Home › Forums › Old Forums › General › No. of Distinct Categories
This topic contains 56 replies, has 22 voices, and was last updated by Darth 9 years, 11 months ago.
How do the number of distinct categories are calculated…Anyone having access to this. All I know about this is that the measurement system must divide a process in more than 5 distinct categories but the question is – Why only 5 ?
Hope to get answers in quick time…
Thanks in advance
MKS,
Here is a simple anology for you. (Please note this is my explanation and I’ve not researched any references because I’m don’t claim to be the originator, or even correct. I’ll leave that to you, and others to decide. Make it what you will.
The argument is as follows:
If a measurement system has confidence intervals of +/- 3s, or 6s, then it follows that:
The resolving power of two means is just (2X6)s = 12s
The resolving power of a target is (3X6)s = 18s
[One distribution centred on the target and one each side]
The resolving power of a tolerance window is (5X6) = 30s.
[Two targets with a shared central distribution]
It is much easier to understand if you draw the distributions on a bit of paper. ( I don’t know how to upload drawings!]
Regards,
Andy
I am not sure if the first part of your post was a question or not. If you want to know how NDC is calculated:
(Std Dev for parts/Std dev measurement)*1.41
MKS,
The number of Distinct Categories, (also called the Discrimination Ratio), is the number distinct groups the measurement system can discriminate within the total observed product or process variation. It provides you a reference of how sensitive the measurement system is at detecting changes in the process.
For example, if the number of distinct categories is equal to 2, then your measurement system has the capability of only being able to discriminate between high and low results within the observed variation. With a discrimination ratio of 3 you can use your measurement system to categorize three discrete levels within the observed product or process variation.
The full expression for this estimate is:
many drop the “-1″ from the expression to yield the simplified expression used by AIAG and others with some incurred error.
As an example, using your version of Minitab open up the worksheet called “Gageaiag.MTW”. Perform a crossed Gage R&R to yield the following values:
Total Process Variance = 1.17788Total Gage R&R Variance = 0.09143Calculate the number of Distinct Categories as follows:
Using the Gageaiag.MTW, and working with Minitab version 13 you will obtain 5 distinct categories, but if you are working with Minitab version 14 you will obtain 4 distinct categories. Why the difference? After some time with the Minitab development folks I found out that Minitab version 14 truncates the decimal value instead of rounding it up like Mintab version 13. Minitab version 13 provides a more unbiased estimate of distinct categories. Care should be taken in using the Distinct Categories value in Minitab version 14.
As a final note, AIAG recommends 5 or greater for the number of Distinct Categories. In fact, there are other references that suggest the a value of 4 is reasonable for most applications. Any value of Distinct Categories below 4 is considered unacceptable discrimination.
Cheers,
Ken
MKS,
Let us suppose u have a measuring instrument which has least count of 1 and u want to measure any sample with spec 1.5+/-0.5mm, then what will ur instrument measure….1mm or 2 mm.So u will jave only two readings ie 1and/or 2. Now consider instrument with Least count of 0.1mm then it will measure same as 1.0,1,1.2,1.3,1.4…….to 2.0.Now consider instrument with 0.01mm LC,now it will measure as 1.42 or 1.54 and so on.To sum up, more the capturing of variation by the instrument more will be the no.of distinct categories.Or more the distinct categories, higher are the chances of instrument captuirng factors of variations thru such measurements.
MKS,
Well, my attempt at adding equational graphics seems to have failed. So, I add below the two equations that were stripped out of my earlier posting:
equation 1:
Discrim Ratio = root[(2*Total Variance / GR&R Variance)-1]
equation 2:
Dr = root[(2(1.17788) / 0.09143))-1] = 4.98 or approx. 5
Ken
Ken,
You state you use science and logic to provide explantations, yet your explanation appears to explain nothing. The original question was why 5 distinct categories and once again you’ve appeared to just regurgitate something you’ve read.
This is not real learning or understanding. What does your defference to a discrimination ratio explain? Why do I have to discriminate between five categories?
How do you explain the Gage R&R of a single target, such as a minimum standard? Do you accept there is a problem?
How many distinct categories do you need for a single target?
From my reading of your post it is five; but this is incorrect. To achieve a 95% confidence of a correct decision I only need three categories – reject, marginal, acceptable. Of course, I use the term marginal because these are the reference standards that only achieve a P(CD) = 50%. In other words we only agree with the customer 50% of the time. What could be more simple than that?
