# Reliability

### Reliability :

Reliability is the capability of an entity to accomplish a required function with the given data during a given interval of time.

### Failure :

Failure is the incapability of a device to accomplish the expected function. It can be partial (performance altering) or complete (end of operation).

### R(t)

The probability that en entity E should be in non-failure during a period of time [0; t], assuming that it is not in failure at the time t = 0

### F(t)

F (t) is the cumulative function of failures: F (t) = 1 - R (t)

### Probability density :

F(t)) represents the failure rate of a product, i.e. the probability of a product's failure over an interval of time [t, t+dt]

### λ(t) or failure rate :

λ(t) represents the failure rate of a product, i.e. the probability of a product's failure over a given time interval [t, t+dt] understanding that it was not in failure at the time t.

- λ(t) decreases: the failure rate decreases over time, this corresponds in general with infant failure. Products with intrinsic failures deteriorate quickly wheras other products last much longer.
- λ(t) constant: the failure rate is not dependent on time. There is as much risk that a product should fail at the moment t as over its life time. These are intrinsic failures. This is the type of failure often found in electronic products;
- λ(t) increases: the failure rate increases over time. There is more and more risk of product failure with the increase of lifespan. This is the product's end of life.

### MTTF (Mean Time To Failure)

The MTTF, used more in product Reliability, is the mean time before the appearance of the first failure.

### MTBF (Mean Time Between Failure)

The MTBF (Mean Time Between Failures) is the mean of the time intervals between the appearance of failures