Our basic problem is that of an optimal control whose Bolza payoff is the sum between a simple integral and a function of the initial and final events whose evolution ODE is a reliability flow. The original results include: (i) a list of payoffs with reliability sense, (ii) optimal value of mean time to failure functional constrained by controlled queueing system, (iii) optimal value of mean time to failure functional constrained by controlled Markov system, and (iv) optimal value of mean time to failure functional associated to parallel systems.

reliability integral functional, optimal values of reliability functionals, controlled queueing system, controlled Markov system.