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  1. #46
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    Hi Dom,

    I've heard of and use/used the 2X sigma rule of thumb as well. For the above table the CI's were calculated via a hand entered formula (Ave + (Std. Dev/N1/2) following Confidence Interval for the Mean. I haven't run any tests of the distribution such as skewness and kurtosis but I may ask my statistician to check these and the saw data for me for giggles.

    I went back and re-calculated using the Excel CONFIDENCE function with alpha - 0.05, N = 15 and using the 'group' standard deviations reported. Here are the results. The CONF column gives the returns of the function.


    Again, thanks for asking and noticing. It's nice to have technical comments.

    Cheers,
    Rob
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

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  3. #47
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    Hi Rob

    I'm following and dredging the brain for what I remember from all the statistics I was exposed to (a hesitate to say "learnt") over my career. I'm sure that I got a good result in at least one course in statistics. But that was some time ago.

    I must admit to never being comfortable calculating Standard deviations when the population size is only 3, and even averages can get a bit dodgy when the sample size is very small.

    But as I said, I'm following and trying to draw useful conclusions from your work, especially as to when the diminishing returns from successively finer stones kick in.


    thanks for the effort and sharing
    regards from Alberta, Canada

    ian

  4. #48
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    Ian,

    Thanks for your reply. As to the number of chisels sampled I agree that N is small but remember my purpose here is to get an idea of what the physical and technical characteristics of chisels made by various manufacturers are, I'm not trying to prove what the population characteristics are. On the technical point the results presented are sample standard deviations (Excel STDEVA) not population standard deviations (STDEV).

    Nonetheless the data I've generated does give me some insights into how controlled the manufacturing processes are. The LV PM-V11 chisels are impressively consistent within and between chisels and the LN and Narex mortise chisels are surprisingly and somewhat less surprisingly respectively (given the prices) inconsistent.

    Consider the LN chisels. The maximum hardness measured was HRC 62.2 and the minimum was 60.1. Given the observed sigma (Std. Dev.) of 1.64 I would need a total of 18 chisels to be able to show, with an alpha of 0.05 and power of 80%, that those two chisels are significantly, statistically speaking, different. Doing that comparison wasn't my goal.

    Looking at another extreme of variability in this dataset, the Narex mortise chisels, the softest chisel was HRC 50.97 and the next closest was 56.60 for an effect size of 5.63. Using the sigma of 0.76, N is 1, a nonsensical result so in truth N is two because I need to measure a minimum two chisels to be able to compare them. Thus I can say that the variability observed in the Narex mortise chisels is statistically significant and my assertion that their heat treating and QC departments need some help is stronger.

    Finally, turning to the tightest bunch, the LV chisels range from HRC 58.4 to 59.3 with a sigma of 0.42. To be able to make a similar assertion I'd need to test a total of 7 chisels, exactly the number I've bought.

    Like you I don't consider myself a statistician but I'm familiar with and know how to select and use the appropriate statistical tools for these studies. If I have a question I have ready access to an expert who, fortunately, actually enjoys helping me analyze the results of my various studies. He has for instance validated the results of my study of saws (Hardening of sawplates) which by the way is a study designed to identify population and sub population characteristics and is consequently much larger.

    If these studies were truly important, in the sense of drug development important or cancer diagnostic test development important, they'd be much bigger and extensively controlled but given my more limited goal of understanding I think they'll do.

    Regards,
    Rob
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

  5. #49
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    Thanks Rob,

    It's been a little while since I looked at uncertainties and to be honest it feels a bit too much like work to go back over it right now haha. I think you are right to use the N^1/2 divisor for the standard deviation in each group of measurements.

    Your approach is a little different to what I'm used to with uncertainties, where I am used to looking at uncertainties associated with calibration of transducers. In that case, we typically look at all of the Type A (random or repeatability component - as in your case, and calculate the ESDM - experimental standard deviation of the mean using the same formula you have referenced) and Type B (Systematic) components which include the calibration uncertainty of the reference transducer/mass/measurement device, any temperature coefficients, barometric pressure coefficients, geometric uncertainties, drift, resolution and readability etc. We determine the uncertainty of each individual component, along with the associated degrees of freedom, ensuring that common units are used - usually V or %, and then calculate the combined standard uncertainty as well as the combined degrees of freedom, which provides the coverage factor from the students T table, and then calculate the expanded 95% uncertainty for the stated calibration sensitivity by multiplying the combined uncertainty by the coverage factor. Not sure if that makes sense. You seem to be taking a slightly different approach, but I'll confess I haven't applied the time / brain power to properly consider your case - like I said, feels way too much like work and I just started holidays .

