The Limits of Repeatability

What’s in a Word: Accuracy, Precision, Repeatbility, and Tolerance

We expect that if our scale says a bullet weighs 202.4 grains then that’s it.

But from the title, I suspect you already know that’s not the whole story. There’s accuracy versus precision and, somewhere in there are also tolerance and repeatability. But all those are not what interests me at the moment.

Here’s what does: If I weigh the same bullet twice, will I get the same answer? Will that 202.4 grain bullet read “202.4” tomorrow? And the day after?

I’m interested in this because I want to sort some bullets and, because I have so many to do (3000+), I want to be as efficient as possible on the first attempt. I don’t want to have to go back and do it again. So the question is, how many piles of bullets should I make? Specifically: Will the bullets I put in the “200.0 grain” pile today belong in that same pile tomorrow or will some of them get moved to the “200.5” pile?

There, in a nutshell, is what I’m after. I want to know the range of weight, the tolerance, I can expect from one pile. It is the repeatability of the scale, its ability to measure a given weight from one day to the next and come up with the same answer.

Strategy

To find out how repeatable my scale is, here’s what I decided to do.

I would take ten bullets that weigh slightly different amounts – the batch of moly-coated 200 grain bullets I’ve been complaining about would be ideal – and, one bullet at a time and in random sequence, I would weigh each of them. I would then mix up the 10 bullets and do it again. And then again until I had five weighings and then I would see how much I got for each bullet in each set.

The key question would be whether a given bullet would weigh the same each time or not.

Would the scale repeatedly weigh the same bullet the same each time?

Results

Here are the “raw” results.

The first row, Set #1 above, is the first weighings of the ten bullets, recorded from left to right. Remember that I then shuffled the bullets and did it again. That’s Set #2. I continued this, shuffling the order of the bullets each time before re-weighing them. I stopped when I had completed five cycles, five sets.

Hence, five rows (separate weighings) of ten bullets (the columns). And because I shuffled the order of the bullets in each set, the weights appear in random order from left to right.

But this doesn’t show me how much the same bullet weighed in each set. For that, I need the same bullet lined up from top to bottom over the five sets.

So I sorted each row into increasing weight, left to right. This put the bullets in order by weight.

Here’s the result after the sort.

“But wait,” you might object, “if the scale is reporting a slightly different weight for a given bullet, isn’t it possible that bullet #1 might sometimes weigh heavier than bullet #2 and then sometimes the opposite? That would mean that column 1, for example, might not actually be the same bullet each time!”

I would have to answer, “Yes, that’s quite possible.”

“But my goal,” I would go on, “is to separate the bullets into different piles in a repeatable manner. If two bullets are so close that their weights shift their order from time to time, that variation would really put them into one pile.”

Sorting the weights according to the scale’s reading is really what I’m after, not the actual weight of the bullets.

Therefore, in this second table, if we read down each column vertically, we see what the scale said for something close to that weight. This is where the repeatability, or lack thereof, shows up.

And from the above data, it therefore looks like the scale’s repeatability for things weighing about 200 grains is going to be from 0.1 to 0.3 grains.

To make it easier to quantify this, I added rows for minimum, maximum, the range (maximum - minimum) and finally, the percent of variation (range / maximum). The worst case variation (above) was 0.15%. That means that if I weighed a 200.0 grain bullet but then weighed a bunch of other things before re-weighing that same 200.0 grain bullet a second time, the two readings of the same bullet might vary by 0.3 grains (200 * 0.0015).

That’s the number I’m after. It means that, for 200 grain bullets, a difference of 0.3 grain between two bullets (or the same bullet weighed twice) could be entirely due to the scale.

Conclusion

“So what?”

Good question: Does it matter?

For the scale I use, sorting to identical readings gives me bullets that are within 0.3 grains of each other, not 0.1 grains in spite of what the LCD says. The tests demonstrate that the weight of a given bullet will vary depending on the sequence in which they are weighed. Something in the scale is afffected by what came before.

So, my equipment won’t let me be separate bullet by weight any better than 0.3 grains even though it gives readings t0 0.1 grains. That’s the issue of repeatability.

Sorting

Therefore, my sorting of the moly-coated bullets–for the first 1000 with 3000 still to go–has been into “whole grain” buckets. There is a 200.anything bucket, a 201.anything bucket, and so forth.

For my next round of testing, I’m going to load and test the bullets in the 200 grain bucket. From the above, I know those bullets vary from 199.85 to 201.15 grains, a range of 1.3 grains and, if they perform well, I’ll know “that’s good enough.” (Actually, I’ll know that’s “more than good enough.”)

But if they don’t perform well and I suspect bullet weight variations might still be an issue, then I can sort them down to those that read (on the scale) EXACTLY the same, say 200.5 grains. But no matter what I do, there’s still going to be that 0.3 grains of non-repeatability. Those “identical weight” bullets may actually vary from 200.35 to 200.65 grains. Will that be good enough?

If so, I’ll have my answer. I’ll know how much weight variation is permissible and, in the future, I can sort bullets accordingly.

And if not, then I’ll also have an answer, and that is that at least with some bullets, it doesn’t matter how closely you match their weight. Some bullets will still just not perform at the long line.

So, my hope is that I’ll discover there is a weight variation that can be tolerated at the long line.

Is “within 1.3 grains” good enough or do I have to go all the way to 0.3 grains?

I hope to find out. And when I do, I’ll know its number.

[Phew!] I’m beat.

How about we go and shoot up some targets?

All right!