Re: [802.3_OMEGA] Calculating hazard rate (statistical aspects)

[Rubén Pérez-Aranda <rubenpda@xxxxxxxxx>]

Good morning Ramana, all,

See my reactions below.

El 18 oct 2022, a las 6:51, Ramana Murty <00000dc14a19cb36-dmarc-request@xxxxxxxxxxxxxxxxx> escribió:

The following is a description of the statistical aspects of calculating the hazard rate. We don't need to spend time on this at
the meeting.

Ruben has presented a Matlab code for doing the simulation on the reflector.

Could you indicate which parts of the script are not correct and share a revision of the code in the reflector?

The important thing to appreciate is that only statistical
averages are relevant.

See below comment to 2).

1)  The automotive mission profile shows the probability of a vehicle being at each of five different temperatures. Each vehicle may take
a different path through the temperature profile.

Correct. Already illustrated in my last contribution. 

2) Hazard rate h(t) is meaningful only as a statistical average ⟨h(t)⟩ because the goal is to estimate the failure rate of an ensemble (fleet)
of vehicles.

This is not correct. Failure rate as function of time is used by any industry, and specifically by the automotive industry.

Based on you argument, infant mortality would not be a problem for any IC in the market because the high failure rate 

at the beginning of the component life is going to be averaged in time.

Also based on your premisses, we could argue that OEMs accept high mortality in e.g South Africa because statistically is 

going to be compensated with the cars in the e.g. North of Europe.

The OEMs do not want to have high number of field returns during short periods of time. Moreover, the OEMs do not want any field return.

The goals are two: 

• Number of failures (ppm) under limit, calculated as integration of failure rate in time.
• The instantaneous failure rate (= hazard rate) in each specific time under limit.

The rules are not mine. They are the result of consensus in the automotive industry. 

3) A Monte Carlo simulation can be used to simulate temperature history and determine ⟨h(t)⟩. The simulation should be run
many times and ⟨𝐡(𝐭)⟩ determined by taking the average. Spikes in h(t) for a brief time in any one Monte Carlo run do not carry
much meaning by themselves because it is the resulting failures that count, not the value of h(t) itself. The resulting failures
depend on ⟨h(t)⟩.

See my comments above. 

You can use random temperature in time. But failures (ppm) at the end of mission profile are the same regardless the function of T(t). 

In some cases failures are accumulated sooner and in others later. I already showed this in my last contribution.

Trying to use average failure rate is an indication that the reliability of 850nm VCSEL is marginal.

4) Alternatively, de-rating the hazard rate at EOL by the fraction of time at each of the five temperatures will give the same value
of ⟨h(t)⟩  as the Monte Carlo simulation.

No, it is not correct. It is not mathematically equivalent and this methodology is not used in automotive.

Ramana Murty

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