sigma range
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 This topic has 21 replies, 9 voices, and was last updated 18 years, 2 months ago by John Hickey.

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September 23, 2003 at 6:48 pm #33389
When a process has achieved 6 sigma, are there 3 or 6 sigmas on either side of the mean? IE – are there 6 or 12 sigmas between the lower limit and the upper limit?
0September 23, 2003 at 6:59 pm #90202There are 2 * 6 = 12 (actually 2 * 4.5 = 9, see 1.5 sigma shift).
0September 23, 2003 at 7:51 pm #90203
DogFoodParticipant@DogFood Include @DogFood in your post and this person will
be notified via email.9 sigma long term and 12 sigma short term
0September 24, 2003 at 4:13 am #90221
Dr. ScottParticipant@Dr.Scott Include @Dr.Scott in your post and this person will
be notified via email.Lynn,
Normally I would not respond to such a simple question (no offense intended). But the responses prompted me to do so.
There are at least 6 sigma between the mean and the spec limits on either side of a six sigma process.
There is not such animal as long or short term or a 1.5 sigma shift. This is only a cruch for those unable to control their processes once improved.
Dr. Scott0September 24, 2003 at 5:11 am #90222
Tony BurnsMember@TonyBurns Include @TonyBurns in your post and this person will
be notified via email.Dr Scott,
You said: “There is not such animal as long or short term or a 1.5 sigma shift.”
There is indeed such an animal. He was a horse called “Clever Hans” and he was part of what is known as the Pygmalion Effect or the selffulfilling prophesy. If you expect the mean to shift, it eventually will if nothing is done to manage the process … and of course it won’t find any reason to stop at 1.5 sigma. That is one of the reason for quality programs, to keep processes on target. Dr Scott, it’s good to see someone being able to see through the nonsense.
Six sigma programs can bring great benefits to companies, because at last there is commitment to quality from senior management. At the same time, it is important to view all information critically.
Dr Tony Burns
[email protected]0September 24, 2003 at 8:17 pm #90243
Dr. ScottParticipant@Dr.Scott Include @Dr.Scott in your post and this person will
be notified via email.Dr. Burns,
I have toyed with the idea of creating a new program called “4 Sigma”, only because “4.5 Sigma” doesn’t have much of a ring to it.
However, my marketing folks tell me I might have to reduce my price by a third since I am delivering two fewer sigma.
Just a little humor,
Dr. Scott0September 25, 2003 at 2:09 am #90251
John HickeyParticipant@JohnHickey Include @JohnHickey in your post and this person will
be notified via email.Dr. Scott
Re: The 1.5 Sigma Shift
Amen!!
John Hickey0September 25, 2003 at 2:41 pm #90275
Reigle StewartParticipant@ReigleStewart Include @ReigleStewart in your post and this person will
be notified via email.Dr. Scott and John HickeyIt was said in an earlier post There is not such
animal as long or short term or a 1.5 sigma
shift. This is only a crutch for those unable to
control their processes once improved.
Consider this We frequently encounter
situations where we must audit or verify the
capability of a process with a highly limited and
intermittent sample. In this kind of situation the
sample may be limited to about 4 < n < 6
consequtive pieces. For a realitively high
volume process the 4 < n < 6 consequtive
pieces would be gathered within a very short
period of time but we know that not all
sources of random variation have been
captured in such a limited window so we
continue to take sets of samples over time.
Typically for a capability study we sample 25 < g
< 100 groups or sets. Several noted authors
have recommended this sampling range for a
capability study. So it is common to see n=5
and g=50 for ng = 250 observations. We also
know that a process has many sources of
random error. It takes time for all of these
sources to become known. So we have short
term random error and longterm random error.
After an extended period of sampling we can
use oneway anova to compute the within set
variation and the total variation. This gives us
the sums of squares within sets (shortterm)
and the total sums of squares (longterm). In
my experience of conducting process capability
studies the short and long term sums of
squares are never equal SS long term is
always larger than SS short term. The
difference is due to the variation that occurs
between sets This type of variation (SS
between sets) is computed as sum(Xbar.set
Xdouble bar)^2 or just SST SSW = SSB. If
SSB > 0, then the process has natural shift and
drift due to random sources of variation. If the
SSB term gets too big, the difference is no
longer due to random causes alone. At the
threshold value of the alternate hypothesis Ha
for a typical sampling plan and alpha, you will
find the equivalent shift for such a difference in
variation to be about 1.5 sigma (due to random
effects alone). So we can see that with limited
sampling, we can expect some shift and drift
due to expected random sampling error. So you
see it is possible (and likely) to have shortterm
and longterm variation when verifying the
capability of a process. These calculations
have been worked out by Dr. Mikel Harry when
he designed the MiniTab Six Sigma modules as
being used by MiniTab to this day. It was Dr.
