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This discussion provides an overview of the mathematics of reliability theory. It is not presented as a complete (or mathematically rigorous) discussion of probability theory and statistics but should give the reader a reasonable understanding of how reliability is calculated. Before beginning the discussion, a key point must be made. Reliability is a design characteristic that indicates a system's ability to perform its mission over time without failure or without logistics support. In the first case, a failure can be defined as any incident that prevents the mission from being accomplished; in the second case, a failure is any incident requiring unscheduled maintenance. Reliability is achieved through sound design, the proper application of parts, and an understanding of failure mechanisms. Estimation and calculation techniques are necessary to help determine feasibility, assess progress, and provide failure probabilities and frequencies to determine spare part requirements and other analyses.
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