Theoretical Statistics and Mathematics Unit, ISI Delhi

Two component load sharing systems with applications to Biology

by J. V. Deshpande, Isha Dewan and U. V. Naik-Nimbalkar

Life times of load sharing parallel systems have been considered in the statistical literature at least since Daniels (1945). The
main characteristic of such a two component system is that after the failure of one component the surviving component has to
shoulder extra load and hence is prone to failure at an earlier time than what is expected under the original model. In other situations, the failure of one component may release extra resources to the other, thus delaying the system failure.
Gross et al
(1971) observed that similar considerations affect the functioning of a two organ system. In this paper we first consider
several observations schemes and identifiability issues under them. Then we construct a general semiparametric bivariate family of
distributions which explicitly models this phenomenon through proportional conditional hazards. McCool (2006) has suggested a
test for the hypothesis that the failures take place according to the original model against the alternative hypothesis that the
second failure takes place earlier than warranted within the Weibull model. We propose nonparametric tests for the same problem
which may be used for any continuous distribution for the component life times. We obtain estimates of the
power of the test and observe that it is quite high even for moderately distant alternatives. The tests are applied to several real
data sets to illustrate their use.

isid/ms/2007/06 [fulltext]

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