GRR and Anova assumptions
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 This topic has 67 replies, 18 voices, and was last updated 16 years, 8 months ago by Randa.

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August 17, 2005 at 8:46 am #40392
One of the assumptions of Anova is that samples are random and independent. Do members of the forum believe this condition is satisfied in GR&R, even when samples are sampled with replacement, which is often not the case?
If replicated measurements of small sample sizes cannot be considered random, what sample size can?
Just interested ..
Andy0August 17, 2005 at 6:20 pm #125262GR&R ANOVA tables are created differently than standard ANOVA table analysis. Here’s a quote from http://www2.chass.ncsu.edu/garson/pa765/anova.htm:
“If the data involve repeated measures of the same variable, as in beforeafter or matched pairs tests, the Ftest is computed differently from the usual betweengroups design, but the inference logic is the same. There are also a large variety of other ANOVA designs for special purposes, all with the same general logic.”
I ran through this exercise a few months ago and calculated the GR&R in Excel, running through the entire value splitting process. If you’d like a copy, let me know.
If you’re using Minitab, the help menu will walk you through the math used, along with each mean square used to calculate the different variation components. Also, I recommend http://www.itl.nist.gov/div898/handbook/ for lots of good online info.0August 17, 2005 at 6:40 pm #125268Thanks .. I’ll check it out!
Cheers,
Andy0August 18, 2005 at 12:48 pm #125314FTSBB:
Can you paste the different formula for repeated measures ANOVA. I have the same doubt as Andy. I could not find a proper answer. I read the comments you posted before for the same doubt by someone else, but it did not help me. If you go to Minitab formula and calculation, the ANOVA calculation they used is no different than the normal method. You can get the same Gage R&R ANOVA results if you do the analysis by normal ANOVA method. I did this before.
I dont knw what i am missing here. If you can help me, i will really appreciate it. Thanks in advance
Deep0August 18, 2005 at 1:13 pm #125315The mean square values are equivalent, but I’ll bet your Fvalues (and subsequent pvalues) are different between regular 2way ANOVA and the gage R&R ANOVA output for part & op. The difference is which error structure is used to calculate the variation components. Instead of using the same error term across all factors, the gage R&R uses the following formulas to calculate F:
F part = MSpart / MSpart*op
F op = MSop / MSpart*op
F op*part = MSoperator*part / MSrepeatability
If you just used regular 2way ANOVA, the output is calculated as:
F part = MSpart / MSrepeatability (aka error)
F op = MSop / MSrepeatability
F op*part (aka interaction) = MSoperator*part / MS repeatability
The best web source I’ve found for ANOVA is http://www.itl.nist.gov/div898/handbook/ppc/section2/ppc23.htm. This is a great exercise in value splitting and shows you exactly how ANOVA works. ANOVA is computationally easy, but it takes a while to calculate by hand. I strongly recommend running through a 1way and 2way analysis by hand until you get the feel for it, then you’ll see why computers are a godsend!0August 18, 2005 at 1:23 pm #125316Agree with FTSBB,
F test is computed differently for RnR, (as opposed to 2way) i also like the word that FTSBB used ‘computationally’. A fine word indeed!
check out various ANOVA sites (through google search) & the difference is apparent (if a little difficult to get head around it – like me!)
E0August 18, 2005 at 1:52 pm #125321Ftsbb,
I’m also a statistical idios, so please bear with me …
My understanding is that the main difference between Anova and Repeated Measures Anova is that the latter uses differences between ‘paired observations,’ but the same assumptions as Anova apply:
– independent random sampling
– normal distributions, and
– sphericity (homogeneous variance)
In one reference I found the author expresses a concern about small ‘operator’ sample sizes:
http://www.stat.fi/isi99/proceedings/arkisto/varasto/does0107.pdf
I had not considered the question of sphericity and I’m not sure whether or not the assumption is reasonable or not.
From the point of view of understanding, a bivariate plot seems a lot easier to understand, as does a regression of a measured value on to a known ‘standard’ value,’ especially when using automatic test equipment and there is no operator influence other than to run the correct program.
Andy0August 18, 2005 at 2:18 pm #125323Idios?
Beware the internet sources – there’s a lot of stuff that is just plain fuzzy, and other stuff that is flatout wrong. I can’t give you a good source for ANOVA, as I haven’t been able to find one that really explains the assumptions well. Not sure about this source, but I did notice the Van den Heuvel and Trip that is cited has been submitted for publication, not actually publised! Just an observation…
Don’t get me wrong – I’m not a stat guy myself. If the whole issue of ANOVA assumptions has you in a tizzy, use the Xbar and R charts. When I was in training, we did not mess with the gage R&R components, but rather looked at the control charts for deeming the measurement system worthy. There’s debate about which method is better, but it sure is easier to look at a graph than grind out ANOVA tables all day long.
For the ultrashort course, look for a range chart in control and an Xbar chart wildly out of control. The in control R chart suggests low within subgroup variation (repeatability) and the Xbar out of control suggests high between subgroup variation (parttopart variation, also hint about reproducibility). Also, I was trained to use 3 parts, 3 operators, and 3 measurements/part/operator. Man, talk about a tough MSA to pass! The deck isn’t stacked quite as much in your favor versus the 2/10/2 AIAG thing…
Now that I finally read your last line, looks like this is an automated measurement system! Maybe I’m too much of a simpleton, but the whole point of the MSA is to make sure when you measure the same thing that you get the same measurement, regardless of time, operator, etc. Start pumping that machine with the same parts over & over and see what you get. I’ll bet with enough samples, common sense will prevail over ANOVA.0August 18, 2005 at 2:27 pm #125325Ftsbb,
Good advice indeed – thanks!