Now if I want to discriminate between two targets – a minimum quality standard and a maximum quality standard (unlikely) then I do need five categories. Four is definitely incorrect!
Why is a single target relevent? Because most inspections are conducted to determine if the process meets a minimum standard – not a tolerance window! Therefore, five is incorrect! (Note: This argument is based on reasoning and not on references. If you don’t agree … why not try to find a contradiction, instead of another incorrect reference.)
How do I know – from my own experience! I don’t need to perform a literature survey to see if anyone else came up with the same approach because I’m not claiming to be an originator, or even an inventor. I only need to be successful.
How do I know my claim works, because I’ve applied it to a wide range of applications, which has included setting up libraries of reference inspection standards, training, databases of digital images, and achieving 100% out of box quality in Japan over a period of six months.
My explanation left a ‘Tiger in the Mountain’ and I find it interesting that no one bothered to seek further clarification – not even the original poster. How does it explain NDC = 5? I’ll leave that to you to figure out!
Andy
Ken, it was just released new Minitab upgrade 14.20 version. Did you checked if there are any new modifcation on the matter ? Just to keep you aligned with “standard & reference”.
Rgs, peppe
Basically today’s sick sigma training is telling you how to memorize formulas and never explain the logic behind 5:1 ratio.
I had explained this similair concept a year ago for GRR %.
You plug in 5:1 ratio into the root-mean-square formula will reveal that 98% of total tolerance would come from the product and another 2% from the instrument itself. Increase to 10:1 does not improve precision very much but costing more money to attain a little improvement.
The answer is not the AIAG manul says so. There is a rational logic behind 5:1.
Basically today’s sick sigma training is telling you how to memorize formulas and never explain the logic behind 5:1 ratio.
I had explained this similair concept a year ago for GRR %.
You plug in 5:1 ratio into the root-mean-square formula will reveal that 98% of total tolerance would come from the product and another 2% from the instrument itself. Increase to 10:1 does not improve precision very much but costing more money to attain a little improvement.
The answer is not the AIAG manul says so. There is a rational logic behind 5:1.
Peppe,Minitab v14.20, the latest version still truncate the resulting Distinct Categories estimate.Ken
Andy,
Gee, it seems there is nothing I can post on this forum that you don’t find some fault with these days! What’s really getting your goat? In my last posting on this thread, I tried not to include any specific reference callouts, and still you’re not happy. Hmm… So, you think I sit here regurgitating stuff, and don’t answer the questions.
Let’s see.. What do you provide? Here’s your answer to MKS, with a few of my comments added for spice:
The argument is as follows:
If a measurement system has confidence intervals of +/- 3s, or 6s, then it follows that: (Andy, you refer here to confidence intervals, but in fact the correct term is natural process or tolerance intervals–the two are not the same, confidence intervals are used for estimates not for systems–tolerance intervals are ranges for individual values given the assumption of a particular distribution. Therefore, this statement does not make any sense. This first premise in your logical construction is either inaccurate, incomplete, or incorrect. I don’t know which, because I haven’t a clue what you’re talking about!)
The resolving power of two means is just (2X6)s = 12s (Andy, you use the term resolving power on your second premise. You also refer to two means here. Neither references have anything to do with the fundamental questions posed by MKS. In a measurement system, you’re concerned with how much bias there is between the mean of repeated measures and the reference value, and how much variation exists with repeated measures–generally referred to as gage precision, (Gage R&R evaluations assess the precision of measurement systems)–the greater the variation in repeated measures the greater the imprecision. There is nothing in my previous statement about two means. If you would like to evaluate the measurement system over a range of values in the process, then you would evaluate the linearity of the measurement system. In linearity evaluations I’ve supported in the past working with electronic, chemical, pharmaceutical, and other systems I’ve used a minimum 3-point calibration to evaluate how close the measurement system tracks to the true values over the range of interest. While “0” is sometimes used in linearity evaluations, it’s not always the best due to non-linearity effects in the low value measures-typically with chemical and pharmaceutical measurements. Pepe, I hope I’m adding enough practical stuff to satisfy you! In using the words “resolving power” one could also talk about measurement resolution–which is a fundamental property of the measurement system, and an element in the gage precision. So, where are you going with the arbitrary assignment of standard deviation multiples tied to resolving power? There appears to be some scattered cogent thinking behind the development of these ideas.)
