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Derivation of the Distribution Function for the Tampered Brownian Motion Process Model
Arthur Fries
Institute for Defense Analyses
The tampered Brownian motion process (BMP) arises in the context of partial step-stress accelerated life testing when the underlying system fatigue accumulated over time is modeled by two constituent BMPs, one governing up to the predetermined time point at which the stress level is elevated and the other afterwards. A conditioning argument obtains the probability distribution function (pdf) of the corresponding time-to-failure random variable. This result has been reported and studied in the literature, but its derivation has not been published.