Andy0August 18, 2005 at 2:49 pm #125327Sorry for the delay.
FTSBB: Please check the normal ANOVA equation when factors are random. Your F values for Gage R&R ANOVA and the F values of normal random factors ANOVA will match. The dfference in calculation comes from the difference in Expected mean square calculation. I cannot remember where did i read this, I think John Neter or Agresti ‘s DOE book, where they mentioed about the calculations of gage R&R and normal ANOVA. They dont mention anything about the assumption.
Deep0August 18, 2005 at 2:57 pm #125328Don’t you mean your expected mean squares will be equivalent? There’s no getting around the MS value (try the value splitting exercise – it will drill this concept into your head); there’s no fancy statistics involved in creating the MS value (other than degrees of freedom).
Like you state, I can’t find a good reference for the assumptions of ANOVA. Here’s a quote from NIST:
“For estimation purposes, we assume the data can adequately be modeled as the sum of a deterministic component and a random component. We further assume that the fixed (deterministic) component can be modeled as the sum of an overall mean and some contribution from the factor level. Finally, it is assumed that the random component can be modeled with a Gaussian distribution with fixed location and spread.”0August 18, 2005 at 3:05 pm #125330Thanks FTSBB. I was trying to say that there is no difference between the calculation of gage R&R ANOVA and normal ANOVA with random factors. (You can try this using Minitab treating your operator and part as random factors and do an ANOVA calculation).
I also could not find any source regarding the assumption. My last resort is always to ask one of my friends, who a hack statistician. I will get back after I hear from him.
Thanks
Deep0August 18, 2005 at 3:35 pm #125334Believe you are running this through ANOVA>Balanced ANOVA and selecting the variation components manually. This is correct; it matches the proper variation component with the effect. Only difference you might encounter is the pvalue cutoff for the interaction term. If the pvalue is below your specified value, it combines the interaction & repeatability into one SS value. This is the only case I’m aware of when the SS value (and hence the MS value) are altered.
That’s digging pretty deep in the theory bucket. I’ve been interested for quite some time on the restriction of and randomization between whole and split plots. Stuff like the balanced & GLM ANOVA are pretty slick, but they make my head hurt pretty quick, too.0August 18, 2005 at 4:41 pm #125340For automated measurment equipment such as a scale, only the measurment error caused by the equipment variation (EV) must be calculated for G R&R. In this process the Appraiser Variation (AV) does not exist.
Sampling: Select 10 items which cover the range of the items. Use only one Measurement system. Each item must be measured at least 2 to 10 times (the more the better). Perform Calculations
Calculation steps:
1) Calculate the STDDEV from the trials for each part
2)Calculate the average standard deviation, sBar from the step above
3)Dived the c4 from Duncan in table below. The number of observations in the sample, n, is the number of trials
4) Multiply by the number of Sigma you want to use (ie 5.15 or 6)
5) Divide by the tolerance and multiplying by 100 to obtain the P/T as a percentage of tolerance.
The formula is R&R as a % tolerance= ((6*sBar/c4)/(USLLSL))
sBar=the sum of the standard deviations for each part measured divided by the number of parts in the study.
For c4 values over 10 c4=1Values for C4
# of Trials0.7979
20.8662
30.9213
40.9400
50.9515
60.9594
70.9650
80.9693
90.9727
10
This method will immediately tell you if your gage is adequate for the process tolerance. Since Tolerance is used for the calculation
I have this in a real slick spreadsheet if anyone wants it.
CT0August 18, 2005 at 5:15 pm #125342>>If the pvalue is below your specified value, it combines the interaction & repeatability into one SS value. This is the only case I’m aware of when the SS value (and hence the MS value) are altered.
I dont understand this, anyways thanks for the comments.
Deep0August 18, 2005 at 5:18 pm #125343Minitab will truncate the interaction term with the true error term if the pvalue for the interaction term is small. That is, if it’s so small as not to be valuable, it combines the sum of squares for the interaction and the error term into just an error term (i.e. repeatability). Try it with a data set and see; you should get two ANOVA tables: one with interaction and without interaction.
0August 18, 2005 at 5:24 pm #125345Others might disagree, but I have issues with P/T ratios. Seems to me this is a second chance if your gage R&R isn’t what you want it to be. I think the P/T ratio is good protection against limited part variation, but the samples you take should be “representative” of variation, so it’s a tough point to sell. P/T shows you how well your measurement system compares to the spec, but you may not be able to differentiate parts from one another. I’ve seen several gage studies that looked like crap on the control charts and variation components until compared with the spec – more than just the gage to consider in an MSA.
0August 18, 2005 at 6:55 pm #125365Agreed…………but if the Gage is not adequate to begin with then there may lie the problem with other forms of charting.
CT0August 18, 2005 at 8:10 pm #125377Sample size does have a big effect but it doesnt limit GR&R. for small sample size use formulaes for sample and not for the population.