Terry Zimmer that programmed the modules
when he worked for MiniTab. These modules
have been thorougly tested and have been
availible for around 6 years now. The modules
make all of the necessary calculations I have
just discussed and are annotated in the help
menues.Regards,Reigle Stewart0September 25, 2003 at 5:27 pm #90288Poor control methods do not justify the assumptions you are making.
0September 25, 2003 at 11:05 pm #90325
Tony BurnsMember@TonyBurns Include @TonyBurns in your post and this person will
be notified via email.Reigle,Your note focusses on the differences between “short term” and “long term” variances:”…After an extended period of sampling we can use oneway anova to compute the within set variation and the total variation. This gives us the sums of squares within sets (shortterm) and the total sums of squares (longterm). …”This is precisely what the range chart of a control chart does ! Range control charts compare the variation within groups (short term) to the variation between all the groups (long term). The +/ 1.5 theory confuses the differences in variances with means. I suggest reading Wheeler “Advanced Topics in SPC” Chapters 4 and 6 for a detailed understanding.It would be extraordinary if we could do some theoretical calculations that would force our process means to drift, despite our best efforts to keep processes on target with minimum variation !Dr Tony [email protected]
0September 26, 2003 at 12:41 am #90330
Reigle StewartParticipant@ReigleStewart Include @ReigleStewart in your post and this person will
be notified via email.Dr. Tony Burns:Yes, I have the book you referenced and
frequently use it; however, it has nothing to do
with the discussion I offered concerning the
shift factor. I guess we will just have to agree to
disagree on this point. On another angle, you
kindly stated: “It would be extraordinary if we
could do some theoretical calculations that
would force our process means to drift, despite
our best efforts to keep processes on target
with minimum variation !” I do believe you mean
“to not drift” rather than “to drift,” or were you just
adding some humor?Reigle StewartThe OldBaldFatGuyReigle Stewart0September 26, 2003 at 3:41 am #90334
Tony BurnsMember@TonyBurns Include @TonyBurns in your post and this person will
be notified via email.Reigle,
It’s great to see that you follow the Wheeler “bible”. It is a wonderful book that everyone on the forum should read and study. The chapters I referred to discuss control charts in great detail and the difference between “short term” variation within groups and “long term” variation. For Wheeler’s view on six sigma, you have to go to page 202:
” Failure to operate a process on target with minimum variance will inevitably result in dramatic increases in the Average Loss Per Unit of Production. Such losses may be severe and are always unnecessary.
…SixSigma Quality and all other specificationbased nostrums miss this point. … The sooner one wakes up to this fact of life, the sooner one can begin to compete.”
And in a personal correspondence from him:
“The only antidote to ignorance is education. My most effective antidote is known as Understanding Variation, the Key to Managing Chaos.”
Dr Tony Burns
[email protected]0September 26, 2003 at 1:56 pm #90349
Reigle StewartParticipant@ReigleStewart Include @ReigleStewart in your post and this person will
be notified via email.Dr. Tony Burns:Thank you for the reference to page 202. My
humble opinion is that Wheeler missed the
point about six sigma. I guess its a matter of
perspective. Without question, when you look at
processing for six sigma (PFSS) the task is to
minimize variations about the mean of a
process and to keep the mean on target over
time for those parameters that are truly critical
but how do you (as a process engineer)
know which design features are critical? But
when you look at designing for six sigma
(DFSS) the task is somewhat different. As a 30
year design engineering veteran I can assure
you that my job IS NOT to put processes on
target with minimum variance my job (from
the big picture view) is to configure a product
concept that has form, fit and function (by the
customers edict) and then specify optimal
tolerances for each of those key design features
that are critical to Y, where Y is just about
anything serviceability, reliability,
maintainability, cost, delivery, satisfaction, and
so on and so on. The trick is to find the ones
that are critical to The tolerances I then assign
must be robust to process (and
environmental) variations that I cannot possibly
foresee but know will exist (at some point in
time). I must specify optimal nominal
conditions for all design features (target
values). Guess what? The laws of physics
usually governs the assignment of target values
and tolerances not process engineers
working with control charts. Their control charts
are only as good as the specifications I assign
