Order Statistics Distribution for General Multivariate Distribution

A mission-critical service has three batteries with mean times to failure , , and . Dependencies of the failure times are assumed to be given by Farlie-Gumbel-Morgenstern copula with parameter . Consider the event of the second battery 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 :
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Find the expected time to failure:
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Plot the survival function for tau_1⩵8.0, , and for different values of copula parameter :
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