On a method for mending time to failure distributions

Many software reliability growth models assume that the time to next failure may be infinite; i.e., there is a chance that no failure will occur at all. For most software products this is too good to be true even after the testing phase. Moreover if a non-zero probability is assigned to an infinite time to failure, metrics like the mean time to failure do not exist. In this paper we try to answer several questions: Under what condition does a model permit an infinite time to next failure? Why do all non-homogeneous Poisson process (NHPP) models of the finite failures category share this property? And is there any transformation mending the time to failure distributions? Indeed, such a transformation exists; it leads to a new family of NHPP models. We also show how the distribution function of the time to first failure can be used for unifying finite failures and infinite failures NHPP models.