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Calculating MTBF Today.

Calculating MTBF Today.

Calculating MTBF Today.

(OP)
Forget about Mil 217. it was very conservative and its been dicontinued by the US military for many years.

Forget about TellCordia/BellCore which at least attempts to represent commercial applications.

Just concentrate on the semiconductors and the electrolytics.
Use recent HTOL (High Temperature Operating Life)test data from the semicondure manufactures web sites. My company asks for this data up front. Also use there quarterely reliability report/ and look at their intrinsic failure rates for mainstream ICs. This will be based on very large samples, hence very low FIT rate.

Using the HTOL data, calculate failure rate of all semiconductors at the accelerated bake temperature. Typically,

 Junction temperature 125C for 1000 hours.

 No failures.

Typical activation energy of 0.7eV.
This is lower for memory but the manufacturer will specify.

Calculate failure rate at the bake temperature, eg 125C

Use  Chi squared distribution which give us a statistical figure even with no failures, this is typically the case with semiconductors. Plenty on this on web.
Failure rate= Chi square / number samples x test hours

Use Arrhenius chemical equation to derive Acceleration
Factor, A.F in order to extrapolate the actual failure rate at your given operating temperature.


AF = exp{Ea/k  [1/(Top+273) -1/(Tstress+273]}

where k = Boltzmann's constant (8.63 x 10 -5 eV/K)

Ea =Activation energy used

Do this for all the semiconductors, using  "Relex" or even a humble Excel spreadsheet.

Ignore the failure rates of all the SMD 0805/0603/0406 chip resistors /inductors. There contributions are in "the noise".

Do not derate electrolytics. Its a reliability myth.
They simply reform to the reduced operating voltage!

Get modern electrolytic capacitor reliability data from Japanese manufacturer,Elna Capacitors. Bellcore and Mil 217 models will ask for capacitance but this is pointless and goes back to the days of enferior CV ratios when large capacitance meant very large can size.
What is needed is capacitor ripple current, esr and its can size /surface area.  

Sum all failure rates, work in FIT's'(Failure In time) a sensible unit for electronics of one failure in 10^9 hours.

Calculate MTBF, Mean Time Between Failurs,

           MTBF= 1/ Lamda (Total failure rate)
 
Calculate what management want to know! AFR, Annual Failure Rate, I.e predicted field failure returns/year.

I use unreliability (after 1 year) = {1- e -(Lamda x t)}
Where t= hours for one year,  8760 hours

Convert to % and roundoff.

Note:
This only applies to random failures which is only relevant to semiconductors operating in the useful life part of the system reliability bath-tub curve.

The exponential math models assume Lamda is constant.
 This cannot be overstressed in my experience with the continual confusion I always find of the subject in corporate minds.

If you have wear-out mechanisms such as fan's and hard drives then the subject gets more involved as their failure rates are of course increasing with time. I will just mention here, look at web sites concerning use of Weibull plots. Reliasoft in particular.

Remember there are lies, damm lies and statistics!

Happy predicting

analogue alan

Further web reading

Burr-Brown application Bulletin AB-059 for a kick off.

"Calculation of Semiconductor failure Rates"
 by William J Vigrass.

RE: Calculating MTBF Today.

The last person is absolutely correct with a few exception.

No manufacturers data is without massage. Posted low FIT rates are going to be assumed, not necessarily derived. Know your supplier.

Also, remember your application. Some devices have activation points that are below 125C.

Below the activation point, no failure. Above the activation point the mechanism starts. Testing a device beyond its threshold (activation point) is meaningless.

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