The resolving power of a target is (3X6)s = 18s (I can’t even provide a comment here, because you’ve done such a poor job of developing the basis by which you explain the concept of distinct categories using multiple of standard deviations. I don’t know where the multiple SDs come from… Perhaps you’re developing some relationship based on references to tolerance analysis, but I really don’t know!)
[One distribution centred on the target and one each side]
The resolving power of a tolerance window is (5X6) = 30s.
[Two targets with a shared central distribution]
Andy, your last comments don’t really provide any value to the overall objective, but hey, perhaps I’m missing the point. If you were willing to share with me and others the foundation references that you used to develop your ideas, then we could look it over and talk it through together. Hey, I’m always willing to learn something new and different. I suspect the reason why you did not receive any response to your explanation is because no one understood it–except perhaps Pepe…
OK, did I do any better? Perhaps I’m also lost…
In my original response to MKS, I provided a general definition of distinct categories. Next, I provided a couple of examples of how the estimate “distinct categories” is interpreted with respect to the total process variation. I provided two examples how to interpret distinct categories. I did not include an example for 5 distinct categories, because I would have repeated myself from the example for 3, e.g., the measurement system is able to discriminate 5 levels within the observed product or process variation, ibid. (5-levels is given as the standard for automotive suppliers via AIAG requirements and QS 9000)
I next attempted to answer MKS’s question of how the DC’s are calculated equationally. I provided an exact equation for the calculation based on the Interclass Correlation Coefficient, and yes you’re right, here I refered back to a text to insure I didn’t make a mistake in transposing the equation to the posting. I next tried to draw a connection between the AIAG estimate for DC, and that provided by “faceman” earlier. I closed the discussion point with an observation I found in the newest version of Minitab. Something I expected others would comment on, but only received one comment from your buddy Pepe…
Now, in this posting I’ve reviewed, in reasonable detail, your previous answer online to MKS–which I saw from the start was nonsense. BTW, I choose not to make a direct comment to your answer, because I know how sensitive you are to comments from anyone who has some facts. Next in this posting, I diagramed my answer to MKS to assess your recent comments and concerns.
You know Andy, I think that I covered the bases. I was hoping you would come back with a few useful comments in hopes of promoting a formative discussion. But, alas this interactive discussion activity with me still remains a sensitive issue for you despite my efforts to avoid your ire.
I’m sorry good buddy. I don’t know know the source of your problem(s). But, I’m certain of thing–it’s not me. Try looking inward. But, most importantly–try to mellow out a bit! This stuff is only for fun anyway, right?
Your fellow shipmate,
Ken
Ken,
Well done … you’ve provided a much better rebuttle this time. I was right to have confidence in you. As someone else pointed out; it is not much of a discussion when a person uses the arguement it is so because I told you so; or more accurately in your case … because it says so in a textbook.
Unfortunately, you seemed to have missed the point again … because you still didn’t get the right answer!
What’s the difference between ‘resolving power’ and resolution? Have you not worked with engineers or physicists? I believe I was right in refering to confidence limits of the mean. You on the other hand refer to the process tolerance of a measurement system, which is hardly correct and seems to suggest you’ve missed the point again.
Why do you focus on triva when the more important question of how to Gage R&R of a single target seems far more important? After all many transactional processes use targets, and we wouldn’t even be having this argument if we just followed ‘standard 6s.’ How do you tackle the problem of a single target – please describe the principles and not another reference?
The real point of my post is that inspection systems depend more on the choice of ‘reference standards’ than the inspection per se. Why .. because the eye/brain interface is pretty constant from one person to another! Just ask the OR guy!
It is easy to blame one operator than another but most of the problems can be resolved by admitting some samples are difficult to disposition (manufacturing term.)
