A PERSPECTIVE ON RELIABILITY: PROBABILITY THEORY AND BEYOND

Reliability assessment in the coming era is inclined to be characterized by a difficult dilemma. On the one hand units and systems will be required to be ultra reliable; on the other hand, it may not be possible to subject them to a full-scale testing. A case in point occurs where testing is limited is one-of-a-kind complex systems, such as space exploration vehicles or where severe testing constraints are imposed such as full scale testing of strategic nuclear weapons prohibited by test ban treaties and international agreements. Decision makers also require reliability assessments for problems with terabytes of data, such as from complex simulations of system performance. Quantitative measures of reliability and their associated uncertainties will remain integral to system monitoring and tactical decision making. The challenge is to derive these defensible measures in light of these dilemmas. Because reliability is usually defined as a probability that the system performs to its required specification, probability enters into the heart of these dilemmas, both philosophically and practically. This paper provides an overview of the several interpretations of probability as they relate to reliability and to the uncertainties involved. The philosophical issues pertain to the interpretation and the quantification of reliability. For example, how must we interpret a number like 10{sup {minus}9}, for the failure rate of an airplane flight or an electrical power plant? Such numbers are common, particularly in the context of safety. Does it mean one failure in 10{sup 9} identical, or almost identical, trials? Are identical trials physically possible, let alone the fact that 10{sup 9} trials can take generations to perform? How can we make precise the notion of almost identical trials? If the trials are truly identical, then all of them must produce the same outcome and so the reliability must be either one or zero. However tautologies, like certainty and impossibility, can be claimed only on the basis of pure logic, not empirical evidence. Thus, from a practical point of view, an interpretation of reliability that is devoid of abstractions like 10{sup 9} identical trials, appears to be in order. It is the meaning of probability that lies at the core of the interpretation of reliability