ebook: Engineering Analysis using Scilab and C

## 11.2 Component Failure Rates

Failure rate is the expected number of failures per unit time, and is shown with the constant (lambda), with the units of failures per hour.

Basically,

Failures tend (but do not have to) follow exponential failure rate curves. This also suggests a failure function.

A constant failure rate is the most commonly assumed. When this is the the case the failure rate is also the Mean Time Before Failure (MTBF). Note that the reliability is also the probability that the system will be operational.

Even when the e-to-the-t function is a good model for system failure a system MTBF can be varied during system life by variations in product usage. Example of these include,

- high heat levels
- excessive stresses
- "pot holes"
- etc.

The bathtub curve shows typical values for the failure rate.

The basic reliability equation can be rearranged, eventually leading to a compact expression,

MTTF (Mean Time To Failure) - this is the expected time before a failure.

The MTTR (Mean Time To Repair) for a system is the average time to repair a system. This is not simple to determine and often is based on experimental estimates.

The MTTF and MTTR both measure the time that the system is running between repairs, and the time the system is down for repairs. But, they must be combined for the more useful measure MTBF (Mean Time Before Failure),

The difference between MTBF and MTTR is often small, but when critical the difference must be observed.

availability is the chance that at any time a system will be operational. This can be determined experimentally, or estimated. For a system that is into it's useful lifetime, this can be a good measure. Note that at the beginning, and end of its life, this value will be changing, and will not be reliable.

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