RELIABILITY Explained! Failure Rate, MTTF, MTBF, Bathtub Curve, Exponential and Weibull Distribution
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- Опубликовано: 22 май 2024
- The basics of Reliability for those folks preparing for the CQE Exam
1:15- Intro to Reliability
1:22 - Reliability Definition
2:00 - Reliability Indices
06:48 - Failure Rate Example!!
08:19 - Mean Time to Failure (MTTF) and Mean Time Between Failure (MTBF) Example
10:03 - The Bathtub Curve
11:56 - The Exponential Distribution
15:40 - The Weibull Distribution
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It is pleasure to say thank you for this wonderful contributions to education worldwide.
Thank you so much for uploading this! It was really easy to understand and covered everything I needed 💖
Rashika!!!!!
I'm so glad you liked it, you're very welcome!
-Andy
Great explanation. Easy to understand than any other book. Thank you! God bless you.
Awesome, Amazing, Excellent
Best content about reliability I've found so far! Great and simple explanation, very helpful! Thanks for the content
You're welcome Jonas!
You made it so simple to understand the reliability concept, Thank you
After looking at different articles, this was the best
Awesome, thanks Praveen!!!!
@@CQEAcademy hello Sir. İ need some deep knowledge from the subject "Reliability and safety theory". İ failed at this subject and i need to pass. İ need some private lessons. Could you please help me?
@@warrior_number Hey Orxan, unfortunately i don't do any personal coaching, and I don't have a course (yet) for the CRE Exam (Certified Reliability Engineer).
Clear explanation and to the point. Thanks very much.
Could you make some more practical examples of FR, MTBF, MTTF and how Planned Maintenance comes in?
Just what I needed. Thanks!
Great video!!! Very good analysis and on point! Great work!!!
Wow, thanks Christos!!!
thank you for this presentation
Thank you very much. Great information in a very less time !
You're absolutely welcome Mohammad!
Thanks for the clear explanation. Really appreciate it.
You're welcome!
Great material. Keep it up.
You are fantastic, explained so well. Thank you
Thanks!
Your teaching is sooo clear, and it helps me a lot for this reliability statistics, thx bro
Thanks!!!
Thanks you so much for this video.
A really easy and nice explanation. Thank u so much.
Hey Sourabh, I"m glad you like it!!!
Very clearly explained.Thanks!
Thanks!!
Thank you for the upload, very helpful!
You're welcome, I love to teach and help people grow!
Absolutely amazing. Thanks
You're welcome Kai!!!!!
I have one thing to add for the MTTF, I believe it should be divided by the total number of units and not the total number of failures.
The reason is the units that did not fail should also be included in the mean calculation.
The hours of those units were already included when the summation of operational hours was added so it should be counted.
Thanks for the Awesome Video. Helped me to get my coursework Done.
You're absolutely welcome, I'm so glad I could help!
you literally save my brainn..thank you sir..have a great day!
hahaha, thanks!!!!! You have a great day too!
Thank you so much for sharing you are the best!
Wow, thanks, you are absolutely welcome!!!
That is a very clear explanation of the content.
Thanks Bhargav!
Thanks so much for this! I really enjoyed it and learned a lot!
Thanks Rahim, I'm glad you liked it, and I appreciate the comment!!
really appreciate your efforts! thanks so much!
You're welcome!
Thank you for explaining basics of reliability... :)
You're welcome!
He is a Master in quality better them books
Very informative.. got clear understanding
Thanks!
Thanks a lot. very clear explanation. Great work..........
Thanks Shaik!
very added value thank you so much
You're absolutely welcome!
Excellent
Thank you very much, it was really helpful.
You're welcome!
hats off... well explained
Thanks Adolfo!
Thanks.
Thank you for this vedio and its very simple explanation.
Thanks Mahgoub !!
Thanks for this
You're welcome!!
Amazing, thank you!!
You're very welcome!
Great video-can you go through part b of the question below...
A non-repairable item exhibits a constant failure rate of 8% per 100 operating hours.
A)If the initial stock is 150 units, and all items are operating simultaneously, how many items would be expected to be still operating after 200 hours?
