ishikawa, Ohno,
Shingo, Taguchi and Shainin. All tools used in
Six Sigma programs are actually a subset of the
Quality Engineering discipline and can be
considered a part of the ASQ Certified Quality
Engineer body of knowledge. The goal of Six
Sigma, then, is to use the old tools in concert,
for a greater effect than a sum-of-parts
approach.
The use of "Black Belts" as itinerant
change agents is controversial as it has created
a cottage industry of training and certification.
This relieves management of accountability for
change; pre-Six Sigma implementations,
exemplified by the Toyota Production System and
Japan's industrial ascension, simply used the
technical talent at hand—Design, Manufacturing
and Quality Engineers, Toolmakers, Maintenance
and Production workers—to optimize the
processes.
**Methodology**
Six Sigma methodology consists of
the following five (5) steps:
- Define the process improvement goals that
are consistent with customer demands and
enterprise strategy.
- Measure the current process and collect
relevant data for future comparison.
- Analyze to verify relationship and
causality of factors. Determine what the
relationship is, and attempt to ensure
that all factors have been considered.
- Improve or optimize the process based
upon the analysis using techniques like
Design of Experiments.
- Control to ensure that any variances are
corrected before they result in defects.
Set up pilot runs to establish process
capability, transition to production and
thereafter continuously measure the
process and institute control mechanisms
**The ±1.5 Sigma Drift**
The ±1.5σ drift is the drift of
a process mean, which is assumed to occur in all
processes. If a product is manufactured to a
target of 100 mm using a process capable of
delivering σ = 1 mm performance, over time a ±1.5σ
drift may cause the long term process mean to
range from 98.5 to 101.5 mm. This could be of
significance to customers.
The ±1.5σ shift was introduced
by Mikel Harry. Harry referred to a paper about
tolerancing, the overall error in an assembly is
affected by the errors in components, written in
1975 by Evans, "Statistical Tolerancing: The
State of the Art. Part 3. Shifts and
Drifts". Evans refers to a paper by Bender
in 1962, "Benderizing Tolerances – A
Simple Practical Probability Method for Handling
Tolerances for Limit Stack Ups". He looked
at the classical situation with a stack of disks
and how the overall error in the size of the
stack, relates to errors in the individual disks.
Based on "probability, approximations and
experience", Bender suggests:
A run chart depicting a +1.5σ
drift in a 6σ process. USL and LSL are the upper
and lower specification limits and UNL and LNL
are the upper and lower natural tolerance limits.
Harry then took this a step
further. Supposing that there is a process in
which 5 samples are taken every half hour and
plotted on a control chart, Harry considered the
"instantaneous" initial 5 samples as
being "short term" (Harry's n=5) and
the samples throughout the day as being
"long term" (Harry's g=50 points). Due
to the random variation in the first 5 points,
the mean of the initial sample is different from
the overall mean. Harry derived a relationship
between the short term and long term capability,
using the equation above, to produce a capability
shift or "Z shift" of 1.5. Over time,
the original meaning of "short term"
and "long term" has been changed to
result in "long term" drifting means.
Harry has clung tenaciously to
the "1.5" but over the years, its
derivation has been modified. In a recent note
from Harry, "We employed the value of 1.5
since no other empirical information was
available at the time of reporting." In
other words, 1.5 has now become an empirical
rather than theoretical value. Harry further
softened this by stating "... the 1.5
constant would not be needed as an
approximation". Interestingly, 1.5σ is
exactly one half of the commonly accepted natural
tolerance limits of 3σ.
Despite this, industry is
resigned to the belief that it is impossible to
keep processes on target and that process means
will inevitably drift by ±1.5σ. In other words,
if a process has a target value of 0.0,
specification limits at 6σ, and natural
tolerance limits of ±3σ, over the long term the
mean may drift to +1.5 (or -1.5).
In truth, any process where the
mean changes by 1.5σ, or any other statistically
significant amount, is not in statistical
control. Such a change can often be detected by a
trend on a control chart. A process that is not
in control is not predictable. It may begin to
produce defects, no matter where specification
limits have been set. |