First-Passage Time Distribution of Brownian Motion as a Reliability Model

Since the inverse Gaussian distribution arises as the distribution of first passage time of Brownian motion, its applicability to lifetime or survival situations is a natural consequence. The failure rate for the inverse Gaussian distribution first increases until it reaches its maximum value somewhere to the right of the mode, then it decreases monotonically to a non-zero asymptotic value. This paper fits the inverse Gaussian distribution model to observed failure data of high speed steel tools in machining low carbon steel. Then the lognormal distribution model is hypothesized for the same failure data. The inverse Gaussian fits better.