A Stochastic Justi cation of Some Simple Reliability Models
نویسنده
چکیده
In this paper we give conditions on the internal wear process under which the resulting time-to-failure model will be of the simple collapsible form (Oakes, 1995, Duchesne and Lawless, 2000) when the usage accumulation history is available. We suppose that failure occurs when internal wear crosses a certain threshold and/or a traumatic event causes the item to fail (Cox, 1999 and Bagdonavi cius and Nikulin, 2001). We model the innnitesimal increment in internal wear as a function of time, accumulated internal wear and usage history, and we derive conditions on this function to get a collapsible model for the conditional distribution of time-to-failure given the usage history.
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