0August 18, 2005 at 11:05 pm #125391Hi Andy,
I was reading the thread from your base post, and found some of the comments interesting. This is in fact a great question, and perhaps I might give the answer a try.
FTSBB suggests that Gage R&R studies produce ANOVA results that are different or unique from other ANOVA analysis. He cites this is due to the repeated measures associated with the analysis, which are handled a bit differently to compute the Fvalues in the table. (I hope I summarized your comments correctly)
I was curious about this comment, so I went back to a few of my references, “Design and Analysis of Experiments”, by D. C. Montgomery, 3rd and 5th Editions. The appropriate parts of these texts are Section 7.4(3rd), and Section 53.7(5th). In fact, the Gage R&R ANOVA analysis is not really too unique. It differs in the way of computing the Fvalues, because we are analyzing the data using what is called a “Random Effects Model” of two or more factors.
In random effects models the expected mean squares for the error variance and the interaction variance cannot be separated in a direct manner. In a random effects model the Mean Square Error term for interactions is considered the best estimate of the error variance when the interaction effect is significant. Therefore, the Fvalues for the main effects are calculated with MSinteraction in the denominator. Otherwise, if the interaction term is not significant the model reduces to the main effects, in our case operator and part, and is analyzed the same way as a fixedeffect model with the base error variance estimate as MSE.
Replicated measures for Gage R&R ANOVA are assumed to come from selecting test samples at random from a larger population of samples, and selecting operators from a representative number of operators at random from a larger pool of operators. There are many papers on “Mixed Effect” models where the samples are random, but the operators are fixed. While this approach is a nice discussion point during coffee with Statisticians, its usefulness does not merit the complexity for the analysis. In Minitab, “Mixed Effect” models would require the use of General Linear Modeling, yuck! Crossed repeated measures are handled by Minitab in a manner to minimize potential bias from sample handling between operators.
While the assumptions for ANOVA have been stated many ways over the years, I tend to work with the age old fundamentals. They are as follows:
1. The various effects are additive, (meaning their variances are additive to form the effects model)
2. The “experimental” or “residual” errors must be independent of the main effects, interactions, and of each other. (there are no dependencies between the factors or their interactions)
3. The “residual” errors must have a common variance, and
4. The “residual” errors must be randomly and normally distributed.
Well, I hope this helped a little. I trust my science and math reference is reasonable.
Ken0August 19, 2005 at 7:30 am #125409Hi Ken,
I have been following this thread quite closely as it also got my grey matter ticking a little. For the first time in a while there has been no mud slinging (sometimes a good thing i guess) & it can be seen going back through the thread that there is probably half a dozen people who have tried to gain an understanding into it (by carrying out a little research) probably just for piece of mind & clarity (i am one of them!) I am nor going to eloborate further as i think (from my point of view) certain questions have been answered. Your last post has finally nailed this one for me, excellent research & answer (as always)
Also well done ftsbb & Andy (sorry if i mention no others) for the questions & answers that have been concise (& if not understood, not shot down in flames) & answered to the best of alls ability & the time you took to delve into this somewhat ‘riddle’
keep up the good work & regards
E0August 19, 2005 at 10:51 am #125417Ken,
Thank you for the information provided. It’ll take me some time to absorb it. But you are correct when you point out Anova assumes a ‘Random Effects Model.’
Although measurement uncertaintly is certainly a random effect, measuring the same part seems to introduce some covariation???
Taking the difference between two repeated measurements, as suggested, seems to satisfy the requirement ;but what has been lost? Is the variance now greater?
I can well understand your reticence towards GLM, modern software might make it more accessable. It does seem more reasonable to assume that repeated measurements in Gage R&R are highly correlated; especially when taken as an ensemble.
Why all the trouble? I think it is important to understand the probability of a correct decision. If the probability is too low why bother to take a measurement? Why not just flip a coin.
It seems to me the only options for poor measuement capability are to:
– buy new equipment,
– take repeated measuements and average, or
– widen tolerances.
Regards,
Andy
0August 19, 2005 at 12:42 pm #125425Hi
This is a different question, i asked this question before and i did not get a satisfactory answer. I was asked to do a gage R&R. We use this gage for checking many things (Height gage). This is not a dedicated gage for any parts, My manager wants to know if this gage is good or not. What i did was i took some standard blocks (known height) of different height and did a gage R&R. My manager told me that is the wrong way of doing gage R&R. He could not give me a proper answer, why that is wrong..
Can anyone tell me what did i do wrong? I used standard height blocks, because the only aim for the study was to see if the gage is acceptable or not, moreover we check many different parts using this gage.
Thanks in advance
Deep0August 19, 2005 at 1:01 pm #125427
Paul GibbonsParticipant@PaulGibbons Include @PaulGibbons in your post and this person will
be notified via email.Deep,
Not my area of expertise but I would say that all you have achieved there is to validate that the reading on height gauge corresponds with the indicated height of the block gauges.
R and R is more about application to a specific measurement activity rather than a general on in this case. The tolerance of the component you are measuring is important as usually (from my apprentice days) you would expect the measuring tool/system to be 10 times more accurate than the tolerance.
For your height gauge, that is used for general measurement, I would suggest that you have it calibrated. See link for info about calibration: –
https://www.isixsigma.com/dictionary/Calibration794.htm
Good luck
Paul
PS, I thought that height gauges were mainly used for manually marking things out?
