
shoo
Apr 9, 2008, 1:28 PM
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The standard deviation of this sample was 434 lbf. You get a 95% confidence interval of 48225734 assuming normal distribution. That means that you would expect that 95% of all quicklinks of this manufacture tested would fall within this range, and more importantly that 97.5% of all quicklinks would fail above 4822 lbf. Tested at 3sigma, the already very conservative standard used by most climbing manufacturers, you find that these quicklinks would get rated at 3974 lbf, or about 17.6 kn. You would thus expect that 99.87% of all of these quicklinks would fail at above 17.6 kn. It seems to me that the safe working load printed on the links is ridiculously conservative. In fact, it works out to well over 8 sigma. Edited to rework numbers.
(This post was edited by shoo on Apr 9, 2008, 3:26 PM)





adatesman
Apr 9, 2008, 1:35 PM
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shoo
Apr 9, 2008, 1:39 PM
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If you remove sample 3, you get the following, assuming normal distribution. Standard Deviation: 242 lbf 95% CI: 48465402 lbf Rating at 3 sigma: 4399 lb
(This post was edited by shoo on Apr 9, 2008, 3:25 PM)





tradklime
Apr 9, 2008, 1:48 PM
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Aric, Thanks for your efforts! I find the results encouraging. I was hoping they would at least double the SWL, and they all exceeded that. Strength wise, I think they are appropriate for rap stations especially if the rope runs through 2, as would the case be with a bolted anchor. The strength of the links exceeds that of SMC rings and 1 inch tubular webbing (without a knot). So I don't think its a concern. Regarding size, I have encountered similar sized links many times before and have never had an issue. Quicklinks are nice because they are easy to add to existing stations and are easy to replace. I purchased them from the following site awhile back: http://www.stageriggingonline.com/...iesquicklinks.html At the time, with shipping, it worked out to about 75 cents each. So the cost was very low. The label on the box was "Fehr" which is the online company's name, so not much info there other than "made in china". One thing about made in china stuff, this testing probably only represents links from that particular batch. It seems that quality control on both materials and manufacturing can be highly variable there. Regarding the lack of visual indication prior to breaking, the forces involved are high enough that an anchor of any type would, in reality, never see it. And if it did, other failures or indications would likely occur. And when redundant... just not an issue I believe. Thanks again





shoo
Apr 9, 2008, 2:03 PM
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I'm a little curious as to how precise the measurements are. If you want the 2nd Petzl video, it was left at 6901 lbf for a while before it broke. I would assume that means that the link would have broken at significantly lower forces than the final reading. Edited to change "accurate" to precise. My stats proffs would have killed me if they saw that. I'm also interested in accuracy, but precision was the topic of the discussion above.
(This post was edited by shoo on Apr 9, 2008, 2:25 PM)





jt512
Apr 9, 2008, 2:54 PM
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shoo wrote: The standard deviation of this sample was 434 lbf. You get a 95% confidence interval of 48225734. That means that you would expect that 95% of all quicklinks of this manufacture tested would fall within this range, and more importantly that 97.5% of all quicklinks would fail above 4822 lbf. Tested at 3sigma, the already very conservative standard used by most climbing manufacturers, you find that these quicklinks would get rated at 3974 lbf, or about 17.6 kn. You would thus expect that 99.87% of all of these quicklinks would fail at above 17.6 kn. It seems to me that the safe working load printed on the links is ridiculously conservative. In fact, it works out to well over 8 sigma. Edited to rework numbers. Your calculation of the confidence interval is correct, but you've drawn the wrong conclusion from it. The mean of the sample is 5278.2 lb, and the sample standard deviation is 434.7 lb. This is not the population standard deviation, only an estimate of it. Since the population SD is unknown, if we assume that the population is normally distributed, then the sample mean has a tdistribution with 5 degrees of freedom. The 95% confidence interval of the mean is equal to the mean +/ 2.571 SD/sqrt(5), or 48215734 lb. This gives us an indication of how precise our estimate of the population mean is, and not much else. In particular, it does not tell us that 97.5% of all such quicklinks would fail at or above 4821 lb. You are confusing the lower confidence limit of the mean with the 2.5th percentile of the population. Confidence limits are not estimates of population percentiles. What we do know is that the variability in breaking strengths is unacceptably high for applications on which lives depend. Assuming a population SD of 435, the coefficient of variation is 435 / 5278 = 8.2%. This shows that the manufacturing process is poorly controlled. I don't know what an acceptable CV is for climbing equipment under CE or UIAA standards, but my guess is that this result is at least 10 times too high. Take a look at the test results for the Petzl links, for comparison. Although there is not much we can conclude from such a small sample size, the two units broke only 6 lb apart. Given the availability of such a superior product, there is probably no excuse for using the Chinese links for any climbing application. Given the evidence of poor quality control, I would not rely on a single Chinese link for any climbing application whatsoever. Given the low loads expected from a rappel station, I would rap off two such links. However, I would use superior equipment if equipping the rap station myself. Jay
(This post was edited by jt512 on Apr 9, 2008, 5:07 PM)





