Order Statistics Distribution for General Multivariate Distribution
A mission-critical service has three batteries with mean times to failure _{1}, _{2}, and _{3}. Dependencies of the failure times are assumed to be given by the Farlie-Gumbel-Morgenstern copula with parameter . Consider the event of the second battery's going out of order.
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Compute the survival function, i.e. the probability for the system to be in order after epoch t.
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Find the expected time to failure.
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Plot the survival function for _{1}=8.0, _{2}=5, and _{3}=4.5 for different values of copula parameter .