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On the collapsibility of lifetime regression models. (English) Zbl 1057.60080

The authors consider deterministic and stochastic failure time models for the accumulation of internal wear given the usage history. In their models the infinitesimal increment of internal wear is a function of time, accumulated internal wear and usage history; failure may be due only to excessive wear, only to a traumatic event, or to both (whichever occurs first). They characterize classes of such models that are collapsible, meaning that for any time \(t\) the probability of survival past \(t\) only depends on \(t\) (and not on the entire usage history up to \(t\)).

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
62N05 Reliability and life testing
90B25 Reliability, availability, maintenance, inspection in operations research
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