shoo
Apr 9, 2008, 3:23 PM
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jt512 wrote: Your calculations are incorrect and you've drawn the wrong conclusion from them. The mean of the sample is 5278.2 lb, and the sample standard deviation is 434.7 lb. This is not the population standard deviation, only an estimate of it. Since the population SD is unknown, if we assume that the population is normally distributed, then the sample mean has a tdistribution with 5 degrees of freedom. The 95% confidence interval of the mean is equal to the mean +/ 2.571 SD, or 41606395 lb. No, you are incorrect. The 95% CI at 5df is the mean +/ 2.571 * Standard Error SE = SD/sqrt(n) Yes, I am assuming that the there is a normal distribution of failure points, mostly because it's the same assumption that major gear manufacturers make. With more data, I can verify this. It's also a pretty standard assumption to make when you're doing things like this. However, you are correct in that I should state my assumption of normal distribution, and I have edited my posts to do so.
(This post was edited by shoo on Apr 9, 2008, 3:42 PM)





tradklime
Apr 9, 2008, 3:49 PM
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jt512 wrote: This gives us an indication of how precise our estimate of the population mean is, and not much else, since we do not have sufficient evidence evidence to conclude that the population is normally distributed. In fact, we know essentially nothing about the distribution. For instance, who is to say that 1 link out of 100 isn't simply pure junk and breaks at say 500 lb. I'm sure I'm showing my statistical ignorance with the following questions... How would you go about determining distribution? Don't you have a similar issue with any manufacturing process that doesn't test every item made? What's to say 1 in 100 Petzl links won't fail at 500 lbs?





jt512
Apr 9, 2008, 4:20 PM
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shoo wrote: jt512 wrote: Your calculations are incorrect and you've drawn the wrong conclusion from them. The mean of the sample is 5278.2 lb, and the sample standard deviation is 434.7 lb. This is not the population standard deviation, only an estimate of it. Since the population SD is unknown, if we assume that the population is normally distributed, then the sample mean has a tdistribution with 5 degrees of freedom. The 95% confidence interval of the mean is equal to the mean +/ 2.571 SD, or 41606395 lb. No, you are incorrect. The 95% CI at 5df is the mean +/ 2.571 * Standard Error SE = SD/sqrt(n) Yes, I am assuming that the there is a normal distribution of failure points, mostly because it's the same assumption that major gear manufacturers make. With more data, I can verify this. It's also a pretty standard assumption to make when you're doing things like this. However, you are correct in that I should state my assumption of normal distribution, and I have edited my posts to do so. You're right, so you've calculated the CI correctly, but you're missing the bigger picture. The lower 95% confidence limit is not an estimate of the 2.5th percentile of the population. The width of the 95% confidence interval will be (much) narrower than the difference between the 97.5th and 2.5th percentile of the population, precisely because the standard error of the sample mean is (much) smaller than the standard deviation of the population. I've edited my original post to reflect that your calculation of the CI is correct, and to hopefully clarify why your inference from it is mistaken. Jay





jt512
Apr 9, 2008, 4:33 PM
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tradklime wrote: jt512 wrote: This gives us an indication of how precise our estimate of the population mean is, and not much else, since we do not have sufficient evidence evidence to conclude that the population is normally distributed. In fact, we know essentially nothing about the distribution. For instance, who is to say that 1 link out of 100 isn't simply pure junk and breaks at say 500 lb. I'm sure I'm showing my statistical ignorance with the following questions... How would you go about determining distribution? Hehe. That's kind of a loaded question. In practice, you need a larger sample size. You can then use a number of graphical methods, such as histograms and QQ plots to check if the data reasonably approximate a normal distribution. There are also various statistical tests for normality, none of which, to the best of my knowledge, are very useful.
In reply to: Don't you have a similar issue with any manufacturing process that doesn't test every item made? What's to say 1 in 100 Petzl links won't fail at 500 lbs? Our problem is that we're basing a decision on just 6 units. Legitimate manufacturers test thousands of units, so they have a very good understanding of the distribution of failure loads. In a properly controlled manufacturing processes the SD is quite small compared with the mean. Published independent tests of climbing gear have demonstrated this. When a legit manufacturer quotes a 3sigma rating you can be confident that even the < 1/1000 unit that doesn't meet the 3sigma standard will still have a failure point that is quite close to the standard (since the SD is small). Jay
(This post was edited by jt512 on Apr 9, 2008, 5:06 PM)