B)If the design of the unit is improved so that the failure rate falls by 25%, i.e. to 6% per 100
operating hours, what would be the proportional increase in the number still working after
2000 hours
Nice explanation.. Thanks for an informative video
Thanks Jignesh!!!
Very elaborate 😊
Thanks!
Thankyou so much sir
you concpetual explaination is awsome
Thanks so much Rohith!!!
Excellent work. I teach statistics, and reliability engineering. Your videos will be a recommended tutorials for my students.
Wow, thanks!!! I appreciate that!
Hi, could you assist with where i can find articles that discuss these concept further? Great explanation!
Very nice presentation
Thanks!
Awesome!😀
Thanks!
Thank you!
You're welcome!
Important to note for folks is that the graph starting at 17:00 is a Probability Density Function (PDF) for the different beta values.
That's a great shoutout Billy!! Thanks!
Excellent explanatio
Thanks!
These are greatnd thank you...my question is - how do you calculate Beta and separately, are there known methods of calculating MTTF without test data? I ask for the instance of a large system where it's not production but a one off built system
thank you dude
You're welcome!
hello , first thank you for this amazing video , second, i 'm actually getting more interested in this area of statistics , could you please suggest me some books to read to get more information on this
thank you so much can we some more vedios brief things about quality and reliability
Awesome explanation, if i have peak stress and time of peak stress of 10 samples, log normal plotting weibull destribution of its time or stress which will be more helpful ? Which i did using excell and plotting weibull destribution, giving me the modulus intercept and slope , from which i cacluate the beta and eeta. Your insights means a lot to me
Thank you
You're welcome!
thank you so much
You're welcome!
Andy,
Have you authored any book or recommend one or two that I can buy to prepare for the CQE? I also want to take your course, How long does it take?
How much does it cost?
A great professionally presentation of the concepts as such not easy to digest. Any recommendation for the Certified Reliability Engineer exam? This is the toughest one of ASQs as said but I desparately love to get it done
Unfortunately I don't have any direct experience with any of the resources for the CRE exam, so I can't make a good recommendation.
Your teaching is much easier to understand compared to my lecturer (from my master's degree, oops).
Wow, thanks Christina!!!
Hi Andy, great video. I actually got to finaly understand the weibul distribution!
Question, say in operating setup (not manufacturing or product testing), failure data for repairable equipment are highly influenced by the maintenance strategy for that specific equipment. Can we use that data to calculate MTBF? Is there MTBF with maintenance and MTBF without maintenance?
Great question! So one of the underlying assumptions here is that when a unit is repaired, the item is repaired to "its original condition" (or near it's original condition).
If different maintenance techniques are used, and the unit is not repaired to its original condition, it's hard to define a reliable estimate of MTBF.
Does that make sense?
Thanks so much 💚💚💚🇩🇿💚💚, please more videos about reliability and probability and statistics , I must pass the doctor exam (PhD)
Will do!
Thank you for these videos, your brilliance is in the way you simplify concepts.
Just a question, when calculating the MTBF for repairable machines during the data measurement process in calculating MTBF are only newly 1st time manufactured parts taken into calculation or are repaired parts (2nd repair, 3nd repair, 4th repair, etc is there an upper limit to number of repairs?) also taken in the MTBF calculation ?
Great question Harsh! Sooo, that depends on what you assume.
If you assume that repaired parts have the same reliability as new parts, then I would include it.
Obviously if you think that repaired parts have worse reliability, just know that it'll impact your MTBF.
The last comment I'd make is, if your product will routinely be repaired with repaired parts, then i would calculated MTBF for this scenario because this estimate of reliability will reflect your products actual performance. Hopefully that makes sense.
@@CQEAcademy Thank you for your response. This makes great sense. Would you have any suggestions on best industry practices of choosing an optimum product sample size to calculate MTBF and the optimum ratio of repaired product vs new products to use in MTBF & how the selection is done? E.g lets say for low volume manufacturing, 60 products manufactured / year ?
Also, on another related topic regarding warranty calculation - does the business strategy team include MTBF when calculating the warranty period of products and are there any situations where the warranty can be also renewed after product has been repaired to new since its MTBF would also be restored? Philosophically, what is considered morally right when providing warranty to customers ?
