Life Distributions Derived from Stochastic Hazard Functions

Most of the familiar time-to-failure distributions used today are derived from hazard functions whose parameters are assumed constant. An unconditional time-to-failure distribution is derived here by assuming that a parameter of a classical failure distribution (viz., exponential and Weibull) is a random variable with a known distribution. With the use of the derived compound distributions and Bayesian techniques, it is possible to join the test data with prior information to arrive at a combined, and possibly superior, estimate of reliability. The prior distributions considered here are the two-point, the uniform, and the gamma. Conceptually, such a scheme may be a more realistic model for describing failure patterns under specific conditions.