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Original question:

TL084: Quality data at 70% confidence level

TL084: For calculating kai square (confidence level(%), degree of freedom)

Shinichi Inoue
Guru 20726 points
Part Number: TL084

Dear Specialists,

I'm considering the application note (SPRABY3) for calculating kai square (confidence level(%), degree of freedom) 

To begin with, 

As stated in equation (2), even if the confidence level of 60% and degree of freedom (2*1+2) are set, Kai Square (60%, 2x1+1)  does not become 0.917.

When 0.917 was used in the calculation example, the FIT values were almost the same value(50.5).

Assuming 0 failures from 231 samples for 1000 hours HTOL @ 125°C, the FIT would calculate to be 50.9 FIT with 60% CL at 55°C.

Could you please let me know where I am wrong.

What we actually want is the value of Kai Square at the confidence level of 70%.

I appreciate your great help in advance.

Best regards,

Shinichi

  • +1
    TI__Genius 12890 points

    Hi Inoue-san, 

    Equation 2 in the Apps Note is intended to calculate FIT rate after you have determined what chi-square (kai square) is. It may be easier to see the equation like this as it is shown in the JEDEC standard: 

    Chi-square needs to be calculated using the confidence level and degree of freedom. With a 60% confidence level and 0 failures (degree of freedom = 2*failures + 2 => 2), that would result in a chi-square value of 1.83. I just used an online calculator (https://stattrek.com/online-calculator/chi-square) or you can find other online resources or use Excel functions. 

    Substituting the values we know for 60% confidence level, sample size, time, and AF (acceleration factor), we get about 50.5 FIT. 

    To calculate with a 70% confidence level, you will need to re-calculate the chi-square value. To get the new FIT value, you plug it into the same formula as above. 

    I added a table below to show a comparison between 60% and 70% confidence level. All the other variables stayed the same and the FIT rates were calculated for each condition. 

    AF 78.61 78.61
    CL  0.6 0.7
    Chi-square 1.832581464 2.407945609
    t 1000 1000
    ss 231 231
    FIT 50.456 66.297

    Please let me know if you have further questions.
    Thank you!

    Best Regards,
    Ashley

  • 0 in reply to Ashley Kang
    Guru 20726 points

    Hi Ashley,

    Thank you for your reply.

    I understand.

    It's a very helpful information because I could not see JEDEC standard.

    Could you please provide JEDEC standard number？

    In this case, It should be use confidence level 0.6 (60%) and degree of freedom 2 (2x0+2), then I could obtain 1.83.

    The same result was obtained CHISQ.INV (0.6, 2) by Excel Function.

    I'll share your suggestion with the customer.

    I appreciate your great help and cooperation.

    Best regards,

    Shinichi  

  • +1 in reply to Shinichi Inoue
    TI__Genius 12890 points

    Hi Inoue-san, 

    The JEDEC spec is the one that is referenced at the bottom of the Apps Note (JESD85):

    Regards,
    Ashley

  • 0 in reply to Ashley Kang
    Guru 20726 points

    Hi Ashley,

    Thank you for your reply.

    I understand. Perfect!

    I appreciate your great help and cooperation.

    Best regards,

    Shinichi