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You are correct, however If I knew some shells have little or no powder, I would weigh ten that I knew were fine, with all other things as equal as you can expect. Then weigh the flat that is known to have an issue and would take out any that was off by 10 or 12 grains.

It's not a perfect system, but you'd limit the odds of shooting shells with no powder.

That being said, my more likely solution is curse at myself for ten minutes, get all pissed off, put the shells I messed up over in the corner and forget about them.
If the problem is truly no powder (since the original problem was powder clumping this might not be true) then your approach is easily implemented. I used Recoil Sissy's numbers from above to run a quick analysis. With a mean of 684.64 and standard deviation of 3.432 (from the 10 shells listed - it would be nice to have a little larger sample but 10 is OK for playing around) the chances of a shell that actually had the right amount of powder being 14 grains low are 23 in 1 million. Only 2 in a million will be 16 grains low.
At the same time, the false negative rate (keeping a bad shell) can be calculated by looking at the chances a shell with no powder would have so much excess weight in the other components that it would seem to weigh the right amount. Using the same numbers, the chance a no-powder shell would come in at the mean is again practically zero (1 in 10 million). What is more important is choosing a threshold for tossing suspect shells. Using the data we are playing with, I tried to choose a point that made good sense (again assuming there is no powder in some shells and 18 grains is the proper amount of powder). Depending on personal preferences, here are some examples.
1. Toss any shell that is 10 grains or more below the mean. This would give a false positive rate of 0.2% (this is the chance of throwing away a good shell). At the same time, the false negative rate is 1% (chance of keeping a bad shell).
2. Toss any shell that is 8 grains or more below the mean. This would give a false positive rate of 1% (this is the chance of throwing away a good shell). At the same time, the false negative rate is 0.2% (chance of keeping a bad shell).
3. Toss any shell that is 6 grains or more below the mean. This would give a false positive rate of 4% (this is the chance of throwing away a good shell). At the same time, the false negative rate is 235 in 1 million (chance of keeping a bad shell).

Since the consequence of a false negative is a "poof" a chance of keeping a bad shell isn't too distasteful. At the same time, tossing a good shell or two won't hurt too badly either. I'd probably rather toss more good ones than sit and wonder when I'll embarrass myself. If the problem was overloads, I'd tend to toss a lot more to avoid any chance of bursting a barrel.

Of course, the numbers would change for the OP because the variation could be different for his reloader/components. The real problem would occur if instead of powder/no powder there is something more complicated going on (which, with powder clumping, is certainly possible). If some shells have no powder, some have short throws, and some are overloaded this is a much more complicated problem and I'd just toss the bunch rather than spend the time and effort trying to set limits. This approach would work well for those of us who forget to fill the powder bottle sometimes...

I would be sure to weigh a bunch of empties and stike an average as the gentleman did above. I would be sure to use all one brand of shell.

I'll bet no conclusive facts will prove anything.
 

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Start with a big piece of cardboard and cut a slot in it the length of a loaded round ... in addition a couple of notches at one end for the rim of the shell to fit into.

Place a 100 watt bulb behind it and turn off the lights.

Roll the shells into the slot and it is like an x-ray!

You can see the end of the wad and any stray grains of powder!

PS ... doesn't work worth a damn on paper hulls!
 

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I have not weighed 100 but I often weigh 25 if the rounds are for league or registered....... Its only my standard on using the 10 grains light..... something is askew if 10 grains of anything is missing...... Larry
 

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Shoot them at a practice session. Don't waste your time cutting them up or trying to figure out your mistake. I couldn't tell you how many times I screwed up and made a similar mistake. I just shoot them up on the 16.
 

