# Predicting component failture with joint density functions

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• Nov 17th 2009, 05:04 AM
Intsecxtanx
Predicting component failture with joint density functions
A device contains two components. The device fails if either component fails. The joint density function of the lifetimes of the components, measured in hours, is f(s, t) , where $0 < s < \infty$ and $0 < t < \infty$. What is the probability that the device fails during the first half hour of operation, expressed in terms of the cumulative distribution function F (s, t)? Thanks for your help (Bow)
• Nov 17th 2009, 03:48 PM
mr fantastic
Quote:

Originally Posted by Intsecxtanx
A device contains two components. The device fails if either component fails. The joint density function of the lifetimes of the components, measured in hours, is f(s, t) , where $0 < s < \infty$ and $0 < t < \infty$. What is the probability that the device fails during the first half hour of operation, expressed in terms of the cumulative distribution function F (s, t)? Thanks for your help (Bow)

You need to express Pr(S < 1/2 or T < 1/2) = 1 - Pr(S > 1/2 and T > 1/2) in terms of the cdf.