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## Reliability Function

The reliability function is one of the widely used functions in both data analysis and reliability engineering. It is used to compute the probability of a system operating for a particular amount of period without failing. As such, we can say that the reliability function is bounded by time. Meaning, all reliability values are linked to an associated time value. In simple terms, you should specify a reliability value with a time value. For example, 90% reliability at 80 hours.

## Reliability Coherent Systems

Coherent systems are used in reliability theory to represent the structure of technical systems. A coherent system is made up of elements that have random lifetimes. These systems should also satisfy these two conditions:

- Every component is relevant
- A working system will not fail if you replace a working component with a working one

## Bivariate exponential distributions

Exponential distributions are lifetime models used in several areas such as telecommunications and life testing. The stress-strength model is often used in reliability theory to explain a component’s life based on random strength and subjected random stress. If this system is exposed to stress greater than its strength, then the system will fail instantly. Similarly, as long as the strength is greater than the stress exposed to it, the component will function correctly. Here are some examples of this type of distributions:

- Gumbel’s
- Hougaard’s
- Downton’s