Hi.

(I took one stats class and for some reason I get stuck with this stuff... :confused: )

Here is the situation ( I apologize in advance if this makes no sense - the more I think about this the more confusing it seems to be. I also apologize if I start to ramble on...)

I'm reviewing a product which has a spec of 0.66 ml -0.70 ml with a target of 0.68 ml.

Each lot consists of about 150 samples. Both lot (57) and lot (98) have means which round to 0.68 ml. Their standard deviations are very small, 0.004 and 0.007 respectively.

(Here (http://b-logarithm.blogspot.com/2005/05/jmp.html) is a screen shot of a JMP analysis I ran on the two lots -- Just scroll down a little.)

Since a few lots have a cpk less than 1 - the idea of increasing the upper spec was brought up - (there are 8 lots total - they are pretty evenly divided regarding how the bell curve lies - no values ever go out of spec though and ones that have the curve going out of spec are so only minimally like the one I showed above...)

If I recall - if the equipment used to measure these samples only reads to the hundredth place - I should only use that many places for any calculated values. In most cases this means my sd would be zero.

Something about this whole situation just seems wrong - though I'm not really sure what.

Can I really trust the values I am getting via JMP since it seems to be using way more decimals places (and I can't seem to change that...)?

Would there be some benefit in using equipment which calculates to a higher decimal place?

With such a tiny sd - wouldn't any value which does not exactly hit the target totally mess anything up even when it's within the specs? For example the machine can only give values of 0.66, 0.67, 0.68 0.69, 0.70 - yet with the sd being used - wouldn't we want to see if that 0.67 were actually a 0.665 or a 0.669? Would that make a difference in the long run?

I don't think changing the specs is the answer. If anything - more precise equipment seems to make more sense to me.

Comments? Suggestions? Answers to my rather nebulous questions?

Thanks so much.

Short answer, yes you need to go out more decimal places. go to 5 or 6 if need to show the actual variation

Hi Ralph.

Is the reason for that sort of what I had mentioned - the values we are getting are not really valid b/c of the decimal places?

Forget about capability for a minute. Before you can calculate a reliable Cpk number you have to assure that the process is in control. That is to say, that it's subject to only random variation. In order to determine whether or not the process is in control, you need to be able to identify variation to the extent necessary to see what it is you need to see. Changing the specification will not alter the fact that special-cause variation is present, if indeed it is present. If you construct a chart using 2-decimal-place numbers and everything piles up around the mean to the extent that you can't differentiate between individual points and their proximity to control limits, it's the same as putting on a blindfold before looking at the chart. Remember also that points beyond the +/- 3 sigma limits is just one test for normality; you also need to be able to detect runs, trends and other signs of instability, which might not be possible if everything is aggregated around the center ine.

Stick to your guns, as you are on the right track, and those who want to change the spec to make the cap index improve are not on the right track!

Like other posters, IMHO, I suggest you first improve the gauge out to 5 decimal places. Run gauge R&R for the tool. Then plot your data in a histogram to check for normality. Plot the points on a control chart (20 or more points over a significant amount of time), either using X bar or individuals charts. Since you have JMP, you can do an s chart for the process variation. Once you know the process is in control and data is normally distributed, then you can determine Cpk. Since you have a target, you could do Cpmk.



--QG

Like other posters, IMHO, I suggest you first improve the gauge out to 5 decimal places.
There probably isn't a need to use a more sensitive gauge; the question had to to with the scale of the chart, and the number of decimal places displayed.

Then plot your data in a histogram to check for normality. Plot the points on a control chart (20 or more points over a significant amount of time), either using X bar or individuals charts.
Sorry, QG, but this is a little confused. What's the purpose of the histogram? How can it be used to "check for normality"? Isn't that what the control chart is for? Are you saying that twenty points is sufficient for either an X-bar or an individuals chart?

YES you need more resolution in your gage. your spec limits go to .0X and your measurement equipment goes to .0X then you don't have enough resolution. You need at least .00X capability. The rule of thumb is 1:10 - your measurement device should have 1/10 the resolution of the spread of your data... You and the JMP chart have hit the nail on the head - you have what is known as chunky data. It will behave essentially like ordinal data. All discussions about normality, control and capability are only theoretical until you can improve the resolution of the gage.

YES you need more resolution in your gage. your spec limits go to .0X and your measurement equipment goes to .0X then you don't have enough resolution. You need at least .00X capability. The rule of thumb is 1:10 - your measurement device should have 1/10 the resolution of the spread of your data... You and the JMP chart have hit the nail on the head - you have what is known as chunky data. It will behave essentially like ordinal data. All discussions about normality, control and capability are only theoretical until you can improve the resolution of the gage.
The "spec limit" is not ".0X." The specification width is .02, and you have no way of knowing whether .01 is "enough resolution." The 1:10 thing is a rule of thumb that's subject to the application of common sense. You may well be right, but it doesn't seem to me that accuracy is at issue here. The OP said,
if the equipment used to measure these samples only reads to the hundredth place - I should only use that many places for any calculated values. In most cases this means my sd would be zero.
This is where the problem lies--he should be using as many decimal places as it takes to see the spread of the data--if the SD calculates out to 5 decimal places, it shouldn't be truncated or rounded down to 2, and the y-axis scale should allow for the spread (and any signs of instability) to be seen.
Note that I agree that there should be GR&R (or some form of MSA) so that the contribution of gauge error can be ascertained.

