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In the reliability theory th,e joint life distribution of units is usually derived under the assumption of stochastic independence for the behavior of units. But it is seen in the practical situation that the stochastic dependence arises by the cause of putting the units in a same environment and so on. A shock model is used to formulate the joint life distribution in the existence of correlation. For example bivariate exponential distribution function and bivariate Erlang distribution function are ones formulated using the shock model. In the present paper the wider class of bivariate distribution function which is called bivariate shock model is defmed, and some properties are discussed. Using these properties the practically observable characteristic trend is explained and some bounds for the distribution function are given.

BIVARIATE SHOCK MODELS : NBU AND NBUE PROPERTIES, AND POSITIVELY QUADRANT DEPENDENCY