    Aside from the correction applied using the "known" hardness sample, I don't think I saw you considering the uncertainties associated with that reference block (which should have an associated uncertainty from its calibration cert), or the test apparatus (not sure there are many associated with it though). Seems like you are going about it in a logical and well thought out manner in any case, and probably more rigorous than strictly necessary. Good work.

    Cheers,

    Dom

  6. #50
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    Hi Derek,

    Sorry for the delay in responding to your post, lot's of things on my plate these days. I've been studying these:

    Powder metallurgy books 122217.JPG

    Quite by coincidence I was reading the chapter in the 10th ed. (green covered volume) on Cold Isostatic Pressing when the LV chisels arrived. On the basis of their appearance and characteristics I wouldn't be at all surprised that this method was used in their manufacture. Fascinating books and highly recommended.

    Regards,
    Rob
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

  7. #51
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    Dom,

    The spec on these blocks is + 0.5 units. Most of my calibration data are better. These are the current cal data and a graphic showing how the measured hardnesses compare to the actual hardnesses.



    It's also important to remember that this is a handheld portable tester. I was amazed at how tight the results it produces are. Not as good as the HR-150A but I can put it in a large pocket.

    P.S., the 1/8" PM-V11 chisel just arrived. HRN45 = 72, which corresponds to HRC 65! More data later...
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

  8. #52
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    Quote Originally Posted by rob streeper View Post
    Dom,

    The spec on these blocks is + 0.5 units. Most of my calibration data are better. These are the current cal data and a graphic showing how the measured hardnesses compare to the actual hardnesses.



    It's also important to remember that this is a handheld portable tester. I was amazed at how tight the results it produces are. Not as good as the HR-150A but I can put it in a large pocket.

    P.S., the 1/8" PM-V11 chisel just arrived. HRN45 = 72, which corresponds to HRC 65! More data later...
    Hi Rob,

    This is where I'm not sure if I understand your approach and where I believe that I may differ in my understanding; possibly because I haven't properly understood what you have done. Just to be clear, I'm not trying to say you've done anything wrong or nit-pick, and I am just as likely to be wrong in either my interpretation of what you are doing, or in my own knowledge so don't take it as criticism, but rather a discussion.

    If your reference hardness blocks have a +-0.5 HRC uncertainty, presumably at 95% confidence interval, and you have made 3 measurements on a block, where you therefore have an associated measurement uncertainty on your measured average which would be the ESDM of your measurements, then you need to combine the uncertainty of the calibrated blocks (0.5 @ 95%) and the ESDM of your measurements. So your ESDM would be the standard deviation of your 3 measurements divided by root 3. The associated degrees of freedom of this would be n-1 = 3-1 = 2, and so the corresponding k-factor would be approx 3 (+-3 x ESDM for 95% confidence of the actual mean). You would then assume that the degrees of freedom of the uncertainty of the calibrated blocks to be perhaps 30 (indicating you are pretty confident of the +-0.5 HRC being correctly derived) and therefore the corresponding k factor would be about 2.04. You would then divide your 0.5 HRC uncertainty by 2.04 to get your component uncertainty, and use this and the component uncertainty from your measurements (ESDM) to calculate the combined uncertainty. Then use the degrees of freedom for each to calculate the combined degrees of freedom. Then look up the corresponding k-factor for that combined degrees of freedom to get your multiplication factor that you multiply the combined uncertainty by to get the expanded uncertainty - which is your +- uncertainty for 95% confidence. Now, we still haven't incorporated systematic sources of uncertainty such as resolution, readability (depending on the analogue graduations and your own eyesight), any temperature effects etc. But this would give you a starting point.

    Edit - This, after applying the correction, would basically give you the uncertainty of your reference / hardness tester - you then use this uncertainty to combine with the other uncertainties, including the ESDM for each tested chisel to get the uncertainty of measurement for the hardness of each chisel tested.

    Sorry, it would probably help my explanation if I worked through the numbers and showed the formulas etc, but I don't have time at the minute. Not sure if you follow my logic above.


    Cheers,

    Dom

  9. #53
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    Dom,

    I understand and agree with all you've written. Great to have your technical insights, my slide deck is getting close to 100 pages.

