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Re: [802.3_25GAUTO_POF] Reliability calculations

Hi Ramana,

My feedback:
  • You are right with _expression_ of ppm. Correct one is ppm = integral(0, t, lambda(x)/1000·dx). 
  • With respect the cumulative failure plot shown in giovane_3cz_01_080621.pdf, I understand the point of short time as small cumulative value. It is true that sigma will decrease. However location parameter will also decrease, which goes against reliability. I will do calculations with that.
  • lambda(t) is a function of F(t). F(t) will evolve in time depending on the evolution of temperature with time. To calculate F(t) you can consider constant mu for a reference temperature, then calculate acceleration factors with respect reference temperature, and than calculate an equivalent time coordinate at reference temperature, which you use to calculate F(t). You can use any of the temperatures in the mission profile as reference temperature. The result will be invariant for F(t).
  • In the spreadsheet: 
    • For all the temperatures, I calculated the equivalent time at the highest one. Then I accumulated the equivalent time in the highest temperature and used the mu of the highest temperature to calculate failure rate at the end of the mission profile. 
    • This corresponds to consider that the devices are first in cold, and then the temperature increases in time. The device ends life in hot. This is not consistent with the reality, however it allows to calculate a failure rate at the end of the mission profile similar to the max failure rate achieved with a more realistic story of the devices, e.g. a distribution of temperature in time that is consistent with the histogram on one year and repeat every year during life time.
    • You may consider the devices starts the life in hot and end in cold or random temperature distribution of temperature in time. The lambda(t) function will be different with time, however, the ppm at the end of the mission profile will be constant regardless evolution of T with t.
  • Direct derating of lambda with percent time spent at each temperature is not correct IMHO.
  • I will prepare some slides to illustrate everything.

I appreciate the discussion. Thanks.


Rubén Pérez-Aranda 
CTO at KDPOF
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El 11 oct 2022, a las 7:56, Ramana Murty <00000dc14a19cb36-dmarc-request@xxxxxxxxxxxxxxxxx> escribió:

Thank you, Ruben, for the reference.

(Slide 23, perezaranda_3dh_01_2209_vcsels.pdf)
The _expression_ for ppm failure does not apply to a lognormal distribution.

The _expression_ for lambda(t), otherwise known as the hazard rate, is fine. Two things to note regarding the calculation of hazard rate:
a) The cumulative failure plot shown in giovane_3cz_01_080621.pdf shows experimental measurements in accelerated tests on a heterogenous population of VCSELs.
When extrapolated to very short times, it will overstate the hazard rate because the value of sigma does not hold.
b) The hazard rate is a function of temperature, and should be de-rated by the percent time spent at each temperature according to the automotive mission profile.

These and other observations will be explained in a presentation slated for Oct. 19.

Ramana

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