Andy
Andy,Glad to see you’re a bit calmer in this recent posting over the last. Please help me out a bit, as you seem intent to treat me, a trained Physicist, as a grasshopper. A grasshopper whose been working in R&D, manufacturing, and transactional environments for the better part of my life. What answer should I have gotten this time? I figured I addressed your claim that I did not properly answer MKS’s original questions? So now you present me with the next puzzle, “Why do I focus on trivia when the more important question of how to Gage R&R of a single target seems far more important? Hmm! “Gage R&R of a single target…” Andy, I’d like to make a deal with you… I would like to hear from a few others on this forum, say, Darth, Stan, or M. Carnell on this challenging mind-bender of a question concerning transactional targets and MSAs. I certainly have my answer and a few comments, but I don’t think you would appreciate them much. Perhaps my mind is taking a vacation, and you’re right on the button with these questions. At least I get that sense from the other heavyweights on this forum. They all seem to feel your the closest thing to Newton that exists today. So, why don’t you have them explain this simple concept to me without your guidance.Let’s give someone with at least an equal understanding as you on this complex subject a chance to explain it to simple old me… You can decide if they get it right, and let me know. Then, I’ll give their answer some thought, and ask some questions for clarification. At the very least it will provide some fun and info for the other forum members. At the most, you’ll be able to put me in my place, which I suspect is you true desire. Does this request sound fair to you? If so, let’s give the knowledgeable forum members about these ideas no more than two days to respond. After that we can resume our fun… Is it a deal?Ken
Good morning Ken …
Let me give you a list of some of the ‘statistical heavy-weight’ people I respect in this forum, in no particular order …
BHDT, Stan, John H, Darth, Vinny, Robert Butler, Mario Perez-Wilson, Statman … there are others, but it is a too early for me!
I’ve already sent a copy of my poorly written article to Stan and John H, and I would be happy to send copies to anyone else interested in having this problem highlighted. My goal has been to explain measurement uncertainty in terms of the probability of a correct decision, and in particular to highlight the problem of a single target.
As I’m sure you appreciate this is a real probelm in the UK where there is a predeliction for setting single targets without due regard for measurement uncertainty or capability.
Andy
PS: You seem to ‘read to much’ into this artificial world of the internet. For all I know I could be talking to Mickey Mouse :-) I’ve never been angry, on the contrary I’ve had a lot of fun! Unlike you I have nothing to lose because I’m retired; and I don’t mind being contradicted or even being wrong!
Andy,
Great! So you agree to my request… Let’s give it at least 2 days for one of the listed “heavyweights” to comment on your previous post.
Oh, I don’t place as much in this “artificial” world as you give me credit. I’ve always contended that half of what you see on the internet is fancy, and the other half may have some value. The challenge is identifying the correct half. I much prefer to base my technical comments on peer reviewed journal articles, or tertiary sources such as text books or other references that are known for their accuracy. I’ve done business that way for as long as I can remember. It minimizes the chances of me loosing what ever you suggest I would lose!
Good luck with your article. Do you plan to publish it in a peer reviewed journal? Do you have the name of the journal so that I may be on the look out for your article in the near future?
P.S. I always thought selecting business targets and requirements was a management job, and evaluating the systems that measure the business processes responsible for the targets was the domain of Measurement System Analysis.
Cheers,
Ken
Ken,
No .. the agreement is to comment on the article!
Good luck!Andy
Dang… There is so much ego out here you couldn’t cut it with a chain-saw.
Lighten up eh?
Or, I could just post “WRONG” that seems to go over well for some….
If Stan or John H say I’m wrong I’ll accept it.
You can post wrong by all means – but what would that prove?
Your article is right and I like the idea of extending Shainin’s methods for MSA. Sorry for not commenting earlier.
Ken, lighten up.
It would prove nothing… That is my point. I don’t claim to have the stats knowledge that many people on this forum have (or claim to have) – probably not to the level of either yourself or Ken. Just frustrated by this string, seems like a lot of bantering, bashing for no reason.
Excellent. I have now reached my nirvana of irony. Stan has asked another poster to lighten up. This was indeed a good day to screw around on the internet. Thank you all.
Vinny
Stan,
Thank you for your comment Stan .. I should like to send you the second part covering the use of a discrete metric, and some of the items raised in this very interesting but ‘heated debate’ with Ken.
Cheers,
Andy
Vinny,
We have to thank Dr. Phil, it appears the intervention worked. I forget how well lithium and shock treatment worked.
Chris
Mr. Iam,
Please accept my apologies ….
One of the points I’m trying to make is that you don’t have to have a detailed stats knowledge. You can use Minitab simulations and graphical analysis to gain a far greater insight than struggling with maths. Anway, confidence intervals are difficult to incorporate into mathematical analysis unelss I’m mistaken – by I am open to persuasion.
Please don’t be put off by academic learning – it does has its place.
Andy U,
Not a problem. Actually, I’d be interested in reading your doc as well. I am a fan of Shainin stuff – mostly pre-control and variable search, decision tree.
