Which would be the best distribution

[Stephane]

Which distribution?

I have great difficulties to estimate the good law for this distribution.
The sample size is 40 components, and we obtain the following table:

interval TTF and the number of failures

before t = 9600, there are no failures
9600 => 12800 : 3
12800 => 19200 : 9
19200 => 22400 : 5
22400 => 35200 : 7
35200 => 48000 : 1
48000 => 73600 : 2
73600 => 99200 : 2
99200 => 124800 : 0
124800 => 176000 : 2
176000 => 278400 : 1
278400 => 380800 : 0
380800 => 585600 : 0
585600 => 790400 : 2
790400 => 995200 : 0
995200 => 1200000 : 0
1200000 => 4149120 : 0

The distribution looks like a three parameters Weibull with a positive
location parameter and a shape parameter < 1. But this distribution fit
the first points very poorly.
The lognormal don't give better result.

Thanks in advance for any help you can provide.

Stephane Forster
LMP - STMicroelectronics

[RS Support]

At first look the data seem to exhibit mixed characteristics and do not seem to fit well with any single distribution. Have you looked at a mixed Weibull or a competing failure modes model (if you can identify different failure modes)?

[stephane]

Effectively, it looks like a mixed distribution but I think it's not.
A mixed Weibull with 4 parameters (alpha1, beta1, alpha2, beta2) always gives
a first line followed with a second line with a greater beta. It's not our case.

A competing failure with 5 parameters (alpha1, beta1, alpha2, beta2 and the portion
defective p) gives a first line and then there is a shift to a second line. This second
line doesn't appear of the data.

Moreover, it seems that the components have only one failure mode (a silicon fusion).