this is hands down the best explanation i have seen. I am a master's student in materials engineering and we covered this a few days ago. Thank you so much!!
Taylor, your lecture style is super engaging and very informative. This lecture on Weibull Analysis has me going into my next exam with great confidence!
Haha. I'm supporting bad habits! do me a favor and like subscribe and share so I can continue to grow this channel and help other homework procrastinators ;)
@@TaylorSparks I already did it, and I shared it also with all my classmates, so thank you again. But can you believe me if I told you that I saw your replay exactly at the time when you comment it, but as I'm a big procrastinator, I left it till today in order to view the video again Haha, Thanks so much
@@TaylorSparks No it was David W. Hoeppner. He was the ME chair. He would emphasize that strength data was not a straightforward look up number. He required BSME students to take a “Manufacturing Methods” class in order to understand that how a part was made, would alter its properties. Not only one of my favorite classes, but I was a guest lecturer at one session. Dr. Hoeppner was not the instructor for that class. Another idea that Dr. Hoeppner was passionate about was that “ ductile” and “brittle” were not material properties. They are failure modes. To demonstrate, usually, a teaching assistant would take some silly putty and produce a “brittle” failure. I think his main strength was fracture mechanics.
so glad to help! Check out the different playlists my channel has for materials science. We have our Materialism Podcast, intro to MSE, software tutorials, and a new python and materials informatics class that I'm putting together for the Spring.
ok, i came back here to leave this comment because i am stuck on a real-world situation. I have 25 samples of 3d printed parts i tested in the tensile machine. The maximum was about 55MPa for PLA+ and the low was around 46MPa. I have used the same rank formula as you, as well as the median rank method. I have found the slope (beta) also known as the shape parameter, but now i am trying to find the scale parameter known as n. The scale parameter (characteristic life), representing the time at which 63.2% of items are expected to fail. This value should be in the range of all my tensile strengths. when plotting the data in excel and getting a line, i have y=27.26x-86.048, if i do e^-86.048 to get n, its a HUGE number. so i have messed up somewhere haha. below are my tensile values i tried to use chatgpt but got some serious random errors. I am a mechanical engineer working on my masters but none of my classes went over this haha I am trying to use the cumulative distribution function (CDF) but it requires beta and n. CDF=1−e^-(t/n)^b any help would be excellent. Maybe chatgpt confused 46.1 46.7 47.3 47.9 48.3 48.6 49 49.2 49.8 50.1 50.4 50.7 50.9 51.5 51.8 52.1 52.5 52.8 53.1 53.2 53.9 54.4 54.6 55.2 55.6
Thanks for this great explanation. I'm confused about ln(ln(1/(1-F)) vs F. If I want to have a 1/1,000,000 chance of failure, I find the log(stress) value corresponding to the F = 1/1,000,000 along the data trendline. I don't use ln(ln(1/(1-F)) for that, right?
Hi Taylor, I am researching the strength of eggshells for two different diet groups. For the strength values, the Weibull distribution fits both groups very well, and I want to know if there is any statistical difference between these groups. Do you know how could I do this?
You will need to check to see if the confidence intervals of your Weibull fitting overlap or not. I didn't cover confidence intervals in this video but you can read about it
One thing you might try would be bootstrapping. Bootstrapping will allow you to create many many versions of your data and you could do Weibull fitting for each one and then take the average and standard deviation of those fits and see how they compare with one another.
This is the clearest explanation I've seen so far. It is unintuitive for me on how the failure rate is based on a rank and not a bucket, or histogram that counts failures. I'm going to have to spend some time looking into that. Any book or source you recommend for learning about F?
If what you mean is F, that is not the failure rate but the probability of failure. Say that you have 25 samples and length 5 mm is ranked at 6 in ascending length, this means that 6 out of 25 samples fail at length between 0 and 5 mm i.e. F(5 mm) = 6/25.
Hello Taylor, thank you for sharing these useful insights. I am wondering how we can determine the Potential Failure using the weibull analysis, or how can we plot the P-F curve using weibull
Thank you for the informative lecture. Could you also share the link to the Ch.15 Composites lecture as listed in the course outline shown at the right-side?