PPS, In the past I have used a height gauge as a comparitor fitting a DTI to a known position using gauge blocks. This eliminates any human error or interpretation from trying to get the scribber as close to the thing being measured as possible without overloading it.0August 19, 2005 at 1:10 pm #125430Eliz,
Thanks for the kind feedback!
Ciao,
Ken0August 19, 2005 at 1:28 pm #125433Thanks Paul;
I have used multiple operator to see if the gage is reproducible. I did not use the our production parts because there are many different parts we measure using that gage. So i thought i use some standard blocks instead of our parts (i did not see any difference between using a standard block or using one of our production part). We were not planing to include the tolerance component (% tolerance) at the first place. The only two things which i was planning to study is repeatability and reproducibility.
If this was the only aim for my study, please tell me what was wrong with the study? Thanks once again for the comment
Deep0August 19, 2005 at 1:59 pm #125437
Paul GibbonsParticipant@PaulGibbons Include @PaulGibbons in your post and this person will
be notified via email.Deep,
I don’t think I am qualified to help you any further.
Sorry
Paul0August 19, 2005 at 2:03 pm #125438My Experience;
When performing R&R on a gage that is used to measure many different parts, I have found the best way to do this is simple this.
1) Pick 10 samples from the variety of parts (10 of ea sample)
2) Have at least 3 appraiser and a 4th Master Appraiser check the parts. Compare the 3 appraisers to the Master (I assume you would be the master)
Although this takes longer, you should always use production parts and not “Known” gage blocks, these blocks give you false since of checkability for your production parts. As I understand the question unless your parts are made like Gage blocks then they are not the same, and what you are checking is not the same.
I am not always the best at explaining these so I hope this helps and maybe someone better versed can explain it better.
For P/T ratio, you are correct in not using it at this point. But after you have finished your initial R&R you should run at least 3 trials per subgroup of parts to see if the gage is adequate for your tolerance range.
CT0August 19, 2005 at 2:15 pm #125443Thanks Paul and Thanks CT;
Appreciate your time to help me. One thing which i wanted to stress again is “The ONLY thing which i was trying to study is repeatability and reproducibility” I was not studying , if the gage good to measure the parts we make. The only reason for this study was to check if the gage good enough to check any parts.
Thanks
Deep0August 19, 2005 at 2:32 pm #125446Deep,
If all you want to do is check the gage then have it calibrated. If all you want to do is check gage variation then perform R&R with gage blocks. But you really want to know if your gage can check your parts then you have to run an R&R using production samples. Sorry but it has to be done.
Another way to check the gage is to run XBar R chart with it on a process of known stability as a secondary check in production.
Anything other than this and I cant help you.
CT0August 19, 2005 at 2:37 pm #125447
Paul GibbonsParticipant@PaulGibbons Include @PaulGibbons in your post and this person will
be notified via email.Hi Deep,
In your last message you appear to contradict yourself. You say “”The ONLY thing which i was trying to study is repeatability and reproducibility” I was not studying , if the gage good to measure the parts we make”. So you don’t want to know if the gauge is good enough to measure your parts. But then you say “The only reason for this study was to check if the gage good enough to check any parts”.
Unless you mean that you want to be sure the gauge will give a good R&R measure of any parts as long as they are not the ones that you make????;¬)
Still think you should get the equipment calibrated.
Paul0August 19, 2005 at 4:27 pm #125453Thanks for all inputs, I am confused now =:)
0August 20, 2005 at 2:52 am #125475Andy,Just got a chance to look at your response to my earlier post on GR&R. Not sure if you expected a followup, so will try to keep it short.Listen, perhaps there are a few things I may be confused about concerning measurement systems evaluation, or possibly there are other areas of confusion about this process that both of us are confused about, but not sure. Here’s my take on your concern about “convariation”:We both know that taking repeated measures of something should not inandof itself incur “covariation.” Covariance is a bivariate measure. Repeated measures are characterized as a single(one) variate. Perhaps you mistakenly used the word “covariation” when you meant auto or serial correlated, but I’m not sure. Regardless of which property you are concerned about neither should be a great concern. Taking repeated measures of the same quantity simply allows us to quantify the precision and possibly the consistency of the gage, nothing more. In destructive testing senarios, there may be a small chance of autocorrelation in the data, but even in the worst case it should have minimal effect on the overall gage precision determination. Let me know if the above clarification helps.Ken
0August 20, 2005 at 9:27 am #125478Ken,
You’ve hit the nail on the head …
If a person plots a scatter diagram of measurements taken from a number of ‘reference samples’ at time one and again later, at time two, then the resulting ‘scatter’ forms a bivariate distribution, provided the references are normally distributed.
If we follow Ct’s good advice and use a ‘flat’ distribution instead, covering the entire range of interest, then Pearson’s regression coefficient should indicate a high degree of correlation. If it doesn’t we really have a problem!
The reason I should like to try to get to the bottom of this is because the route from a bivariate plot or a ‘calibration’ regression’ to an operating curve P(CD) – Probability of a correct decision seems straightforward, while it appears more tenuous using Gage R&R.) There is also the question of ‘single targets.!’
In other words, once we understand it is pointless making decisions based on low levels of confidence, the sooner we’ll take immediate corrective action, rather than just file a report stating the metrology system is ‘acceptable, might be acceptable, or not acceptable.’
