Reliability is the capability of an entity to accomplish a required function with the given data during a given interval of time.
Failure is the incapability of a device to accomplish the expected function. It can be partial (performance altering) or complete (end of operation).
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) 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