An accelerated life testing is conducted to obtain failure data in short test durations. The...

An accelerated life testing is conducted to obtain
failure data in short test durations. The objective of the test is to subject
the aluminum-alloy-based devices to high current density and high temperature.
The following test parameters are applied:

Current density of J = 1.8 × 10^{6} A/cm^{2}.
Temperature of 60∘
C. The material-processing constant is

A_{0} = 6.99 × 10^{−4}. The
activation energy of this alloy is Ea = 1.1 eV. The current density exponent is
1.8.

(a) Obtain the median life of the device.

(b) Due to the sensitivity of the devices to small
variations of the test parameters and materials properties, the test engineer
assumes that the failure time distribution is lognormal. The mean of the
lognormal distribution is m = eμ + σ2 2 ; its median is median = e μ
. Assume σ = 0.5 obtain the mean of the distribution.

(c) Obtain the reliability function and estimate the
MTTF.