Theoretical Statistics and Mathematics Unit, ISI Delhi

Bounds for reliability of IFRA coherent systems using signatures

by Jayant V. Deshpande and Isha Dewan

The reliability of any coherent system is the probability that it completes a mission of time $t$ without failure.
To calculate it one needs to know the structure function of the system and the distribution of the component life times which we assume to be independent and
identically distributed continuous positive valued random variables.
In this paper we bring together (i) the single crossing property of IFRA distributions , (ii) the concept of a signature and (iii)
the fact that the life distribution of a coherent system of IFRA components is itself IFRA (the celebrated IFRA closure theorem)
to obtain useful functional bounds for the reliability of coherent systems of IFRA components.
These bounds are in terms of the quantile of a specified order or the mean of the common component life distribution and the signature of the coherent system.
This obviates the need of the knowledge of the entire survival function and the knowledge of the coherent system beyond its signature.
We tabulate these reliability bounds for several 3, 4 and 5 component systems and show that they are very close to the true reliability in certain instances.

isid/ms/2011/17 [fulltext]

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