I think that you need to have a good handle on the gage. Ideally the gage should be:
* precise (lots of decimal places = high resolution)
* accurate (if you measure a known standard, you get the correct value)
* repeatable (if you do the measurement several times, you get the same answer)
* reproducible (if someone else measures, they get the same answer)

Wow, I just invented (or maybe reinvented) an acronym - you want your gage to be up to PARR.
And while we're on memory aids, I used to have trouble remembering which was which between repeatable and reproducible until I realized: I know lots of people who repeat themselves, but it always takes at least two people to reproduce. :tg:

Anyway, it appears that the biggest problem is that your gage is not precise. If (and this is a big if) your gage is indeed repeatable, reproducible, and accurate but just not precise (i.e. the gage always rounds off to the correct 0.01), then I expect that you can pretty well trust the results of the JMP analysis and believe more decimal places in the caclulations than the original measurement. The idea of "significant digits" is a useful myth perpetuated by chemistry & physics teachers - it is a rough rule of thumb, but not foolproof. One big problem with limited precision is that it makes GR&R more difficult.


For your first data set, you got
x-bar = 0.677667
s = 0.004399
SE = 0.000359
N=150

0.0044 probably is a reasonable estimate of the standard deviation (if anything, it would tend to be a bit big, but it would also tend to have a big uncertainty). Similarly, 0.00036 is probably a reasonable esitmate of the strandard error, so 0.6777 +/- 0.00036 is a reasonable estimate of the mean of the sample. The extra digit and a half comes from the fact that you measured so many parts.

Again this assumes the gage is ARR and the distribution is close to normal. It also assumes that a significant number of data points are not the same as each other, which seems to be the case here. One problem is that typically the accuracy is designed to be about as good as the precision. If this is the case, then the mean could easily be shifted +/- 0.01, although s & SE would still be pretty good. If the R&R part is bad, then all bets are off.

Bottom line, buy a gage with at least 1 more digit of precision and do a GR&R. You (and your boss and you customer) will breath a lot easier.
Tim F

Just my $0.02 worth

...... you have what is known as chunky data......

Bev D

Now I know what to call it - chunky! Great description for insufficient resolution.

I am getting all too familiar with this chart pattern...I first saw it with really bad MSA results on our co-ordinate measuring machine.

We also had it on SPC charts of chemistry data, and I just noticed it last week on hardness data. And it's all my fault. All three of these devices allow the user (me) to set the number of decimal points reported. So I set them same as the customer spec. D'oh!

The SPC charts have what I called a sawtooth pattern, but now I like chunky better. A classic pattern right out of the textbooks. D'oh again.

Setting the devices to output one extra decimal place makes everything look much better.

The AIAG MSA manual calls this number of distinct categories (ndc) of data, and there are several threads that beat that topic to death, including one where I learned all of the above.

It seems to come down to "chart and perform calculations with all the decimal points you can get".

Can you "extend" the resolution by estimating another place. If it is something analog you can sometimes do this by estimating between divisons.

Thank you all so much for your help. I totally appreciate it.

(The process is in control btw - I should have mentioned that.)

Wish me luck trying to convince the big-guys!

:thanx:

Wow, I just invented (or maybe reinvented) an acronym - you want your gage to be up to PARR.
And while we're on memory aids, I used to have trouble remembering which was which between repeatable and reproducible until I realized: I know lots of people who repeat themselves, but it always takes at least two people to reproduce. :tg:
:agree1: I like it!!!!!

Now I know what to call it - chunky! Great description for insufficient resolution.


Yes, chunky data provides wierd results for standard deviations (it makes them calculate out too 'large', regardless of how you round the number or how many decimal places you carry. This makes for funky control charts and capability studies.
I believe that Dr. Donald Wheeler coined the phrase - he wrote an article about it soem time ago - although I've dealt with the phenomenon for 20 years or so now...

The 'chunky' part comes from the fact that the data can only 'fit' into very few categories. typically 2-4.

In his book Understanding Statistical Process Control (SPC Press), Wheeler writes about chunky data in a discussion of inadequate measurement units. He says the solution is to use smaller measurement units or "increase the variation within the subgroup to a detectable level". By taking data over a longer period of time, he says there will often be enough of an increase the variation make it detectable using the original measurement unit.

He adds that the problem of inadequate measurement units impacts a control chart when the measurement unit exceeds the standard deviation.

He suggests is that when you see only 5 possible values in the range chart, then your measurment unit borders on too large. Four units indicates inadequate measurement units.

This book, by the way, have saved my hide on one than one occasion.

In his book Understanding Statistical Process Control (SPC Press), Wheeler writes about chunky data in a discussion of inadequate measurement units. He says the solution is to use smaller measurement units or "increase the variation within the subgroup to a detectable level". By taking data over a longer period of time, he says there will often be enough of an increase the variation make it detectable using the original measurement unit.

This is a Quality Magazine, April 1999 atricle about that, or are you talking about autocorrelated data?.

The article by Wheeler describes the situation we are discussing (not auto correlated data

I believe that Dr. Donald Wheeler coined the phrase - he wrote an article about it some time ago - although I've dealt with the phenomenon for 20 years or so now...The 'chunky' part comes from the fact that the data can only 'fit' into very few categories.... typically 2-4.

BevD

Here is the chart where I saw it first. As you say, the data only fits 4 categories. It kind of jumps right off the page doesn't it!

Caster - great example! it does indeed jump right off the page...it's why I always tell my students to plot their data and think about it BEFORE they go perfrom a bunch of statistical tests on it. The graph "makes the stats make sense"

Why don't you apply Box-Cox transformation or take log of all your data and then try putting on normal distribution. See what patterna emergs.

Your compliments will be welcomed. :D

Thanks,

This is a Quality Magazine, April 1999 atricle about that, or are you talking about autocorrelated data?.

Bev is correct. We are talking chunky data not autocorrelation.

If the gage only reads to the 0.01, then the raw data should only be to that level of significance. You can have as many decimal places as you like in calculated values. But when you report the mean or sd, you need to round to 0.01. I trust the JMP output, as long as the raw data was correctly rounded.