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Two alternative statistical descriptions of device and chip failure by multiple breakdown events in thin-oxide MOS devices are compared: the successive breakdown approach and the hard-breakdown prevalence ratio method. Both methods are demonstrated to be compatible descriptions of the experimental breakdown data. It is confirmed that the successive breakdown events are uncorrelated and that the relative probability of soft and hard breakdown is independent of the time to breakdown and of the number of previous breakdown events. As a consequence, the prevalence ratio concept is applied to the distribution of successive events, thus closing the loop of a fully consistent picture. Applications of these statistical methods to reliability assessment are discussed, and the criterion that should guide the choice of methodology is established.