AlexCV
Apr 9, 2008, 8:52 PM
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jt512 wrote: Our problem is that we're basing a decision on just 6 units. Legitimate manufacturers test thousands of units, so they have a very good understanding of the distribution of failure loads. In a properly controlled manufacturing processes the SD is quite small compared with the mean. Published independent tests of climbing gear have demonstrated this. When a legit manufacturer quotes a 3sigma rating you can be confident that even the < 1/1000 unit that doesn't meet the 3sigma standard will still have a failure point that is quite close to the standard (since the SD is small). Another thing is that a reputable manufacturer with good quality control processes will also performQC checks on every batch they produce and use tools like the WECO rules (the curious might want to google this) to make sure their batches are all very close to the target and to detect deviations early in the production cycle, before the products gets out of specs.
(This post was edited by AlexCV on Apr 9, 2008, 8:53 PM)





majid_sabet
Apr 9, 2008, 8:57 PM
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nice work





tradklime
Apr 9, 2008, 9:46 PM
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jt512 wrote: Our problem is that we're basing a decision on just 6 units. Legitimate manufacturers test thousands of units, so they have a very good understanding of the distribution of failure loads. In a properly controlled manufacturing processes the SD is quite small compared with the mean. Published independent tests of climbing gear have demonstrated this. When a legit manufacturer quotes a 3sigma rating you can be confident that even the < 1/1000 unit that doesn't meet the 3sigma standard will still have a failure point that is quite close to the standard (since the SD is small). And yet well respected climbing manufactures have recently implemented recalls of defective equipment that has made its way into the hands of consumers. I hear what you're saying, but what does that say of the many thousands of climbs equipped with similar quicklinks, hardware store chain, welded coldshuts, and god knows what types of bolts (and how they were installed), all the while failures are extremely rare. This is for many reasons, but mostly because the equipment is more than adequate for the loads exerted upon it. Another thing, the manufacturer only declares a SWL of 1550. It could be that they have tested 1,000s and due to variability are unable to state (based on statistical standards) anything more. That doesn't make it a bad product per say, and it doesn't necessarily make it unsuitable for all climbing applications. Ultimately, climbers need to employ judgment and common sense when using gear, 3sigma or otherwise. We need take responsibility for our own safety and decide if the gear we are trusting our lives to is adequate. And this, of course, speaks nothing of the rock, trees, and other natural features that we routinely trust our lives to.





jt512
Apr 9, 2008, 10:05 PM
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tradklime wrote: jt512 wrote: Our problem is that we're basing a decision on just 6 units. Legitimate manufacturers test thousands of units, so they have a very good understanding of the distribution of failure loads. In a properly controlled manufacturing processes the SD is quite small compared with the mean. Published independent tests of climbing gear have demonstrated this. When a legit manufacturer quotes a 3sigma rating you can be confident that even the < 1/1000 unit that doesn't meet the 3sigma standard will still have a failure point that is quite close to the standard (since the SD is small). And yet well respected climbing manufactures have recently implemented recalls of defective equipment that has made its way into the hands of consumers. Yes. In spite of the QC. Take away the QC and things would be much, much worse.
In reply to: Another thing, the manufacturer only declares a SWL of 1550. SWL is an industrial/construction industry term. I'm not too familiar with it. I have a vague notion that SWL is 1/4th the anticipated maximum load.
In reply to: It could be that they have tested 1,000s and due to variability are unable to state (based on statistical standards) anything more. The large standard deviation indicates that the quality control process is inadequate for use in a process on which lives depend. I've already stated that.
In reply to: That doesn't make it a bad product per say, and it doesn't necessarily make it unsuitable for all climbing applications. Yes, actually it does, and it does. Jay





shoo
Apr 9, 2008, 10:18 PM
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JT: There are many ways to interpret a CI, all following different paradigms of statistics. In these case, I am using the convention consistent with what has been stated by Black Diamond on their testing website. http://www.bdel.com/about/3_sigma.php It is not the only interpretation, nor is it the most technically correct, but it is arguably the most useful interpretation in this case. Alternatively, you can state that you are 97.5% sure that the biners will fail after the lower confidence level. I believe this is the interpretation to which you are alluding. It is also a correct, albeit vague, definition. Strictly speaking, if the failure of point quicklinks is in fact distributed normally, my interpretation will hold true and only 2.5% of quicklinks of that manufacture would be expected to fail above the lower limit stated. Yes, it's true that I don't know if failure is normally distributed, but it's really the best assumption in this case since similar objects tested in similar ways have normal distributions of their failures. Here's my personal take on the matter. I am confident that the results show breaking strength consistent enough to use in most climbing applications. That being said, I'd generally rather use equipment from companies whose consistency is constantly being monitored, such as a reputable climbing company. However, being the economist I am, there is value in using alternative producers, in that it helps drive the price of similar goods down. Ultimately, it depends on just how big the consistency and price differences are.