Thanks for the tutorial! I have one question regarding how you calculate F (in your case F = n-0.5/N). I have encountered other approximations for F like F = n-0.3/N+0.4 (mean rank approximation) or F = n/N+1. When is it more appropriate to use one or the other? Is there a relationship to the sample size? Thanks!
I'm currently designing a cost model for solar power plant, in which I should define the "average failure rate" of devices over its lifetime....how can I benefit from the Weibull distribution .....thank you.
One question, can anyone explain how the calculations are performed at 33:00? Otherwise, this is the first video that ever made sense to me. I've been trying to understand this for at least a year.
Any limitations of Weibull distribution? considering that we consider the data distribution to be linear. Also, can we use this Weibull distribution for the particle size distribution. Video was awesome!!!
When you ranked them, some of them have the same length (16th and 17th), so it should be the same rank otherwise it gives different failure rate for the same length ?
Hi Taylor! Fantastic explanation!! Thank you...My question is: the Length of failure in your excel spreadsheet it CAN BE MTBF??? Can I calculate reliability as you have done using the MTBF?
I imagine so. The first thing to try would be to see if it can be fit with the wibble equation. If so, then you should be able to use it as a probabilistic analysis tool
Thank you sir for this video. Can you please help me out for plotting weibull curves in excel based on service life prediction of building data. Plotting of Condition index vs.Time in years
@@TaylorSparks I will definitely share these Weibull classes with my materials engineering undergraduate colleagues here in Brazil. Also, I have some friends that already know the podcast, keep going with the awesome work!
Thanks for the great lecture. I'm confused on the intuition behind length of elongation of the component computation. Is it akin to the idea of that: we have 100 bars so we must calculate at least 1 failing and hence this is like changing the required 1 / 1 million to 1 / 100 million in the original equation?
So the example towards the end is estimating the component length elongation with 100 x area of bar with same failure rate, right? And the length is much shorter. If the component had the same area as the bar but 100 bars were used (so that force area is 100 times) then we would expect 1 of the components to break earlier than the average failure rate. And that is why we should have component length much shoter. Equivalent’ish to looking for 1/100 million failure rate in the original bar intuitively? I hope it makes sense now.
Once you get the EXP to one side of the equation you can take 1 over that entire side of the equation and it simply removes the negative sign from inside the EXP.
The weibull equation is not linear. It has an exp in it. We make it linear by plotting it the way we do. In those axes, the slope becomes the weibull modulus.
If i wanted to learn more about using excel in this way and this type of statistics, what would i take? thanks. I am graduating this month in mechanical at UVU but even in my undergrad, we hardly touched on this stuff, even at SLCC I actually learned more stats in my black belt independent study i did through an online company than i did my schools haha
Probability theory. That's what you want. If you want to keep learning, and since you are in Utah already, you might consider applying to our graduate program.
@@TaylorSparks i have thought about haha. I travel 120 miles one direction for school as i live in Brigham city. But i could check out the U and see. Thanks for replying.
@@LT72884 Salt Lake City is even closer than UVU. Actually, my most recent PhD grad from my group is living up in Brigham City because he works for Northrop Grumman. Once you are done with classes after the first two years, some programs even allow remote work. For example, my students typically do machine learning and so they can work from wherever.
@@TaylorSparks true, i grew up in draper :) but then went to usu for some school before switching majors. Slc is alot closer, even if the u is east. I really enjoy what i have learned about weibull and predictive failure from your videos. Ill start researching more on probability theory
@@TaylorSparks No sir. Annual rainfall of 22 years is given in cm (1960-1981). Q1: Estimate the annual rainfall with return period of 10 years and 23 years. Q2: What would be the probability of annual rainfall of magnitude equal to or exceeding 'X' cm. X is given. I have found using P= m/(N+1) formula just one hour ago but failed to understand clearly why using this
@@sayemasaliha1152 are you specifically being asked to use a wibal distribution? Have you tried fitting it to a weibel distribution yet? It might be the case that another distribution is going to be more accurate.
20:10 the ranking :: what if we left the data is it comes, in other words, without reranking it, let the first sample rank to be first, second be second and so on
this is hands down the best explanation i have seen. I am a master's student in materials engineering and we covered this a few days ago. Thank you so much!!
So glad I could help! Like, sub, and share so I can keep making content.
I like your teaching style. After 40 years as an Engineer, you're the first person who has explained Weibull and how to use it clearly and succinctly.
