The existing researches have shown that internal degradation processes
and external shocks may simultaneously interfere with the reliability of
dynamic systems in uncertain random environments. Assume that failure
processes are dependent, that is, shocks may accelerate degradation
processes by additional degradations. Wear and additional degradations
are uncertain, while shocks are considered to be random. As a natural
consideration, it is necessary to maximize the reliability of
multi-stage uncertain random systems. In this paper, a maximizing
reliability problem is presented, and recurrence equations are provided
by Bellman's principle. These are successfully applied to maximize
reliability index in two special cases with linear and quadratic state
equations. In addition, two effective algorithms are developed to
achieve optimal solutions. Finally, a numerical example of a metallized
film pulse capacitor is proposed which aims to indicate that
optimization method is beneficial to maximize the reliability of
multi-stage systems.