rjtrials
Apr 9, 2008, 10:29 PM
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jt512 wrote: tradklime wrote: In reply to: That doesn't make it a bad product per say, and it doesn't necessarily make it unsuitable for all climbing applications. Yes, actually it does, and it does. Jay Jay, Im not familiar with the ratings on most 5/16 quicklinks, but you seem to be opposed to their usage in climbing. I have seen MANY quicklinks in action on permadraws and/or anchors. What is your take on the general usage of quicklinks over biners? RJ





jt512
Apr 9, 2008, 10:49 PM
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shoo wrote: JT: There are many ways to interpret a CI, all following different paradigms of statistics. No there are not. No, you are not. As I said before, you are confusing the confidence interval, which is based on the distribution of the sample mean, with the distribution of the population of the individual quicklinks. Go back to your elementary statisitcs book.
In reply to: It is not the only interpretation, nor is it the most technically correct, but it is arguably the most useful interpretation in this case. No, it is just plain wrong. You are confused.
In reply to: Alternatively, you can state that you are 97.5% sure that the biners will fail after the lower confidence level. I believe this is the interpretation to which you are alluding. It is also a correct, albeit vague, definition. No, it is not what I'm getting. The confidence interval says nothing whatsoever about what percentage of units will fail at loads beyond some value.
In reply to: Strictly speaking, if the failure of point quicklinks is in fact distributed normally, my interpretation will hold true and only 2.5% of quicklinks of that manufacture would be expected to fail above the lower limit stated. No, it won't. The CI gives you information about the sample means, not the individual units.
In reply to: Yes, it's true that I don't know if failure is normally distributed, but it's really the best assumption in this case since similar objects tested in similar ways have normal distributions of their failures. I'm not aware of a single statistical application in which it is acceptable to assume normality without evidence, and I do statistics for a living. Regardless, it is a minor point in comparison with your gross failure to understand the difference between the distribution of the sample mean and the distribution of the population of individual units. Jay





jt512
Apr 9, 2008, 11:02 PM
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rjtrials wrote: jt512 wrote: tradklime wrote: That doesn't make it a bad product per say, and it doesn't necessarily make it unsuitable for all climbing applications. Yes, actually it does, and it does. Jay Jay, Im not familiar with the ratings on most 5/16 quicklinks, but you seem to be opposed to their usage in climbing. I have seen MANY quicklinks in action on permadraws and/or anchors. What is your take on the general usage of quicklinks over biners? RJ I have no opinion on quick links in general. I would, however, not use these particular Chinese quick links, based on the results of this testing. Jay
(This post was edited by jt512 on Apr 9, 2008, 11:03 PM)





shoo
Apr 9, 2008, 11:12 PM
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I'm going to go ahead and concede this one. It's been a few years since I've taken an intro stats course, and it's entirely possible I've misremembered something, and I don't do stats for a living. It looks like I'm going to have to pull out some old textbooks to reread this stuff. Edited to add: Ok, just pulled out my old stats book. Strictly speaking, there ARE multiple interpretations for CI, as I was stating earlier, but that's not relevant. Do a search if you're interested. The better interpretation, at least by the book I'm using, is that there is a 95% chance that the true mean lies within the bounds of the confidence interval.
(This post was edited by shoo on Apr 10, 2008, 10:56 AM)