Glad to hear it! We need more practical applications of principles
thanks
The greatest video about Weibull i have ever seen. Focused on fundamentals!!.
Love you man, Finally found some one who is passionate about explaining this
🔥🔥🔥 my pleasure
Your explanation was superb. I plotted my own data as a Weibull plot as I went along with the video.
i would take this professors evvery class. what a positive attitude man
I teach materials informatics in the spring. Videos are on TH-cam and more coming !
Taylor, your lecture style is super engaging and very informative. This lecture on Weibull Analysis has me going into my next exam with great confidence!
Thank you so much for this feedback! We have a podcast "Materialism" if you're interested in more! Good luck on your exam.
Thank you very much. Really awesome. I'm a experienced engineer and this is the best explanation on Weibull I've seen so far. Tks again.
Super glad to help. Make sure to subscribe to see my other videos!
@@TaylorSparks do you have a udemy course on reliability analysis and FALIURE RATE OT ANY OTHER WEBSITE WHERE YOU HAVE A COURSE
I am doing a structural analysis using steel, this Weibull distribution is exactly what I am looking for. Thank you, professor.
Glad to help homie!
You saved me, I left all the homework till last minute, but luckily I found this awesome video, well explained thanks so much.
Haha. I'm supporting bad habits! do me a favor and like subscribe and share so I can continue to grow this channel and help other homework procrastinators ;)
@@TaylorSparks I already did it, and I shared it also with all my classmates, so thank you again. But can you believe me if I told you that I saw your replay exactly at the time when you comment it, but as I'm a big procrastinator, I left it till today in order to view the video again Haha, Thanks so much
what a nice lecture for Weibull distribution. Thank you so much!
Very cool. While I was at “the U”, Dr. Hoeppner was really big on the Weibull. Glad to see it live on.
Is this Mike hoeppner in chem eng?
@@TaylorSparks No it was David W. Hoeppner. He was the ME chair. He would emphasize that strength data was not a straightforward look up number. He required BSME students to take a “Manufacturing Methods” class in order to understand that how a part was made, would alter its properties. Not only one of my favorite classes, but I was a guest lecturer at one session. Dr. Hoeppner was not the instructor for that class. Another idea that Dr. Hoeppner was passionate about was that “ ductile” and “brittle” were not material properties. They are failure modes. To demonstrate, usually, a teaching assistant would take some silly putty and produce a “brittle” failure. I think his main strength was fracture mechanics.
Taylor, that was impressive. Now, I need the 2 variable model.
This was really good and informative! Thank you so much!
My pleasure!
Doing concrete analysis at university now. Trying to understand what exactly I am looking at on this Weibull linear graph and now I do! Thankyou!
This is great! Thank you for uploading!
You are an amazing professor.
Thanks so much!
Just for records. I was the 1000th user to like this video!
😂
very nice way you teach Taylor..!! I will search more videos of yours.
so glad to help! Check out the different playlists my channel has for materials science. We have our Materialism Podcast, intro to MSE, software tutorials, and a new python and materials informatics class that I'm putting together for the Spring.
Explained it very nicely.Thank you.
Thanks! Share with your peers!
Great explanation Sir
ok, i came back here to leave this comment because i am stuck on a real-world situation. I have 25 samples of 3d printed parts i tested in the tensile machine. The maximum was about 55MPa for PLA+ and the low was around 46MPa.
I have used the same rank formula as you, as well as the median rank method. I have found the slope (beta) also known as the shape parameter, but now i am trying to find the scale parameter known as n. The scale parameter (characteristic life), representing the time at which 63.2% of items are expected to fail. This value should be in the range of all my tensile strengths.
when plotting the data in excel and getting a line, i have y=27.26x-86.048, if i do e^-86.048 to get n, its a HUGE number. so i have messed up somewhere haha. below are my tensile values
i tried to use chatgpt but got some serious random errors. I am a mechanical engineer working on my masters but none of my classes went over this haha
I am trying to use the cumulative distribution function (CDF) but it requires beta and n. CDF=1−e^-(t/n)^b
any help would be excellent. Maybe chatgpt confused
46.1
46.7
47.3
47.9
48.3
48.6
49
49.2
49.8
50.1
50.4
50.7
50.9
51.5
51.8
52.1
52.5
52.8
53.1
53.2
53.9
54.4
54.6
55.2
55.6
Thanks, Prof. Using this for some fiber analysis. Hopefully, the manuscript gets accepted.
