The Epsilon Probability Distribution and its Application in Reliability Theory

This paper elaborates a new probability distribution, namely, the epsilon probability distribution with implications for reliability theory and management. This probability distribution is founded on the so-called epsilon function that is introduced here. It is also shown that the asymptotic epsilon function is just an exponential function. The properties of this probability distribution suggest that it may serve as a viable alternative to the exponential probability distribution. As the epsilon probability distribution function is a power function, it is more convenient than the exponential probability distribution function from a computational point of view. The main findings and a practical example indicate that the new probability distribution can be utilized to describe the probability distribution of the time to first failure random variable both in the second and third phases of the hazard function.