jt512
Apr 10, 2008, 12:08 AM
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In reply to: On another note, we don't know the true population mean or standard deviation. Right, but we have unbiased estimates of both. Therefore, we can compute an unbiased estimate of any population percentile, provided we're willing to accept the normality assumption. The problem is that our sample size is so small that our estimate, though unbiased, will be very unreliable. Say we want to estimate what the 3sigma rating should be. That is, we want an estimate of mu minus 3*sigma. Our point estimate would be Xbar minus 3*S, where S is the sample standard deviation. This works out to be 5278  3*475 = 3973 lb. That doesn't seem too bad, but we've already seen that our estimate of the mean is subject to an error of around +/ 350 lb. S is also subject to sampling error. A 95% confidence interval for S turns out to be 2711066 lb. So it is conceivable that the true 3sigma rating could be as low as (5278  350)  3*1066 = 1730 lb. And this still assumes that the distribution is normal, an assumption which is completely unjustified. For all we know, the Chinese have no QC whatsoever, and some significant percentage of their quicklinks are utterly worthless. Anyway, I've rushed through these calculations in order to finish them before my dinner is ready, so please check my math. I might be a statistician by training, but that doesn't mean I can do arithmetic.
In reply to: It is my understanding that if the true population standard deviation is unknown, you use t at df instead of z, which should yield an estimate of the CI for the population. Please correct and/or PM me if this interpretation is wrong. There's no such thing as a "CI for the population." When the population is normally distributed the distribution of the sample mean from a sample of N has a tdistribution with N  1 degrees of freedom. But, again, if we're interested in determining what percentage of the individual units will fall above or below some arbitrary cutpoint, we don't care at all about the distribution of the sample mean; we care about the population distribution. Jay
(This post was edited by jt512 on Apr 10, 2008, 1:43 PM)





qwert
Apr 10, 2008, 5:16 AM
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Did you know that there is 57,13789346730947593023% risk of a fight breaking out when two statisticians are in the same room I dont want to go into all the statistics stuff, but from what i see i woudl say it is safe to conclude that even cheap quicklinks can be used for rappeling without problems. However you cant tell if your rap anchor will be only used for rappeling. what happens if someone uses it as protection, when linking pitches together and takes a big fall on it? im shure you could find other "misuses" of rap anchors. Still, the breaking strengths from this test are high enough for even the hardest falls, but the small number of chiniese quicklinks, and the lack of any information about manufactuerer and so on, leave a lot of room for speculation. What happens if the next batch is made of steel from another supplier? What happens if the online reseller gets the next batch from another manufacturer? How does the manufacturing company make shure that they produce stuff of the same quality? How did they get the numbers for their (grossly of) WLL? All i all not very confidence inspiring. most likely the stuff will hold about everything you get on it in nomral climbing applictations, but it has some ungood feeling. I see the issue for someone how equips dozends of rap stations, but for the climber wanting to carry somehting to be prepared to enventually build a rap station i woudl say the best solution is to just carry a cheap aluminium biner and a bit of tape. 100% certified climbing gear, and lighter to carry. qwert





adatesman
Apr 10, 2008, 9:56 AM
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shoo
Apr 10, 2008, 11:04 AM
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Summary of statistical argument for those who don't care: My calculation of the confidence interval was correct, but the interpretation of it was not. I maintain that whether or not you can assume normality is largely at the discretion of the user. My apologies for poor tone used earlier.





tradklime
Apr 10, 2008, 11:06 AM
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jt512 wrote: In reply to: It could be that they have tested 1,000s and due to variability are unable to state (based on statistical standards) anything more. The large standard deviation indicates that the quality control process is inadequate for use in a process on which lives depend. I've already stated that. In reply to: That doesn't make it a bad product per say, and it doesn't necessarily make it unsuitable for all climbing applications. Yes, actually it does, and it does. Jay I would agree with you if it were an industrial/ work place application, with all the inherent legal liabilities, but were are talking about a voluntary, relatively high risk recreational activity. There are more ways for a product to be safe than ensuring absolute consistency. If the product is to be exposed to forces at or near its limits, then 3 sigma is extremely important. It becomes less important if the realistic loads are significantly less than the product's ultimate strength. These quicklinks all broke at forces 5 times higher than they would realistically ever experience as part of a rap anchor. Personally, if I came across a rap anchor where I'd be relying on two of these links, I would be much more concerned about the knotted sling they're attached to, or the tree the sling is around, or the bolts that I can't actually inspect, or possibly even the rock the bolts are in.





tradklime
Apr 10, 2008, 11:17 AM
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qwert wrote: However you cant tell if your rap anchor will be only used for rappeling. what happens if someone uses it as protection, when linking pitches together and takes a big fall on it? How much do we need to dumb down this sport? If someone is linking pitches and clips into the quicklink on a bolt rather than the hanger the quicklink is attached to, especially when the quicklink is clearly stamped SWL1550, ...well I don't know what to say about that person's judgement. Sounds like a Darwin Award to me.
In reply to: What happens if the next batch is made of steel from another supplier? What happens if the online reseller gets the next batch from another manufacturer? How does the manufacturing company make shure that they produce stuff of the same quality? We all agree on that, and we all agree that the sample size is too small to make reliable judgements about the manufacturing process in general. However, I do wonder about the statistical signifance of the sample size relative to the box of 50 that I pulled them out of. How does that compare to testing 1000's out of millions produced?