Thanks for this great explanation.
I'm confused about ln(ln(1/(1-F)) vs F.
If I want to have a 1/1,000,000 chance of failure, I find the log(stress) value corresponding to the F = 1/1,000,000 along the data trendline. I don't use ln(ln(1/(1-F)) for that, right?
Hi Taylor, I am researching the strength of eggshells for two different diet groups. For the strength values, the Weibull distribution fits both groups very well, and I want to know if there is any statistical difference between these groups. Do you know how could I do this?
You will need to check to see if the confidence intervals of your Weibull fitting overlap or not. I didn't cover confidence intervals in this video but you can read about it
One thing you might try would be bootstrapping. Bootstrapping will allow you to create many many versions of your data and you could do Weibull fitting for each one and then take the average and standard deviation of those fits and see how they compare with one another.
I loved the explanation .
This is the clearest explanation I've seen so far. It is unintuitive for me on how the failure rate is based on a rank and not a bucket, or histogram that counts failures. I'm going to have to spend some time looking into that. Any book or source you recommend for learning about F?
If what you mean is F, that is not the failure rate but the probability of failure. Say that you have 25 samples and length 5 mm is ranked at 6 in ascending length, this means that 6 out of 25 samples fail at length between 0 and 5 mm i.e. F(5 mm) = 6/25.
Hello Taylor, thank you for sharing these useful insights. I am wondering how we can determine the Potential Failure using the weibull analysis, or how can we plot the P-F curve using weibull
Thank you for the informative lecture. Could you also share the link to the Ch.15 Composites lecture as listed in the course outline shown at the right-side?
Great explanation. Do you have any thoughts/videos on utilizing Arrhenius equation to predict material property?
Awesome teaching
Thanks for the tutorial! I have one question regarding how you calculate F (in your case F = n-0.5/N). I have encountered other approximations for F like F = n-0.3/N+0.4 (mean rank approximation) or F = n/N+1. When is it more appropriate to use one or the other? Is there a relationship to the sample size?
Thanks!
I'm not sure which is actually better. I think the one you cite is much more common though.
I'm currently designing a cost model for solar power plant, in which I should define the "average failure rate" of devices over its lifetime....how can I benefit from the Weibull distribution .....thank you.
Great teaching!
thank you!!
Is there anywhere where F = (n - 0 5)/N is cited as the go-to for rank approximation?
For the x-axis how do you resolve it when given bending strength instead?
Thank you Dr. Taylor
One question, can anyone explain how the calculations are performed at 33:00? Otherwise, this is the first video that ever made sense to me. I've been trying to understand this for at least a year.
4.88=exp(1.587)
Glad the video is helpful!
Do you have anything on log normal distributions?
39:34 what does the “m” represent in the legend of the confidence interval vs sample size plot?
Weibull modulus.
What is the formal name for the scaling equation introduced at 43:50?
Effective area
@@TaylorSparks Thank you!
Any limitations of Weibull distribution? considering that we consider the data distribution to be linear.
Also, can we use this Weibull distribution for the particle size distribution.
Video was awesome!!!
When you ranked them, some of them have the same length (16th and 17th), so it should be the same rank otherwise it gives different failure rate for the same length ?
Yes. There are other failure ranking approaches.
Hi Taylor! Fantastic explanation!! Thank you...My question is: the Length of failure in your excel spreadsheet it CAN BE MTBF??? Can I calculate reliability as you have done using the MTBF?
I imagine so. The first thing to try would be to see if it can be fit with the wibble equation. If so, then you should be able to use it as a probabilistic analysis tool
Superb! One question though. Can you explain the equation F=1/1e^6?
that's 10^6=1million.. they want one failure in one million articles
Simply great!
Thank you sir for this video. Can you please help me out for plotting weibull curves in excel based on service life prediction of building data. Plotting of Condition index vs.Time in years
Thank you for the video.
My pleasure! Check out our podcast Materialism! It's got rad episodes on materials science.
@@TaylorSparks I will definitely share these Weibull classes with my materials engineering undergraduate colleagues here in Brazil. Also, I have some friends that already know the podcast, keep going with the awesome work!