To take immediate corrective action, I have to construct confidence intervals around the specification so that my measurement is ‘de facto’ acceptable. These confidence intervals are not guardbands as such because they have to be adjusted according to how tolerances have been determined, and whether or not I use an average derived from repeated measurement to disposition a sample against a tolerance.
For example, sometimes the next operation defines a tolerance in terms of individual measurements, using the same type of measurement system, in which case there is no justification for adjusting ‘measured’ tolerances. Other times a design team might use a regression analysis and specifiy an ‘average’ tolerance, in which case the tolerance has to be widened to accommodate an individual measurement made in production. Of course, many automatic tests are long and tedious and there is clear motivation for taking a single measurement. But what if the design specification has been determined from simulation?
Peppe and I recently wrote an article uon the subject of graphical interpretation of measuement uncertainty and although it is badly written – solely my fault – I should be happy to send you a copy as it hasn’t been correctly uploaded on to another forum.
Regards,
Andy
0August 20, 2005 at 3:57 pm #125492Andy,
I see you’ve given this subject considerable thought! You have some interesting thoughts that would be challenging to address in an online forum. Usually, when I have similar thoughts I do a bit of research. If you’re interested in a bit of limited research to flesh out your ideas, I would like to suggest one of the best references on the subject of measurement systems analysis. To get a copy for a reasonable cost visit Dr. D. Wheeler’s website at: http://www.spcpress.com . Locate the text called, “Evaluating the Measurement Process”, by D.J. Wheeler and R.W. Lyday. Some call this the “green book,” and it’s one of the best in this area. Perhaps you already have a copy of this reference on your shelf…
When you obtain your copy or pull it from your shelf, look over Chapter 3, “Interpreting Measurements.” Look closely at the sections entitled, “The Characterization of Measured Items: Probable Error”, and “The Classification of Measured Items Relative to Specifications.” These two sections should address your observations in paragraphs 5 & 6 of you last post. I would also suggest you jump to Chapter 5, entitled, “The Relative Usefulness of a Measurement.” Look over this chapter to gain an understanding of the Interclass Correlation Coefficient, and how it relates to the Discrimination Ratio. In fact, it’s not quite correct to use the Pearson Coefficient with measurement data, and this section explains the correct way of handling multiple paired repeated measures in the sense you describe.
I’m interested in your review and comments on this research. Please keep the communication flowing.
Ken0August 20, 2005 at 5:16 pm #125495Ken,
You wrote:I disagree .. it seems quite reasonable to regress a measured value on to an actual value, and to calculate rsquared. In fact, this is the only way to choose a really sensitive metrology system and to recalibrate it back to 1:1 to reduce mesaurement error. This appears to be another disadvantage of Gage R&R …. it doesn’t to detect metrology systems which have been ‘desensitized’ to achieve good precision – a simple software adjustment on most systems!
Of course, the scatterplot method does pose ‘interpretation’ problems when the ‘actual’ values of the ‘reference’ samples are unknown, as is the case with Gage R&R; because residuals are not perpendicular to the yaxis. Perhaps it would be more appropriate to use the Mahalanobis distance?
Although I’m only familiar with aspects of Dr. Wheeler’s Experimental Design, I can see the logic of using discriminant analysis because this approach would seem to support my contention that repeated measurements are in fact correlated. (Standardized covariance.)
If this is the case, then why does ‘standard’ Six Sigma still advocate Gage R&R?
Cheers,
Andy0August 20, 2005 at 6:59 pm #125501Andy,
It would be real useful for you to look over Wheeler’s work as I suggested earlier. His experimental references do not touch upon the subject matter we’ve discussed.
The traditional statistic used for characterizing the relationship between measurement variation and product/process variation is the Interclass Correlation Coefficient. It has been a well accepted theoretical fact that repeated measures are not correlated. This fact was documented back when the error function was first identified by Gauss. If there is correlation in the repeated measures, then there is something wrong with the measurement system. Bytheway, I have seen correlated repeated measures with chemical and biological samples that deteriorate in time.
Wheeler’s use of paired measures to develop the discrimination ratio does not imply correlation between paired values. Instead, it is a way of quantifying the relative error between paired values aggregated across multiple operators. This is done to illustrate how the general precision of a measurement system might be summarized using a single value.
To the best of my knowledge, neither Wheeler nor other researchers on this subject have ever used the Pearson Coefficient to characterize the performance of a measurement system–unless they are interested in comparing two different measurement systems to determine if they provide the same level of measurement performance. If you have any references to the specific use of the Pearson Coefficient being used with repeated measures on a single measurement system, then I would be interested in them.
The foundation and use of GR&R is a well accepted practice, albeit there are some issues with comparing measurement variation to the tolerance range directly. I tend not to ascribe to the rigorous GR&R approach as advocated by most Six Sigma consultants and companies, because I’ve found it produces a greater chance of committing a Type I error. Instead, I’ve developed a modified approach to the standard GR&R practice to ensure reasonable costeffective guidelines to my customers.
Enjoy your journey…
Ken0August 20, 2005 at 7:21 pm #125504Ken,
You state that some researches have used the correlation coefficient to compare two measurement systems – then why not ‘time 1’ vs ‘time 2’, etc.