to the product design. Remember Dr. Burns, it
is possible to EXERT PERFECT STATSTICAL
CONTROL over a product characteristic that
HAS THE WRONG SPECIFICATION. For this
situation defects will be made by the truck
load if spec is wrong no matter how many
control charts you use. What Wheeler says is
true only after the RIGHT design has been
put in place. Putting the RIGHT design in place
requires more than what the good Donald
Wheeler has to offer. For example, a design
engineer can use the 1.5 sigma shift concept to
test how robust his/her design is to process
centering error. By analytical test, the designer
can explore different nominal conditions and
tolerances that maximizes robustness while
concurrently meeting performance
requirements. If the RIGHT combination is
found by diligent engineering methods, the
tolerances of the TRIVAL MANY characteristics
can be greatly widened which then means
we can tolerate the variation and dont need to
even use control charts during production
REMEMBER, WE DONT NEED TO CONTROL
WHAT IS NOT SENSITIVE. We do not need to
Put on target and minimize variation for what is
not sensitive to the design requirements. This
is what causes us to waste so much money
too many design tolerances are way too tight. If
we find the vital few CTQs and properly treat
these during design, then we do not need to
control the trivial many. If we dont need to
control the trival many then we certainly do not
waste our time putting on target and
minimizing variation among the trival many.0September 26, 2003 at 3:24 pm #90351
Dr. ScottParticipant@Dr.Scott Include @Dr.Scott in your post and this person will
be notified via email.Reigle,
You say:“We frequently encounter situations where we must audit or verify the capability of a process with a highly limited and intermittent sample. In this kind of situation the sample may be limited to about 4 < n < 6 consequtive pieces."
First, why would we be “highly limited” in measuring a quality that is critical to either the customer or the process? Based on statements made in your earlier posts I am sure you would agree that if it is critical, it should be measured and controlled. If it is not, it should be ignored.
More important though is the second part of your statement; “In this kind of situation the sample may be limited to about 4 < n < 6 consequtive pieces." Why consecutive pieces?? This is not a correct application of basic sampling procedures. Such procedures suggest that the within subroup variation should represent the natural variation in the process. Consecutive pieces are unlikely (as you point out) to do so. Therefore, consecutive piece sampling would be an improper approach for process control purposes. There ARE times where one WOULD use consecutive sampling, but this is done only in special circumstances, for example where measurement system concerns exist in a destructive test scenario. In such a case, the average of the subroup would be charted using I and mR charts, not Xbar and R.
Bottom line: Sure, if you use improper sampling procedures (i.e., consecutive piece sampling) you would expect more shift and drift than is represented by the within subroup variation. However, to say this is expected to be 1.5 sigma is just a shot in the dark. It might just as likely be .15 sigma or even 15 sigma. Again, proper sampling for control charts dictates that the within subgroup variation (that represented by the Rchart) represent the natural sources of variation in the process.
Dr. Scott0September 26, 2003 at 3:44 pm #90355
Reigle StewartParticipant@ReigleStewart Include @ReigleStewart in your post and this person will
be notified via email.Dr. Scott:The use of destructive sampling often requires
the we use a “highly limited” sample … due to
the economics of testing or other mitgating
circumstances. I do believe that you will find
that “consequtive sampling” is not improper …
that is why sequential proceedures and
sequential tests exist … such as Wald’s
sequential test of the mean and seqential
probability ratio tests (SPRT). Many well known
statistical proceedures are based on sequential
sampling techniques … even certain types of
designed experiments are predicated on
sequential sampling. In the real world it is not
always possible to get a random sample …
especially in continous processes like used the
chemical industry. When typical sample sizes
are used and accepted levels of alpha, it is not
possible to aquire a “.15 sigma or even 15
sigma” shift.Respectfully,Reigle Stewart0September 26, 2003 at 4:46 pm #90363
GabrielParticipant@Gabriel Include @Gabriel in your post and this person will
be notified via email.Haven’t you heard about rational subgroups? It is the recomended sampling strategy in SPC, and cosnsists of taking the parts for each subgroup as close as possible one from the other, so as to have a sample of what the process was doing at one instant.
