Risk Times in Mission‐Oriented Systems

ABSTRACT This article assesses risk times in mission‐oriented systems with high safety standards. We examine critical times under two safety policies. The first requires that the system's reliability function, known the first failure of the components, must exceed a reliability level throughout the mission. The second demands that the conditional distribution of the system's lifetime, given the first failure of the components, must be more reliable, in terms of the usual stochastic order, than the original system's lifetime. Our study analyzes the critical times at which both policies remain viable. Our methodology, applicable to multiple failure scenarios, identifies sufficient conditions for the existence of these times. We offer explicit solutions for parallel systems with IID components and a general method for dependent and identically distributed components. The study includes practical examples and introduces a non‐parametric estimator for the critical times.