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Question 4.5: Tantalum capacitors were tested at elevated temperature, and...

Tantalum capacitors were tested at elevated temperature, and the failure times were Weibull distributed with scale parameter α = 2.5 × 10^5 h and a shape parameter β = 0.5. If the AF is estimated to be 1 × 10^4 , what is the probability that the capacitors will last 1 year?

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The failure probability is given by F(t)=1-exp\left[-\left(\frac{t}{AF\times \alpha} \right) ^\beta \right] . In 1 year there are 8760 h.

Therefor, F(8760)=1-exp \left\{-\left[-\frac{8760}{1 \times 10^{4} \times 2.5 \times 10^{5}} \right]^{1/2} \right\}=0.00187 . Thus the survival probability is equal to 1 – F(8760) \ or \ 0.998.

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