    My goal here is understanding the relative hardnesses of the tools rather than determining the true or absolute hardnesses of the various item's I've been testing. Of course the variability in the measurements is the composite of instrumental, operational/operator and test article variability but the relative variability of the various chisels is my real interest. All of the chisel measurements reported were done with the same instrument using the same methods with similar conditions.
    I'm not for controlling for other sources of variability such as environmental factors like temperature. I haven't noticed any influence on my measurements over time and for a study of this type it's probably trivial. The surface roughness is also left 'as manufactured' and I haven't done anything in the way of polishing or lapping to ensure uniform finish.

    If you'd like to run some numbers I'd say that the New Age instrument has a readability of 0.25 HRC units, I typically only read it to 0.5 though. The particular blocks I'm using are spec'd + 0.5 units but they came to me without the certs so I don't know what the actual manufacturer numbers are unfortunately.

    I'm thinking about expanding the number of measurements of the standards and doing a small scale method of limiting slopes analysis just to see what I get. I'll see how much free time I'm allowed between interruptions over the holidays.

    Happy holidays to you and yours.

    Cheers,
    Rob
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

  10. #54
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    While acquiring the data to answer the questions above another set of chisels arrived. Here are the data.

    Japanese chisels are pretty hard, harder than most Western brands.
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

  11. #55
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    Rob

    Interesting addition of JP chisels. In conjunction with the fish tail set it supports the generally held belief that JP chisels tend to be harder than their Western counterparts. The deviation appears to be mid range and bearing in mind these chisels could be hand forged I would have expected a greater range. Maybe this is a testimony to the skill of the JP blacksmiths. Very interesting particularly as these chisels are not high end.

    Regards
    Paul
    Bushmiller;

    "Power tends to corrupt. Absolute power corrupts, absolutely!"

  12. #56
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    This is my first run through the limiting slopes analysis. I'll audit, beautify, correct and add the other instruments as I go along. We're bunkering down for the upcoming freeze.
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

  13. #57
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    Quote Originally Posted by Bushmiller View Post
    Rob

    Interesting addition of JP chisels. In conjunction with the fish tail set it supports the generally held belief that JP chisels tend to be harder than their Western counterparts. The deviation appears to be mid range and bearing in mind these chisels could be hand forged I would have expected a greater range. Maybe this is a testimony to the skill of the JP blacksmiths. Very interesting particularly as these chisels are not high end.

    Regards
    Paul
    Third highest hardness and third lowest variability of a pack of fifteen t'aint bad Paul, I might have got a pretty good set of chisels here. I was thinking today I should add some Stanley's to balance out the pool. What's the opinion of the newer 750's?
    Innovations are those useful things that, by dint of chance, manage to survive the stupidity and destructive tendencies inherent in human nature.

  14. #58
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    Hi Rob

    Care to name the Japanese chisels here (perhaps I missed this)? It is my understanding (and experience) that there is a variation among makers, some deliberately harder than others. You cannot use one make as representative of all, in the same way that one Western chisel is not representative of all Western chisels

    Regards from Perth

    Derek
    Visit www.inthewoodshop.com for tutorials on constructing handtools, handtool reviews, and my trials and tribulations with furniture builds.

  15. #59
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    Default Japanese chisel identification

    Quote Originally Posted by derekcohen View Post
    Hi Rob

    Care to name the Japanese chisels here (perhaps I missed this)?

    Regards from Perth

    Derek
    Derek

    How's your Japanese?

    P1030163 - Copy (2).JPG

    This is a set Rob bought from me. I suspect they are from the lower end of the market purely on the basis I was able to afford them in the first place, but I don't recall exactly what they cost. Other than that I have no information on them. One of the JP specialists may be able to identify them.

    I have taken the liberty of showing the pic here because I have it and as Rob is dealing with a big freeze way down in Texas.

    Regards
    Paul
    Bushmiller;

    "Power tends to corrupt. Absolute power corrupts, absolutely!"

  16. #60
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    Quote Originally Posted by rob streeper View Post
    Third highest hardness and third lowest variability of a pack of fifteen t'aint bad Paul, I might have got a pretty good set of chisels here. I was thinking today I should add some Stanley's to balance out the pool. What's the opinion of the newer 750's?
    Rob

    I am very pleased you are happy with the JPs. On the Stanley chisels I checked the Aussie site, but they only seem to have the plastic handled (the old ones have a very tough plastic handle with a steel cap) Fat Max type and a limited range too. The 750 series with the Hornbeam handles may be limited to the States. I wasn't familiar with them at all and had to look them up.

    Regards
    Paul
    Bushmiller;

    "Power tends to corrupt. Absolute power corrupts, absolutely!"

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