It seems as though many folks just to personnel attacks on this forum – that just got my hair up.
I’ll send it out next Tues. Where should I send it?
As per Stan’s request, the following arrangements have been made to settle this argument mano e mano.
Ken and Andy U: The Distinct Category Debate has now been finalized and set for Monday, September 26, 2005. All of the arrangements have been made. The debate will begin at 9:00 AM and be located on-campus at Arizona State University, Ira Fulton School of Engineering. You will find the room number at the reception desk. You will need to submit your white papers no later than September 19, 2005 to Mr. Jeff Goss, Director, Center for Professional Development, Arizona State University. This will provide sufficient time for the referees to review your technical white papers and prepare their cross-examination questions and to do their crayon markups. If you decide not to participate, then as a courtesy, please let Stan know ASAP so the arrangements can be cancelled. Copies must be sent to Vinny, Darth, BTDT and Joe BB (who will rule on the color and style). Dr. Phil has made arrangments for media coverage along with appropriate and tasteful concessions. The J O Club will act as ushers to seat all the guests. Mikel Harry has agreed to act as Moderator with Dr. Robert Butler and M. Carnell acting as judges. Mr. Iam will act as tie breaker if Butler and Carnell can’t agree on who won the debate. Dog Sxxt will be flying in to handle security. M Cyger has agreed to post the debate live with streaming video…or was that screaming video…can’t remember. I hope that this event does better than the Great Debate 1. Good luck to both of you.
Ah! This is very excellent! I am humbled to be of service for this event!
please send a copy to bruenning@charter.net
Sorry can’t make it. England is beating Australia at cricket for the first time in about thirty years. For those of you not familiar with cricket; it’s just baseball with a proper bat.
That’s like saying Real Football and football are the same except one uses the proper ball. You had to compare apples and oranges again.
Chris
As a player in college I always considered cricket to be most like american T-Ball…………….Oh well to each his own I guess
CT
No I meant it is almost impossible to hit a round ball with a round bat!
Here is a picture of Andy U decked out for his cricket game. Note all the heavy padding and broad bat. Guess the wittle wackers are afraid of getting hit by the ball. Which by the way has to be bounced on the ground in front of them. Guess the wittle girls can’t reach the plate. Also by swinging at it with such a wide stick, it’s tough to miss it.
Here is the national team practicing at their state of the art practice field.
Finally, here are the joyously happy fans toasting the winning team with their specimen cups. Got to admit, it’s a tough game.
This can be easily resolved using standard Canadian techniques.http://www.cbc.ca/sports/indepth/bertuzzi/BTDT
Stan,Well, I thought we were commenting on the comments in the thread. I don’t have any articles. Never got heavy in the first place. However, I suspect I could lose a few pounds anyway. You guys certainly have your way of doing things. Some of Shanin’s methods are great, but their not a panacea for lack of statistical understanding. So, not too interested in upsetting the balance here… Appreciate the patience of the forum members in all of the lively banter.Take Care,Ken
Where did you find the photo?!!! That’a absolutely amazing; you must consult for the CIA. That’s what you get for being a Motorola spook in Cambridge!
If measurement system is being defined as the total gage RR then number of distinct categories = (SDparts/SDtotalRR)*(sqrt(2)).
I also spoke with Minitab about this and I didn’t have to talk to the development folks. Seems like the folks on the help-line also know the answer too. I was told that Minitab is now choosing to round down instead of up. The formula is the same, so I don’t know how one can say v13 is more unbiased? Version 13 gives a single digit number as does v14.
Now, 5 distinct categories no loger aligns with a 30% total gage RR as is in v13.
Dog,How do you set up this root mean square formula to get the 98% value? Can you show us how the 5:1 ratio works in this way?Thanks.
Andy
I agree with Stan. As a very young QA Engineer and Scientist I had Dorian Shainin as an instructor and was always intrigued by the simplicity of his ideas and creative problem solving approaches. He reminded me of the late Physicist and Nobel Laureate Richard Feynman who gained a “new and profound understanding of nature by thinking things out for himself”. I.e, he wasnt a “tool zombie” and was not fearful of challenging conventional ideas.
I have had a tiring week and I am looking forward to a very cold beer, good hot dog, Baseball game etc.. over the weekend .
Best wishes,
John H.
It’s same method with GRR% to PPM computation. Try to search with these keywords, “GRR+PPM+Dog Sxxt” to find the old posting.
