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8. Assessing Product Reliability
8.1. Introduction
8.1.2. What are the basic terms and models used for reliability evaluation?

Reliability or survival function

Survival is the complementary event to failure The Reliability Function \(R(t)\), also known as the Survival Function \(S(t)\), is defined by $$ R(t) = S(t) = \mbox{the probability a unit survives beyond time } t \, . $$

Since a unit either fails, or survives, and one of these two mutually exclusive alternatives must occur, we have $$ R(t) = 1 - F(t), \,\,\,\,\, F(t) = 1 - R(t) \, . $$

Calculations using \(R(t)\) often occur when building up from single components to subsystems with many components. For example, if one microprocessor comes from a population with reliability function \(R_m(t)\) and two of them are used for the CPU in a system, then the system CPU has a reliability function given by $$ R_{cpu}(t) = R_m^2(t) \, , $$

The reliability of the system is the product of the reliability functions of the components since both must survive in order for the system to survive. This building up to the system from the individual components will be discussed in detail when we look at the "Bottom-Up" method. The general rule is: to calculate the reliability of a system of independent components, multiply the reliability functions of all the components together.
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