Time-Dependent System Reliability (Analytical)

In the previous chapter, different system configuration types were examined, as well as different methods for obtaining the system's reliability function analytically. Because the reliabilities in the problems presented were treated as probabilities (e.g. $$P(A)$$,  $${{R}_{i}}$$ ), the reliability values and equations presented were referred to as static (not time-dependent). Thus, in the prior chapter, the life distributions of the components were not incorporated in the process of calculating the system reliability. In this chapter, time dependency in the reliability function will be introduced. We will develop the models necessary to observe the reliability over the life of the system, instead of at just one point in time. In addition, performance measures such as failure rate, MTTF and warranty time will be estimated for the entire system. The methods of obtaining the reliability function analytically remain identical to the ones presented in the previous chapter, with the exception that the reliabilities will be functions of time. In other words, instead of dealing with $${{R}_{i}}$$, we will use  $${{R}_{i}}(t)$$. All examples in this chapter assume that no repairs are performed on the components. = Sections =
 * 1) Analytical Life Predictions
 * 2) Approximating the System CDF
 * 3) Duty Cycle
 * 4) Load Sharing
 * 5) Standby Components
 * 6) Note Regarding Numerical Integration Solutions