The Bathtub Curve
reliability context, the so called bathtub curve is an idealized
representation of the failure rate (or MTBF) of a population of items
bathtub curve has three phases, each of them representing a product
life phase. Lambda = failure rate = 1/MTBF, and t = time.
failures, also called infant mortality,
are typical for immature products with design flaws.
product life phase. This and only this life phase
should customers encounter with their product.
beyond their useful lifetime.
As said, this curve is idealized. Most real curves are not that smart.
Apart from the 3 product life phases, the bathtub curve shows
an even more important topic: Lifetime and MTBF are *obviously* not the same.
Lifetime is just the duration of the product life (the t-axis), MTBF
(or it's reciprocal lambda, failure rate) is a function of t.
The difference boils down to this:
The MTBF is the mean
time between two failures during the
useful product life phase.
depends strongly on the complexity (= # of single components) of the
system, whereas Lifetime is always in the same range regardless of the
type of product, typically between 10 and 30 years. The table below
gives some examples.
MTBF vs Lifetime
(1 mio h) >> Lifetime (15 y)
||MTBF (15 y) ~
Lifetime (15 y)
(several weeks) << Lifetime (20 y)
bathtub curve is actually a sum of three individual curves
three individual curves can be expressed by the Weibull distribution,
however with different form factors:
distribution form factor
= 1, exponential distribution
||Form factor > 1|