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Generate Reference Book: may be more up-to-date In the 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.,, ), 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, we will use. All examples in this chapter assume that no repairs are performed on the components. Repairable systems analysis will be introduced in a. Analytical Life Predictions The analytical approach presented in the prior chapter involved the determination of a mathematical expression that describes the reliability of the system, expressed in terms of the reliabilities of its components. So far we have estimated only static system reliability (at a fixed time). For example, in the case of a system with three components in series, the system's reliability equation was given by: The values of, and were given for a common time and the reliability of the system was estimated for that time.

However, since the component failure characteristics can be described by distributions, the system reliability is actually time-dependent. In this case, the equation above can be rewritten as: The reliability of the system for any mission time can now be estimated. Assuming a Weibull life distribution for each component, the first equation above can now be expressed in terms of each component's reliability function, or: In the same manner, any life distribution can be substituted into the system reliability equation.

Suppose that the times-to-failure of the first component are described with a Weibull distribution, the times-to-failure of the second component with an exponential distribution and the times-to-failure of the third component with a normal distribution. Then the first equation above can be written as: It can be seen that the biggest challenge is in obtaining the system's reliability function in terms of component reliabilities, which has already been discussed in depth. Sisindri movie songs free download doregama.

Once this has been achieved, calculating the reliability of the system for any mission duration is just a matter of substituting the corresponding component reliability functions into the system reliability equation. Advantages and Disadvantages The primary advantage of the analytical solution is that it produces a mathematical expression that describes the reliability of the system. Once the system's reliability function has been determined, other calculations can then be performed to obtain metrics of interest for the system. Such calculations include: • Determination of the system's pdf. • Determination of warranty periods. • Determination of the system's failure rate. • Determination of the system's MTTF.

In addition, optimization and reliability allocation techniques can be used to aid engineers in their design improvement efforts. Another advantage in using analytical techniques is the ability to perform static calculations and analyze systems with a mixture of static and time-dependent components.

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Finally, the reliability importance of components over time can be calculated with this methodology. The biggest disadvantage of the analytical method is that formulations can become very complicated. The more complicated a system is, the larger and more difficult it will be to analytically formulate an expression for the system's reliability. For particularly detailed systems this process can be quite time-consuming, even with the use of computers. Furthermore, when the maintainability of the system or some of its components must be taken into consideration, analytical solutions become intractable.