Abstract :
It is usually assumed that the underlying distribution of times to failure of systems is the exponential distribution. This is justified on the basis of the bathtub curve or Drenick´s theorem, but the bathtub curve is merely a statement of plausibility and conflicts with Drenick´s theorem. Even if exponentiality is not assumed, it is usually assumed that a system under study is as-good-as-new after repair. This is not a plausible assumption to make for a complex system. If failure data are available they should be tested for trend among successive failure times. If a trend exists, a time dependent (nonhomogeneous) Poisson process (called bad-as-old model in this paper) should be fitted and tested for adequacy. This paper is not intended to provide a rigorous, definitive treatment of bad-as-old models. Rather, it has three main purposes: 1) to point out the glaring, but somehow usually overlooked, inconsistency between the commonly accepted concept of wearout of repairable systems and the a priori use of renewal processes for modeling these systems; 2) to outline basic procedures for evaluating data from repairable systems and for formulating bad-as-old probabilistic models; and 3) to present the results of Monte Carlo simulations, which illustrate the grossly misleading results which can occur if independence of successive failure times is invalidly assumed.
