Positive dependence properties of conditionally independent random lifetimes

Conditions under which conditionally independent random variables are posit ive dependent are described in this paper. For example, it is shown that if the conditionally independent random variables increase in the hazard rate sense in the condition, then they are WBF (weakened by failures). It is al so shown that if the conditionally independent random variables increase in the likelihood ratio sense in the condition, then they are MTP2 (multivari ate totally positive of order 2). The results are given for the cases in wh ich the condition is either a random variable or a random vector. Some appl ications in the areas of imperfect repair, budget allocation, random enviro nments, and discrete-time filtering, illustrate the theory.