Doggie,I think we’ve beat this subject to death. I answered the questions asked earlier. If you’re going to beat me up, at least you could perform the correct calculations. A measurement process able to partition the total process variation up into 5 distinct categories would consume 7.6% of the total variation leaving 92.4% not 98% as a process signal. The estimate of percent contribution is determined using variances, not standard deviations. I’ve prepared a simple Excel spreadsheet that performs all of these, and other calculations for the curious. If you’re interested in it, then please provide your email address.In my original writeup, I suggested sources where one my find reference to using 5 categories. AIAG is a key source for most. However, as it turns out one usually only requires about 80% to 85% signal to adequately observe process changes using such tools as SPC Charts. This would place the number of distinct categories closer to about 4 as a requirement. You can verify this directly with the correct formula for computing the number of distinct categories. Ken
Dog,I used the search parameters you provided, but nothing came up. Could you provide the calculation again once more?BP
MIam,I agree!
Thanks for your comment John …
I hope you have a great weekend!
Best wishes,
Andy
I am absolutely & utterly 100% behind Andy U on this one, for those of you who are not in our great island at present may not realize the fervour (& the importance) to sports fans in the UK that’the ashes’ mean to us, especially now we have compiled a team that is actually capable of taking the treasured urn off the aussies, i suggest less directed banter towards Andy U this weekend & into Monday (which is a holiday in the UK) so he can sit back & enjoy our national sport.
Best regards
Jaybee
Even Darth and his SW buddies have turned out to support Andy U and his Team. GO JIMMINY CRICKETS!! Even Joe BB came out to cheer. He is the one in the middle with the tiara on and wearing red.
Leaving no kidney stone unturned, even the guys in the GiantMedicalProducts analytical lab are working diligently to help assure Andy Us team a win in the big game/match/athleticish event.
Basically the theory has to do with en mass combinatorial testing (which in turn statistically smooths and dilutes the outlier impact) of the results of the team post-game urine sampling.
Cheers Andy.
Vinny
Kean, I not mean to beat you, you are a great contributor to this forum. Don’t feel hurt. I say sorry if you feel so.
I was using a very simple comparative calculation 5:1 to 5:0 without using any calculator or computer to see the effect of measurement instrument. Plug these ratios into RMS separately and my brain says
5:1 gives you total tolerance =5.1 and
5:0 gives you total tolerance = 5.0
Compare these two results will tell me only 2% variation is from the instrument.
Please send your spreadsheet to dogsxxt@yahoo.com
Doggie,Let’s move on… I’ve sent out my worksheet to you via the provided email address. I use this worksheet as a training aid with GBs and BBs so they understand correctly the relationships between distinct categories, measurement variation, process/product variation, and total variation in an MSA assessment. It would be great if you could provide me some feedback on its use when you have a chance… Cheers,Ken
Ken, I am always on the lookout for better ways to present material. Please forward your spreadsheet to me as well, thanks.
DrDarth66@aol.com
DrD,
Glad to with one request. Could you give it a close look for correctness/use, and forward back to me your observations/comments so I may make any needed improvements?
Ken
Will do, but realize that I am not real strong in this topical area. That admission should unleash some stupid responses. Thanks, Ken.
And still further along on the processing value chain, the folks associated with a certain TV home diva, convicted criminal and soon-to-be reality TV star have taken the discarded GiantMedicalProducts sample and recycled it using some fresh vegetables hoping for large profits on a small investment.
Available from the new much smaller division of Giamedproco, GiantMedicalProductsGeneticDiscards in your local frozen food section.
Can you believe I found this image with the caption “Mmmmmmm, pee soup.”
All you need to do is ask, and a stupid response it at your service.
Nonsense, Darth, your knowledge of the topic is excellent. In fact, here is that photo of you accepting the Distinct Categories Society Lifetime Celebrity Service Award for your work in the field.
Our current Executive Director, seen in the photo on the right, appreciates all your efforts with our society and the other groups you volunteer your time in the service of for the betterment of humanity, science fiction characters and huge walking potatoes.
Whoa, a little Atkins might be called for now. This traveling around the galaxy wrecking havoc has been tough on the diet. Thanks for reminding me about the award.
The forum ‘General’ is closed to new topics and replies.
© Copyright iSixSigma 2000-2015. User Agreement. Any reproduction or other use of content without the express written consent of iSixSigma is prohibited. More »