How did you get the graph at 14:00 , Reliability Vs. Time Hours?
How does this video and Reliability relate to FMEA? I'm doing a ppt on both FMEA and this, but want to know how I can relate the two ideas
Thank you for such great explanations about the topics. Could you please also share the pptx links for your video if possible?
Hey Nishant! Those powerpoints are sort of my secret weapon, so I keep those for myself :)
Good explanation I appreciate your time on dedicating making it. What are good books to go deep on this topics ??
Hey Ollie, one book I've always enjoyed is Practical Engineering, Process, and Reliability Statistics by Mark Allen Durivage
🔥
Glad you like it!!!
Great video, I would like to know 1) how to calculate Beta, 2) I have 50 comp installed, 10 failure removals with mean hours of 700, how can I predict the failure hour of rest components or how can I find where to apply a maintenance so as to preclude the failure? Your reply would be highly helpful. thanks in advance.
Hey Gamaliyel!!! Okay, so the beta parameter for your product should be developed through testing. In terms of maintenance that you can do to extend the MTTF, that really depends on your product, and the root causes of the failures that are occurring.
Beta, or Weibull Shape, is calculated using the slope equation. Through MTTF/MTBF testing, you would graph the results on a probability plot and calculate rise over run as normal.
Hello, I am looking for Probability in Quality Control, sadly I can't find this topic on CQE Academy, does anyone know some resources to study that with?
MTTF formula that i see elsewhere is different . denominator for MTTF you mentioned as No. of failures. online i see Total number of devices. can you please clarify?
I'm here for the bathtub curve. What is a CQ-Exam?
Please, how can I confirm the shape type and B value, how can I say this item should be go through increasing failure or decreasing, or may be exponential?
Heyy good video, and ty for expl all this, pl tell me how I can get or calculate betta valuem this example betta=2 howw? ty !
Hey There!
The beta value usually comes from your failure data - historically, when failure data was plotted on a weibull probability plot, the slope of the line from that data would be the beta value for your product
How do you get the beta value in distribution
Question: how would I chose if testing the MTBF for 1000, 5000 or 10000?
Amazing videos by the way, thank you!
Hey Michele, thanks so much!
Okay, so your MTBF value should be calculated from reliability testing.
Then, based that reliability data you can make reliability predictions.
Choosing testing time factor is Reliability testing planning of a product.
Reliability testing can be perform in many ways .
1.Time truncated Testing ( Testing till predefined testing time)
Both have different ways to calculate the MTBF including censoring data types .
2.Failure Truncated testing ( Testing the product till failure but testing time can increase for more reliable product and less for less reliable product) .
To save time and resources we can use the testing strategies according to the product reliability defined by customer requirements and Reliability is part of the design life cycle to save the cost .
Question on MTTF/MTBF example : how can one deduce that the MTTF is nearly 3000 hours when none of the device ran more than 1000 hours and 6 of them failed well before 1000 hours? If none had failed, the MTTF using this calculation would be infinite.
Walid!!!! that's such an amazing question, and I didn't go into this level of detail in the video, but if this were to happen in real life, what I would recommend would be to continue the testing to failure to confirm the MTTF value, because as you point out it's not a best practice to make predictions for MTTF outside of your testing parameters.
Hello,
can you, please, explain how you calculated "e"? is a constant? were you take it from?
it is not explained
Hey There!
I probability should have explained this better.
e is eulers number, it's a mathematical constant (like pi), and it's equal to 2.71828....
Hi - In the example with 6 failure, how would we calculate the MTBF for same example assuming all the units ran up to 1000 with 6 failures and 6 repairs?
Hey Jankesh, I believe the proper procedure is to capture all of the run time of the units, including before the failure and after the repair, and factor all of that time into the calculation for the MTBF. Don't include any time spent in repair
Hi thanks for the wonderful explanation, appreciate it!
why is that the exponential dist is applied only for the "useful-Life Period", what is the reason behind it? is it cuz exponential dist doesn't have a shape parameter and Weibull does and therefore Weibull can adapt any part of the bathtub curve for a dataset?
Thanks
Arav
Hey Arav!