Does everything have to be in a reference book? Surely, people can apply statistical principles while thinking for themselves. Is there no room for creative thought in Six Sigma? Are belts just a bunch of robots going around applying ‘tools’ in a standard way? I think not!
Regards,
Andy0August 20, 2005 at 7:37 pm #125507Ken,
You stated that two repeated measurements on a metrology system are not correlated. Well I just thought of a counter argument!
Let’s say I measure an oxide thickness on a sample and I measure it as 51 Angstrom. Later, I ask another engineer to confirm my measurement using the same system. He comes back and says he got 49 Angstroms.
Do we now consider our measurements correlate? I think a reasonable man would say it does imply correlation. Does 51 and 29 correlate, I would say not; but that requires some knowledge and experience of an ellipsometer.
Regards,
Andy0August 20, 2005 at 7:39 pm #125508Andy,Like you I am a creative thinker. But, in researching any new topic the researcher always evaluates what work has been done previously before embarking on his or her research. Novel ideas are good, but having a firm background in the foundations supporting these novel ideas provides validation.You are welcome to believe any ideas you would like. Please don’t let me discourage you. However, in order for me to follow your premises and corollaries I will need some foundation. Otherwise, this discussion is idle noise. Do you get my drift?Now, consider looking at this article by J.M. Bland and D.G. Altman discussing the merits and use of Correlation Coefficients viz. Measurement Error. http://bmj.bmjjournals.com/cgi/content/full/313/7048/41Andy, we’ve spoken before about good science in past posts. Part of good science is having a firm foundation on all subject matter that has come before your proposed work. I do not propose to have such a foundation. But, if I were to propose a new way to evaluate data, then I would first try to understand the present ways used. Only then can I fully appreciate the value of my offering.Good luck!Ken
0August 20, 2005 at 8:08 pm #125510Andy,
I worked over 13 years in the microelectronics industry, and know just enough to be dangerous about elipsometric measures and the equipment. I think your example illustrates some confusion about the use of the term correlation. But, perhaps I’ve misunderstood your point.
You provided me with a pair of repeated measures of the same quantity, and asked me if they correlate… This doesn’t make much sense to me. Correlation is the strength of relationship between two variables. Granted, repeated measures between two operators can be placed onto a scatter diagram, but what correlation(relationship) are you evaluating? What assumptions of this evaluation are you making? violating? What is the point for pairing these data in the first place? In essense, what is your objective for analyzing these data in this manner. I’m sorry, I don’t follow your logic!
To build a scatter diagram you need paired observations that have some interdependency between them. Your example is of two different operators measuring the same quantity. I guess you could consider the sample and measurement equipment the interdepency, but why would you evaluate these data in this manner. All things considered equal each operator should theoretically get the same value. However, differences due to measurement precision, measured location on the sample, environment, and other gives rise to differences between repeated measures.
What is the chance of the same operator getting the same results on the second measure? Please read the article whose link I sent you. It might provide some conceptual foundation.
Ken0August 21, 2005 at 5:19 am #125518
John H.Participant@JohnH. Include @JohnH. in your post and this person will
be notified via email.Hello Andy
I remember a rather simple but clever statistical argument from my long ago studies in Statistical Mechanics which suggests a direct link between Variance Independence and the Log Linear relationship IV .
Consider a set of measured random variables xN where the sum XN = x1 +x2 + x3 + xN and is continuos but for practical purposes are distinguishable by a discrete number count N , then the joint probabilities P(XN) = P(x1 +x2 + x3 + xN ) illustrating independence obey
P(x1 +x2 + x3 + xN)= P(x1) P(x2) P(x3) P(xN)
Taking the natural Log of both sides of the equality results in
I Ln(P(x1 +x2 + x3 + xN)= Ln(P(x1)) + Ln(P(x2))+ Ln(P(x3))
Expanding left hand side by a power series in the random variables xN yields
II Ln(P(x1 +x2 + ..xN )= K0 +( x1 +x2 + ..xN)K1 + (x1 +x2 + xN)2 K22 +..(x1 +x2 + xN)K N N
where K1 KN are arbitrary coefficients independent of the random variables.
When both sides of equation I are expanded by a power series and the terms are matched, the independence factoring assumption holds only when the higher order terms K2 = K3= ..KN =0 resulting in
III Ln(P(x1 +x2 + ..xN )= K0 +( x1 +x2 + ..xN)K1 This further simplifies to
IV Ln(P(XN))= K0 + XN K1 with XN = x1 +x2 + ..xN or
V P(XN) = Exp(K0) Exp(K1 XN )
Therefore if the random variable XN = VN the total variance of the sample, then a Log Linear relationship must exist between the Probability density P(VN) of the Total Sample Variance and Total Sample Variance VN as a requirement for the independence assumption to hold.
Just some thoughts,
Regards,
John H.
0August 21, 2005 at 6:08 am #125519Sir
can u plz send me the detailed spreadsheat for GRR study by all methods i.e by AVG n RANGE METHOD,by ANOVA method,for PV and for TOLERANCE.
Plz explain me the concept of PV and ndc.
thanx n regards!
SUNNY0August 21, 2005 at 9:22 am #125520Ken,
When I ‘calibrate’ a measurement system I take a number of ‘standards’ and measure them a number of times. Usually, there is software to adjust the ‘calibration curve.’
