Let Tx be the time it takes for a pure jump process, which starts at 0, to cross a threshold x>0. Sufficient conditions on the parameters of this process under which Tx has increasing failure rate average (IFRA), increasing failure rate (IFR) or logconcave density (PF2) are identified. The conditons for IFRA are weaker than those of Drosen. Sufficient conditions on the parameter of a pure jump process for Tx to the IFR or PF2 are not available in the literature.