Great question! So to be fair, the weibull distribution can also be used for the "useful life period", because the weibull distribution can also have a shape parameter (Beta) equal to 1.
The reason that the exponential distribution models the useful life period though, is because the useful life period can be characterized as a time period with a constant failure rate (flat line on the bathtub curve).
And a constant failure rate (lambda) is modeled by the exponential distribution. I know that can be hard to visualize though and it would take another video to explain this more clearly. I'll add that to future videos!
@@CQEAcademy
Hi
I think it makes sense now!
Thank you👍👍👍
@@aravindhanpoopathy6862 You're welcome!!
Sir how to calculate Slope(B)? Please anyone expert answer!
Is there any software recommendation to solve this topic?
Hey Muhammad, I personally don't have a reliability software that I would recommend, but I'd love to have other people chime in with any software that they'd recommend
Hi There. I am looking into this for my company, but I need to cross reference a cost against failure rate. For example. If I spend $100 on something that fails 100 times at $10 per failure against spending $1000 on a better asset but only fails 5 times at $500 per time. What would be the best way to Carry out this equation. Is there a method additional to this method for cost? Thanks
P.S. I am not studying this at college, however I’m keen to learn to bring this knowledge to my company
Hey Ben!
I think this is a smart way to think about the lifecycle cost of a design relative to reliability/maintainability when considering 2 different design options.
I think you could create a formula to estimate the total cost of 2 different design options
Total cost = Upfront Cost + Repair Costs
Design A Total Cost = $100 + ($10*100) = $1,100
Design B Total Cost = $1,000 + ($500*5) = $3,500
Reliability comes into play here when estimating the total number of repairs that would be estimated over the lifecycle of a product.
What is the minimum number of product we have to put to trial for determining the MTTF or MTBF? In the above example you have taken 20 units on which basis?
Hey Sheikh! There isn't really a set standard for the number of units required for reliability testing.
MTTF/MTBF is obviously a sample estimate, and your confidence in that sample estimate grows with more samples, and the number of samples requires can vary from industry/industry and from application to application based on the risk associated with a failure.
And when we have to use lambda /t
Items which are failing on regular basis and repaired again and again, do we calculate reliability of those items also in the same manner...
Yes!
The mean time between failure (MTBF) would be the metric to use when items get repaired when they break.
For Beta=1 it is a constant failure rate (which is the exponential distribution)
Yes, absolutely true!
@@andyrobertson566 Beta =1 assumes random failures. This type of distribution is not typically applicable to mechanical hardware systems, which are designed to wear out due to metal fatigue. When I was at Chrysler, we used a weibull slope (beta) of 2.0 for mechanical components (e.g. suspension system).
Hey @@billyjames6407!! Thanks for sharing the input!
Please how do I solve this
A generating unit contains a large number of n components an a failure of any of these components results in an outage of the unit. Assume there are n component of interest in a generator and each can fail independently of the others, time to failure i can be described by an exponential distribution with parameters i=1,2,3....., n. Determine the system reliability
Hey Etudaya, I don't really understand the question, are you looking for a quantitative estimate of the overall system reliability at a given instance in time? Or are you looking for a subjective description of the system and its design?
I have a question about the question on 15:00
If the probability that it will succeed is 66%, then does that mean the probability that it will fail is 44%?
I have a question just like this in my past exam paper and I'm trying to understand it.
Hey Leon, Yes, the probability of failure would be 34% (not 44%), but your logic is correct.
@@andyrobertson566 Hi, thank you, sorry for late reply, also, last question, are there any feasible ways of increasing the reliability of the system? Like, what can be done?
@@StrengthNational Hey Leon!!! Great question, and there's really no single answer to that question.
The honest truth is, the reliability of your product often depends on the design. The suppliers you choose, the components you choose, the design you choose, and the failure modes associated with that design, all have an impact on the final reliability of your product.
If your product is already in production and you cannot easily change the design, then what you can focus on is the process. Improving the process to eliminate failure modes that might reduce the reliability of your product. That sort of thing.
Does that make sense?
When using a basic calculator, could you walk me through this particular example. I am not getting .6766. Thanks.
