Stochastic reliability functions for failure rates derived from Gauss - Markov processes (Corresp.)

An extension of the well-known Cameron-Martin formula can be interpreted as the expectation of a stochastic reliability function applicable in those situations where nondecreasing failure rates are desired. This follows ff the failure rate is modeled as the square of a Gauss-Markov process. We describe the methodology for the general vector case, and then specialize the results to the one-dimensional case so as to obtain an exact closed-form expression for the reliability function. Using the theory of recurrent and transient processes, we then show how the choice of a model parameter and the initial state influence reliability.