LIFELENGTH IN A RANDOM ENVIRONMENT

Let T denote the lifelength of a component, the distribution of which, conditional on a parameter y, is known. It is supposed that y is a realization of nonnegative stochastic process {Y(t), t greater-than-or-equal-to 0}, reflecting random variation in the environment in which the component is operating. Conditions are determined under which the distribution of T given {Y(t), t greater-than-or-equal-to 0} is IFR, DFR, IFRA, DFRA, NBU or NWU. Further, conditions are determined under which, if the conditional distributions of T1 and T2, the lifelengths of two components, are ordered stochastically or in variability, a similar order holds for the corresponding marginal distributions.