In the example I gave, two people measured a traceable stardard and decided their measurements correlated. Thus we have two points on the curve y = mx +c. For most calibrated metrology systems, c = 0. I think this should answer your objection.
In the other example I cited – that of a bivariate distribution – the ratio of the major axis to the minor axis relates to the correlation coefficient. It is easy to check! Thus if the ensemble is correlated, would an individual member of the ensemble not be correlated?
If someone were to study the rsquared relationship then an rsquared value of 95% would approximate to the wellknown Shainin Isoplot rule of 6/1. This is where the number of ‘buckets’ comes from!
The example I gave is similar to Taguchi’s approach in that he uses a Y= F(x) calibration curve to test metrology systems. Although many statisticians have attacked Taguchi, perhaps he is just more aware of real processes and assumptions.
By the way, you of course are also free to believe what ever you like and to be wrong, and to seek the support of other physchophants, who are also wrong :)
Regards,
Andy0August 21, 2005 at 9:25 am #125521Hi John,
Thanks for the insight. I’ll contact you later.
Cheers,
Andy0August 21, 2005 at 9:45 am #125522Ken,
Thanks for the reference ..
I had thought we were discussing repeated measurements on metrology systems, not repeated measurements in factorial designs – or anything else for that matter!
Regards,
Andy0August 21, 2005 at 1:59 pm #125523Andy,
I’m familiar with and have used both Taguchi’s and Shainin’s methods in the past. In both of their methods, I like you asked why/how do they work? So, many years ago I began my own research much as you have done in the recent past. I eventually found the basis of most of Taguchi’s and Shanin’s methods in much of the literature out there. In my search, I found other methods that were more efficient than that of Taguchi’s and Shanin. So, I decided to use the better methods. I’m not one for sticking with something simply because it’s novel, in vogue, or just easy to use in and of itself.
I never used the Isoplot approach, but reviewed its use years ago. I found there were some fundamental flaws with the approch, and moved on. Additionally, I’m really not one for learning five approaches that do the same thing, and have five different sets of terms. I ‘ve since understood where the 1 to 6 ratio in this method came from by reviewing the work of others. In fact, the ratio is not directly translated to the correlation coefficient, but it involves the correlation coefficient as:R = root[(1+rho / 1rho)]
I moved away from Taguchi’s methods when I found more efficient ways of conducting experimentation. I still use and teach some of the methods advanced by Shainin.
I’m glad you find these methods useful, and it sounds like you’ve been successful using them. It’s too bad you feel that I’m attacking you when I ask you for some foundation in your claims. I understand your difficulties, but don’t appreciate your unwarranted and unjustified comments. As I said nicely earlier–you are welcome to use any methods you would like. Unfortunately, if you want to have a discussion about them them with me, then it would be necessary for you to understand their roots.
Otherwise, we are just talking–but, no value comes from it!
Ken0August 21, 2005 at 2:03 pm #125524You don’t see the corollary relationship?
0August 21, 2005 at 3:56 pm #125526Ken,
I think this is the first time we’re in agreement – no value comes from having a discussion with you.
Andy0August 21, 2005 at 4:17 pm #125530Likewise for sure… Deming once said there’s no true learning without first understanding the theory. No theory, no foundation–just a lot of aimless tools applied incorrectly.
Shainin’s and Taguchi’s work has foundation, but without that understanding–well you know the rest. It’s great to disagree agreeably.. Enjoy your travels into the abyss.
Have a good one!
Ken0August 21, 2005 at 5:21 pm #125535Ken,
2 + 3 = 5 Oh sorry! Do you need a reference for that …
You should get together with Reigle Stewart – you have a lot in common!
Andy0August 21, 2005 at 6:13 pm #125538
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Andy, in defense of Ken, Reigle would say 2 + 3 = 3.5 +1.5 shift = 5. Of course he would then reference Dr. Harry and all his writings so you would now have your references. :). Here is Mikel (left) saying thanks to Stan for all his support on this Forum. This was taken after the Great Debate….oh wait, that never happened. Maybe this was when Stan bought Dr. Harry’s entire collection of books to be stored in his Barn at Chez Stans.
0August 21, 2005 at 9:58 pm #125541
Babe of a SisterParticipant@BabeofaSister Include @BabeofaSister in your post and this person will
be notified via email.Weeeeeeoooooo, cowboy!
Is Mikel packing a 357 under that big old rodeo belt buckle, or is it that he is happy to see Stan?0August 22, 2005 at 7:03 am #125555Darth,
Good one ..
Actually I much prefer Ken when he insults directly …
Cheers,
Andy
0August 22, 2005 at 2:54 pm #125588Sunny
Send Reply to [email protected] and I will send you what I have on Gage R&R’s (3 different spreadsheets) for different applications. All have detailed intruction for use.
Thanks CT0August 22, 2005 at 9:13 pm #125609Insecure folks usually strike back in mean ways. I’m not too surprised at your response. But, I won’t respond in kind. After all this is supposed to be a forum where we exchange ideas, and different ways of thinking.
C’mon Andy, I know you can do a much better job at being mean and hateful. You need to try a bit harder!
Who knows, perhaps you might be able to blend a little comedy with your mean spirit.
Ken0August 22, 2005 at 9:23 pm #125613
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.Ken, what have you done to Andy? I have followed his postings for quite a while and have developed a respect for his knowledge and point of view. I hope he isn’t vying for the rude and crude award. Stan’s got that locked up along with apparently the dumbest award according to Josephine BB.