“Such procedures suggest that the within subroup variation should represent the natural variation in the process”
Waht’s wrong with that? Subgroup variation actually SHULD represent varaition due to common causes only. That’s the key of SPC.0September 26, 2003 at 4:52 pm #90365
Dr. ScottParticipant@Dr.Scott Include @Dr.Scott in your post and this person will
be notified via email.Reigle,
As I said before, I am NOT saying that sequential sampling should never be used. However, it should almost never be used for control charts (again, with very few exceptions one of which I mentioned before). For SPRT or DOE, certainly there might be good reasons for taking consecutive samples (sorry for the mispelling before, my mind works faster than my fingers at times). But again, consecutive samples are generally not appropriate for control chart applications.
With respect to “When typical sample sizes are used and accepted levels of alpha, it is not possible to aquire a “.15 sigma or even 15 sigma” shift.” With all due respect, you are simply mistaken. Consider this example. Two consecutive ounces of a chemical are taken from a 1000 gallon/hr process. The measure is “impurity”. The range of impurity in the first hour’s sample is .00001%, its average is .005%. In hour two, another five consecutive ounces are sampled. Again, the sample range is .00001%, and now the average impurity is .006%. This behavior is repeated for 1000’s of hours with similar results.
To sample this way for a control chart (as you previously proscribed) would result is an estimate of within subgroup sigma of about 0.000009 and between subgroup sigma of about .00033. So in this case the sigma shift as you have described (i.e., between to within) it would actually be about 37 sigma! Similarly, if the averages of the samples were much closer to each other, then the shift could be .37 sigma.
Perhaps we are misunderstanding what each other is saying. It wouldn’t be our first time (humor).
Good to hear from you again,
Dr. Scott
0September 26, 2003 at 6:15 pm #90369
Dr. ScottParticipant@Dr.Scott Include @Dr.Scott in your post and this person will
be notified via email.Gabriel,
Yes, I have heard of rational subgroups. One of the properties of a rational subgroup is that the individual measures within the subgroup be independent. Too often in high volume manufacturing cases, measures of consecutive pieces yield characteristics of autocorrelation, or lack independence. Such was the case in the example I presented.
Dr. Scott0September 26, 2003 at 7:06 pm #90370
Reigle StewartParticipant@ReigleStewart Include @ReigleStewart in your post and this person will
be notified via email.Dr. Scott:I believe we are at a point where a grease board
and some markers would be of huge benefit.
Trying to describe such technical things without
the benefit of drawings is so frustrating. Your
thinking is put forward with great conviction and
I admire that. Your skills and experience is
most impressive. I have no doubt there is
scientific merit to your arguments … we just
need the ability to create drawings and talk in a
highly interacive and graphical manner.
Unfortunately simple textual discussions will
not get us there. Perhaps we will cross paths at
a conference … be able go to a bar with a pad of
paper and pencil and cold beer… then we can
really communicate our ideas, principles, and
practices. Till then, we will do our best with
words. Thank you for your time and effort on the
subject at hand.
The OldBaldFatGuy
Reigle Stewart0September 26, 2003 at 7:19 pm #90371
Dr. ScottParticipant@Dr.Scott Include @Dr.Scott in your post and this person will
be notified via email.Reigle,
Again, I strongly agree with you. Verbal communication via text only is not robust enough to achieve thorough understanding.
And, I am pleased to hear you say “cold beer” rather than the usual response of “A cold beer”. One just wouldn’t be enough.
BTW, what is the next conference of great value in your opinion?
Thanks,
Dr. Scott0September 28, 2003 at 4:08 am #90393
John HickeyParticipant@JohnHickey Include @JohnHickey in your post and this person will
be notified via email.Dr. Scott
Re: SPRT Sequential Sampling and it’s uses
Be advised that Sequential Sampling is not strictly limited to it’s economic applications as implied in your recent post to Reigle Steward. Group Sampling is allowed and it has the effect of lowering the typeI/II errors of the test. Also, random sampling throughout the process is allowed. I.e aside from sampling savings, the difference between say a Binomial Attribute Sequential Sampling Plan and an old MILSTD105D XF2 Plan results from the fixed sampling of the former as opposed to the variable sampling of the latter which is unknown beforehand. The usual procedure in this case is to estimate the samples needed from the test form computed Average Sample Numbers(ASN )and selected Type I/II errors. Listed fro your perusal at the below Website are some application references:
http://citeseer.nj.nec.com/context/78315/0
Respectively,
John Hickey0September 28, 2003 at 11:34 pm #90407
John HickeyParticipant@JohnHickey Include @JohnHickey in your post and this person will
be notified via email.Dr. Scott:
Typo Correction on my message 33511
Fixed sampling of the latter(MILSTD105) and variable sampling of former (Sequential Sampling)
Sorry
John Hickey
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