Cpk's, specifications and tiny sd's - Resolution of measurement equipment

[EMGee]

Hi.

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

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 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.

[ralphsulser]

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

[EMGee]

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?

[Jim Wynne]

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.

[qualitygoddess]

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

[Jim Wynne]

Originally Posted by qualitygoddess

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.

Originally Posted by quality goddess

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?

[Bev D]

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.

[Jim Wynne]

Originally Posted by Bev D

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.