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## Exponential Distribution

Reliability
Reliability

### What is exponential distribution?

The probability of survival and of failure of components or equipment is under the condition of chance failure which means a constant instantaneous failure rate where the die-off rate is the same for any surviving (unfailed) population. An old part is as good as a new part. For any survivors in this memory-less system that have survived to time t, a certain percent of the survivors will die in a specified interval of time such as 2*t. The reliability of the system is often described by the exponential distribution because many times a system is made-up of mixed failure modes which in the aggregate will function like a constant failure rate system. The reliability of exponential distributions are described mathematically as R(t) = e^(-lt) = e^(-t/Q) where t is the mission time, l is the failure rate, and Q is the mean time, given that l=1/Q. The exponential distribution is frequently used as a first approximation to describe reliability based on a simple failure rate or a simple mean time to failure-particularly if the system or component has multiple failure modes.

### Why use exponential distribution?

The constant hazard rate, l, is usually a result of combining many failure rates into a single number.

### When to use exponential distribution?

The exponential distribution is frequently used for reliability calculations as a first cut based on it's simplicity to generate the first estimate of reliability when more details failure modes are not described.

### Where to use exponential distribution?

In electronic systems (which can have many different types of failure modes and the fact that any electrical/electronic system is an amalgam of many different components) the simple assumption is that the electrical/electronic package will have a constant failure rate system defined by the exponential distribution. When in doubt about the failure mechanisms, it is common to assume use of the exponential distribution with it's constant failure rate for simplicity.

These definitions are written by H. Paul Barringer