0August 23, 2005 at 7:36 am #125636Ken,
You’re doing it again .. I don’t hate you and I’m not being mean to you personally; only towards some of your statements, your unwilllingness to follow someone else’s argument, and your seemingly condescending attitude. If you fell into the sea, I should be happy to dive in and pull you to safety, as would many others. Now that’s real value!
Andy0August 23, 2005 at 10:19 am #125639
Ken WaytParticipant@KenWayt Include @KenWayt in your post and this person will
be notified via email.Ken,
I would consider stepping back on this one. Andy U. is a consistent helpful and insightful contributor.
If you are sideways with him, it has to be a problem with you.0August 23, 2005 at 10:52 am #125640Mr. Ken, please, try to answer with appropiate examples about the matter of discussion. You stated you have over a decades of technical background, so use it to argue your opinions, if able. Technical discussion must be argued with technical answers, not with “one minute phychologist” answers. You are right, this is a public forum where ideas can be exachanged, so please, provide ideas.
Rgs, Peppe
0August 23, 2005 at 12:53 pm #125646Slow down there Andy. Thats hastily jumping the gun a little. I know and like Kens inyourface challenges to conventional wisdom, logic and technological status quo but just haphazardly jumping into the sea to save him????
I think a few baseline questions need to be answered first:
· How far from land are you?
· How choppy is the sea?
· Are you in storm conditions?
· Are there sharks or killer eels nearby?
· And you Andy, a physicist, should ask how far is it from the plane of the jump deck to the plane of the water and whats your projected angle of entry?
· Are you yourself wearing any life preserving gear?
· Are there other options, e.g., hurling a life vest or float ring, launching a small rescue skiff, pretending you didnt see him drunkenly lurch off the deck and into the pounding sea, etc.?
Actually any number of things come to mind to seek clarification on prior to jumping into the bone crushing swell. Please reconsider your, I believe, hastily made life saving commitment or at least formally remove me from your implied listing of others that would leap willynilly to Kens rescue.
Vinny0August 23, 2005 at 1:00 pm #125648Vinny, Phlueeze too much focus on detail and far too much concern for the irrelevant – when you take a plunge into the sea all you need to have with you is a bar of soap. Armed with that you can always wash yourself ashore….:)
0August 23, 2005 at 1:17 pm #125649Whoa .. where do you live? Killer eels – they sound scary :)
0August 23, 2005 at 2:14 pm #125651Hi Andy U,
From memory, you are in the London area, i suggest killer eels are nowhere near as harmful as jellied eels – yukkkkk….
Jaybee0August 23, 2005 at 3:48 pm #125659Jaybee,
You should try pie and mash with green gravy ( … from the jellied eels!) … burp #@!
Andy0August 24, 2005 at 4:44 pm #125740
Case250Participant@Case250 Include @Case250 in your post and this person will
be notified via email.Hi Deep,
If I understand your question you just want to know if you have a gage that will measure accurately. You have conducted an R&R on the gage using standard parts. Well if the results show little variability in R&R then just interpret that to mean that the gage will accurately measure your standards. However this dose not mean that the gage will accurately measure your process. For that you will need to do an R&R covering the process range with actual production parts. The truth is the gage can be “good” but not capable of measuring your process. That is, the gage may measure certain parts accurately but not your process parts. It is possible that the gage could fail using standard parts and pass using process parts. Hope this helps.
Thanks,
Casey0August 25, 2005 at 6:09 am #125787Hey Darth,
You know, I thought I was quite reasonable trying to explain to Andy my thoughts on his ideas. I even provided some reference to support my ideas, while carefully suggesting my concerns with his ideas. Perhaps Andy misunderstood my intentions, but I’m not sure. I traced the departure in his even tone at this post:
https://www.isixsigma.com/forum/showmessage.asp?messageID=77752
I can see that Andy has a moderate following judging by the response of Pepe, yourself, and couple others. For me it’s really not a matter of entertainment or popularity. I’m here to both understand and render guidance where I can.
Shainin not withstanding, I work hard to provide guidance with some foundation in science, mathematics, finance, and business operations. Darth, I suspect you tend to do the same thing. So, if some become a bit rattled because they can’t support their thesis with anything other than good ‘ol logic–well, I say to them most businesses in the Western world are pretty screwed up because of good ‘ol logic.
The foundation of Six Sigma is based on facts–both with the data and with the methods used to evaluate the data. If we loose that precept, then we might as well give up the ship!
Sorry for wrinkling your good buddy!
Ken0September 8, 2005 at 8:40 am #126496Deep,
The purpose of a Gauge R&R is to get a ratio of the variation of the measurement system to the variation within a process (or the ratio of the variation of the gauge to the tolerance). You say the gauge measures many different parts. You need to pick a part you want to do the GR&R on. You need to now the process spread for that part. You need to obtain samples that cover that process spread. You then do the GR&R. The results will only be valid for that part because the process spread for that part will be different to the process spread for all the other parts. However, you will be able to drill down into the results to see whether there are any operator or operator / part effects going on. If there are they should be fixed.
Before you start, ensure it’s calibrated. If you want to check the gauge to another similar gauge (customer, other plant, etc.) then the use of standard blocks and a paired ttest would tell you whether the results between the two are the same.0 
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