Good evening. I would like to know how to calculate Mean Time Between Failures = MTBF = Time between two consecutive failures of a component for Arduino + led + PIR sensor + switch button + resistor or if someone can help me.
Do you have the needed MTBF for each of the individual components?
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Just offer a warranty period 
.
To calculate MTBF , divide the total number of operational hours in a period by the number of failures that occurred in that period. MTBF is usually measured in hours. For example, an asset may have been operational for 1,000 hours in a year. Over the course of that year, that asset broke down eight times.
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No, I need to do some sort of reliability calculation for the components in my project.
Then you need to match the MTBF for the component with the worst failure rate.
Paul
Honestly, I don't know how to do this.
Start with the active components in your project. They will have the worst MTBF. Data sheets or other documents should give you a number. You do know how to make a list, and pick the lowest number.
Paul
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That is not good. Can you tell us why you need this? I suspect you need something simple.
Companies that have a reputation of high reliability spend quite a lot of time and resources to investigate this. e.g.,
- reading data sheets, product handling guidelines and reliability reports from manufacturers
- study reliability of base technologies e.g., silicon processes
- consult with suppliers to cover special cases e.g., high temperature
- running aging experiments exposing devices and modules to extreme conditions
- running long time reliability tests
- running failure mode analysis on failed units returned from the field
- follow up with suppliers on improvement measures
I suspect it the mechanical components e.g., switches, potentiometers, ...
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Ex-Reliability Engineer, here! What you've asked is more complicated than you might first think. I'm going to simplify it by making some assumptions you don't need to worry about.
To work out the MTBF for a system, you first need to know the MTBF for each component. This involves Google searches and manufacturer's data. Make sure all the MTBFs you've found are in hours (you can convert them yourself, obviously).
To combine them you first need to convert the MTBF figures into failure rate figures. This is easy - simply invert the figure into a fraction, like this:
MTBF = 1000 hrs, then failure rate = 1/1000 failures per hour
Explanation of failure rate
Invert the MTBF (in hours) to give the failure rate per hour. A component with a mean time between failures of 5 hours has a failure rate of:
one fifth of a failure per hour
one failure per five hours
ten failures per fifty hours
etc...
Does that make sense?
It is traditional in Reliability Engineering to scale failure rates to "failures per billion hours", which is known as "FITs".
So, follow this in your head, if you can.... A component has a failure rate of 10,000 FITs (ten thousand failures per billion hours). Therefore you can express its failure rate as:
10,000 failures per 1,000,000,000 hours
10 failures per 1,000,000 hours
1 failure per 100,000 hours
Invert it again to convert back to the MTBF. Invert 1/10,000 to give 10,000 hours MTBF.
Thus you can see how failure rate and MTBF are related.
Using component failure rates to calculate MTBF for the system
Convert all your component MTBFs into FITS. Then simply add them together. This gives the failure rate for the whole system. Then invert it again to give the MTBF for the whole system. Simple!
Example:
A system comprises an LED, a resistor, and a switch. The MTBFs are as follows:
LED: 200,000 hours
Resistor: 500,000 hours
Switch: 40,000 hours
Convert to failure rate by inverting:
LED: 1/200,000 failures per hour = 5,000 failures per billion hours = 5,000 FITs
Resistor: 1/500,000 = 2,000 FITs
Switch: 1/40,000 = 25,000 FITs
Add them together:
System failure rate = 5,000 + 2,000 + 25,000 = 32,000 FITs
So that's 32,000 failures per billion hours. Now divide by 1 billion to convert to failures per hour:
32,000/1,000,000,000 = 0.000032 failures per hour
Convert to MTBF by inverting:
1 / 0.000032 = 31,250 hours MTBF
Note how the system MTBF is always lower than the MTBF of the lowest component (the resistor at 40,000 hours), and in this case is dominated by the MTBF of the switch.
Caveats
You will also see the term MTTF (mean time to failure), which is actually the proper term for components which cannot be repaired, only replaced. Thus individual electronic components actually have an MTTF, not an MTBF. However, they tend to be used interchangeably (wrongly), so for the present purposes you can treat MTTF and MTBF as the same thing.
Probability of failure
The probability of something failing in a given hour is numerically the same as the failure rate. For example, a component with an MTBF of 10 hours has a failure rate of:
failure rate = 1/MTBF = 1/10 = 0.1 failures per hour.
Another way of saying this is: the component has a 0.1 (1/10 or one-in-ten) probability of failing in any given hour, which is numerically the same as the failure rate.
MTBFs and failure rates have nothing to do with lifespan! Some components have a limited lifespan - that is, they wear out at a predictable rate. Wearing out is not the same thing as the random failures that occur in service, and which the MTBF figure applies to. So, an LED might have a lifespan of 50,000 hours. This is NOT its MTBF! It is quite common for components like LEDs to have an MTBF longer than their lifespan.
In case that sounds absurd, think of it like this. Humans have a lifespan of (say) 85 years. Statistically, a 40-year old male has a 1 in 350 chance of dying in that year of his life. If we assume dying to count as a failure, then his failure rate is 1/350 per year, which inverts to give an MTBF of 350 years. Thus a 40 year old man has an MTBF of 350 years, but will wear out after 85 years.
Finally, professional reliability engineers will see that I've left out a load of stuff, but the fundamental principles outlined here are sound. It's just that in the real world, system reliability depends on more factors than just the reliability of the individual components.
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Hi,
Is this a school/college/university project?
Thanks.. Tom... 
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THX @SteveThackery fir the layman’s ‘splaination.
The article @jremington links in #2 is worth the time also, THX.
Kills me that I knew this stuff once and don’t anymore. Same wit Roman and Greek mythology, man I was up to speed on that, no more. But less important than MT B or T F.
a7
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Thank you
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Yess
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I don't know that I've ever seen am MTBF rating on a microcontroller data sheet 
Maybe there is one for the "automotive" or "space" rated parts (but those aren't what you have on an Arduino!)
This is why we learned about bathtubs with multiple holes back in Algebra, or how long Tommy and Timmy will take if they work together mowing the lawn…
And I am sure y’all noticed a kinda resemblance (!) to the calculations for resistors in parallel.
Compute the conductances, add them up and invert turn the net conductance back into resistance.
So I am guessing one could multiply the MBTFs and divide by their sum.
200K ohms
500K ohms
40K ohms
1/200 + 1/500 + 1/40 is 0.032
1 / 0.032
is
31.25
31.25K ohms
1 / 0.000032 = **31,250 hours MTBF**
Except for the billion years thing.
a7
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No, and getting MTBF data is often very difficult. There are databases around with MTBF data gleaned from recorded field failures, but I don't know what are available on-line these days.
Billions of hours. But we know what you mean. 
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