Motivating the sure bounds

Motivation is provided for a theorem that provides upper and lower bounds for the reliability of configurable digital control systems. The reliability goals for these systems are too high to be established by natural life testing, which means the probability of system failure must be computed from mathematical models that capture the essential elements of fault occurrence and system fault recovery. The upper and lower bound theorem shows that system recovery can be adequately described by its first two moments, provided component failure rate is low and system recovery is fast. This result greatly simplifies both the fault injection experiments that study system recovery and the numerical computations that estimate the probability of system failure from a mathematical model.<>