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Flashmax,
Just got back from a registered event in Colton Wa.
Shot STS at 16, shot Nitro27 at handicap....... Just weighed 50 of each.......STS were high of 126.4 grains and a low of 123.6 grains, the Nitro had a low of 125.1 grains and a high of 127.5 grains. My loading machine delivers very accurate charges of both shot and powder as long as I am using new shot. With reclaimed it is not quite as uniform. That is a reason I set 10 grains low as a requirement for a load check.. I know a particular recipe I use produces a loaded shell with a weight of about 690 grains...... I grab one every so often and weigh it...... if it is 10 grains under that I set it aside.
Larry
 

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Flashmax,
Just got back from a registered event in Colton Wa.
Shot STS at 16, shot Nitro27 at handicap....... Just weighed 50 of each.......STS were high of 126.4 grains and a low of 123.6 grains, the Nitro had a low of 125.1 grains and a high of 127.5 grains. My loading machine delivers very accurate charges of both shot and powder as long as I am using new shot. With reclaimed it is not quite as uniform. That is a reason I set 10 grains low as a requirement for a load check.. I know a particular recipe I use produces a loaded shell with a weight of about 690 grains...... I grab one every so often and weigh it...... if it is 10 grains under that I set it aside.
Larry
Your hulls are a lot more consistent than any I ever weighed. They vary in weight, they vary in length. Some are a full 1/8 th inch longer than others.
 
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The shells were all the same lot number, might make a difference? Never measured for length though..
Out of curiosity I weighed a couple high base Federal GM.. The low base Nitro27 weighs 14 grains more than the Federal brass based GM. Larry
 

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Flashmax....... your thoughts about hull variation got me to wondering about length...... I measured the same batch of STS and Nitro27 for length....... quite interesting as it would seem to indicate there are great variations in hulls based on Lot # or some such thing since your observations are different from mine. I was very surprised so I went through them for a second time....... STS revealed a fired length maximum of 2.707" and a minimum of 2.693" for a difference of .014" and the Nitro's had a maximum of 2.733" and a minimum of 2.714" for a difference of .019". My measuring was with a digital caliper so certainly is not exact but the minimal difference in length is perhaps the reason they were so uniform in weight? Perhaps tomorrow I may do the same with my Gold Medals. I do know that the more uniform the length (whatever it might be) the more uniform our crimps will turn out and that relates to pressures............ Larry
 

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Just measured the length of 50 Fed GM once fired hulls.... Longest was 2.744" and shortest was 2.728" for a difference of .01 6". Fairly consistent for a mass produced item that just suffered a severe internal explosion. In my small sample of 3 different hull types variations from hull to hull are minimal.... Larry
 

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Flashmax....... your thoughts about hull variation got me to wondering about length...... I measured the same batch of STS and Nitro27 for length....... quite interesting as it would seem to indicate there are great variations in hulls based on Lot # or some such thing since your observations are different from mine. I was very surprised so I went through them for a second time....... STS revealed a fired length maximum of 2.707" and a minimum of 2.693" for a difference of .014" and the Nitro's had a maximum of 2.733" and a minimum of 2.714" for a difference of .019". My measuring was with a digital caliper so certainly is not exact but the minimal difference in length is perhaps the reason they were so uniform in weight? Perhaps tomorrow I may do the same with my Gold Medals. I do know that the more uniform the length (whatever it might be) the more uniform our crimps will turn out and that relates to pressures............ Larry
Read this thread.

http://www.trapshooters.com/threads/why-do-remington-empties-vary-in-length-so-much.272218/#post-2536290

My hulls, though I didn't measure them, differ enough in length to visually notice. Joe's measured hulls follow what my eyes tell me. Given that both Joe and myself observe significant variations in length ( and thus amount and weight of plastic ) I still wouldn't use loaded shell weight variance to either keep or reject suspected bad loads.
 
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Good information in that link......... I bought a couple flats of Fiocchi a while back....... one was 1 oz and the other 1 1/8 oz. After firing a couple boxes of each I decided to try a reload and found the 1oz were uniformly shorter, so much so they would not crimp properly with a 1 1/8oz load.......... Larry
 
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