Thanks for the great lecture. I'm confused on the intuition behind length of elongation of the component computation. Is it akin to the idea of that: we have 100 bars so we must calculate at least 1 failing and hence this is like changing the required 1 / 1 million to 1 / 100 million in the original equation?
I'm not totally sure that I follow your question.
So the example towards the end is estimating the component length elongation with 100 x area of bar with same failure rate, right? And the length is much shorter. If the component had the same area as the bar but 100 bars were used (so that force area is 100 times) then we would expect 1 of the components to break earlier than the average failure rate. And that is why we should have component length much shoter. Equivalent’ish to looking for 1/100 million failure rate in the original bar intuitively? I hope it makes sense now.
Thank you for this video!
how is F=1-exp (-sigma_f/sigma_o)^m the following 1/(1-F)=exp(sigma_f/sigma_o)^m ? please explain steps
Once you get the EXP to one side of the equation you can take 1 over that entire side of the equation and it simply removes the negative sign from inside the EXP.
Thank you for this video, please I have a question, how do we estimate the failure function, if I have the number of data exactly 20
(n-0.5)/20 where n is the failure rank (first, last etc ). There are other failure functions. But this one works okay.
@@TaylorSparks thank you
wHY DO WE PLOT LN(LN (1/1-F(X)) ) ON X AXIS TO GET THE SLOPE AND INTERCEPT
The weibull equation is not linear. It has an exp in it. We make it linear by plotting it the way we do. In those axes, the slope becomes the weibull modulus.
Can I use this method for wind loads that don't give a specific direction?
No.
@@TaylorSparks if I have a set a data, in the form of a histograph, how do i make a weibull distribution curve
Mind blown!!
If i wanted to learn more about using excel in this way and this type of statistics, what would i take?
thanks. I am graduating this month in mechanical at UVU but even in my undergrad, we hardly touched on this stuff, even at SLCC
I actually learned more stats in my black belt independent study i did through an online company than i did my schools haha
Probability theory. That's what you want. If you want to keep learning, and since you are in Utah already, you might consider applying to our graduate program.
@@TaylorSparks i have thought about haha. I travel 120 miles one direction for school as i live in Brigham city. But i could check out the U and see. Thanks for replying.
@@LT72884 Salt Lake City is even closer than UVU. Actually, my most recent PhD grad from my group is living up in Brigham City because he works for Northrop Grumman. Once you are done with classes after the first two years, some programs even allow remote work. For example, my students typically do machine learning and so they can work from wherever.
@@TaylorSparks true, i grew up in draper :) but then went to usu for some school before switching majors.
Slc is alot closer, even if the u is east.
I really enjoy what i have learned about weibull and predictive failure from your videos.
Ill start researching more on probability theory
Is there a link to the files used in the video?
No, I generated the data on the spot. It's easy to do the same if you'd like.
How to use Weibull formula for precipitation in hydrology?
What does the data look like? Weight fraction precipitated over time?
@@TaylorSparks No sir. Annual rainfall of 22 years is given in cm (1960-1981). Q1: Estimate the annual rainfall with return period of 10 years and 23 years. Q2: What would be the probability of annual rainfall of
magnitude equal to or exceeding 'X' cm. X is given. I have found using P= m/(N+1) formula just one hour ago but failed to understand clearly why using this
@@sayemasaliha1152 are you specifically being asked to use a wibal distribution? Have you tried fitting it to a weibel distribution yet? It might be the case that another distribution is going to be more accurate.
at 30:00 you calculated F to be 1/1e^6.....shouldn't F= 1/2e^6 because of the formula F= (n-0.5)/N which equal to 0.5/1e^6 or as 1/2e^6
Best professor ever......miss those days!!
20:10 the ranking :: what if we left the data is it comes, in other words, without reranking it, let the first sample rank to be first, second be second and so on
I don't think that will work. You have to rank your data in order to calculate failure probability, F, correctly
@29:35 why the F for the one in a million is 1/e^6. My feel is that it should be 1/10^6.
oh, according to your number for the ln(ln(1/1-F)), the F is 1/10^6，seem it is typo. Thanks. That is a geat video.👍
The length at failure, has nothing to do with the failure rate.
Thanks
Great
pika pika !
⚡⚡⚡⚡
@@TaylorSparks haha. you got it!