Hey Alfred, okay to the first order of operation is to take the ratio of 5,000 to 8,000 (0.625)
Then, take that result and square it (0.390625).
Do not include the negative sign in the square, or you'll lose the negative sign.
Lastly, raise that exponent to the -0.390625 or e^(-0.390625) will give to that the probability of 0.6766 or 67.66%
I hope that helps!
-Andy
@@CQEAcademy Hi Andy, could you please tell me why did you use MTBF not MTTF in this example, since both terms have the same equation? Second, could you simplify solving the exponential equation step by step? Thank you.
@@admorgan967 Hey Adam, You're right both MTTF and MTBF have the same equation, the only difference is that MTTF is for non-repairable units, while MTBF is for repairable units, and I chose MTBF randomly.
In terms of solving the exponential equation, first convert the fraction into a decimal (-1200/2996) = (-0.400).
Then raise "e" to the power of that fraction - e^(-0.400).
@@CQEAcademy hey Andy, in the second example, Weibul distribution, you have mentioned B or beta with a value 2, do you know where can I get this value if I need to perform an actual test? Thank you
@@admorgan967 Hey Adam, to find this shape value you'd have to perform reliability testing to quantify this parameter.
Could one calculate the MTTF/MTBF for the early-failure period?
Hey Lee, you could, most definitely.
Most textbooks though basically give the same advice that in the early life period, your focus should be more on root-cause analysis and improvements to get that product out of the early life period.
@@CQEAcademy Following up with the MTTF/MTBF calculation, for units that didn't fail, do we need to sensor them from the calculation?
@@Mr.Divorce Hey Lee, no you can take credit for the fact that units went through testing and did not fail, that should be captured in the "total test time" when calculating the failure rate.
good presentation can I get the pdf file plz
Yeah! Just head over to CQEAcademy.com/freecheatsheet
Hello sir,
In the formula of reliability what is e? And how R(1200) = e (-1200/2996) = 0.6699?
Can you Please explain this formula?
Hey Shailesh!!
In that formula, "e" is Eulers number. It's a mathematical constant and it's equal to 2.71828.
Think about it like Pi (3.1415926535. . . )
Most calculators have Eulers Number as an available constant to select from.
Work that fraction first (-1200/2996 = -0.40053), and then raise "e" to that power (-0.40053) and you should get 0.6699
@@CQEAcademy Thank you for your reply and explanation, I would further like to know why we considered 'e' only? Sorry it might be embarrassing question.
why did u added 14x1000
Hi Sir I am an aircraft reliability engineer. How do I calculate MTBF if I do not have an estimated data for a number of components that will pass. I only have number of components fail.
Hey Vincent! Do you know the total number of components that are currently being used?
Can you estimate the number of cycles or hours of operation for those other components that are in use (that have not yet failed).
Honestly, without knowing your industry or your component it's hard to give a good answer. I suppose you could make an estimate if you knew the information above, but that would be a very rough estimate. I think your situation highlights the importance of reliability testing during the development/design phase of a product.
How could I determine beta value
Hey Hany, you can only determine your beta value through reliability testing. The beta value used to be derived from a weibull probability plot analyzing reliability data. Now you calculate beta using programs like minitab but it first requires that you perform reliability testing and collect data
When we have to use lambda ×t
It depends on what parameter you're given. If you're given lambda (instead of theta) then use lambda*t, if you're given theta, use t/theta.
When I say that this device has an MTBF equals 500 yrs, how can I illustrate this to the customer?
And you select 20 device in the video, may the reliability value will change if you actually use 50 or 100
Great question, and yes, the confidence that you have in your reliability estimate goes up, when you take more samples.
In terms of the MTBF of a device, 500 years is a big number, and your customer will obviously want to see the test data that generated this estimate.
@@CQEAcademy tell me if the following is right; 500 yrs means reliability is 0.998 and if I produce 10000 device; that means there is a chance to failure of 20 out of the 10000 could fail
Hey @@MS-be9wv so normally we talk about reliability in terms of the MTBF (Mean Time Between Failure) or the failure rate (lambda), both of which are typically measured in hours (MTBF) or failures per hour (lambda - failure rate).
I think it would be challenging to prove a MTBF of 500 years. How are you getting that number?