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Bathtub curve

 

 
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Bathtub curve
 
 
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The bathtub curve is widely used in reliability engineeringReliability engineering

Reliability engineering is the discipline of ensuring that a system will be reliable when operated in a specified manner....
, although the general concept is also applicable to humans. It describes a particular form of the hazard function which comprises three parts:

  • The first part is a decreasing failure rateFailure rate

    Failure rate is the frequency with an engineered system or component fails, expressed for example in failures per hour....
    , known as early failuresFailure

    Failure in general refers to the state or condition of not meeting a desirable or intended objective....
    .
  • The second part is a constant failure rate, known as random failures.
  • The third part is an increasing failure rate, known as wear-out failures.


The name is derived from the cross-sectional shape of the eponymous device.

The bathtub curve is generated by mapping the rate of early "infant mortality" failures when first introduced, the rate of random failures with constant failure rate during its "useful life", and finally the rate of "wear out" failures as the product exceeds its design lifetime.

In less technical terms, in the early life of a product adhering to the bathtub curve, the failure rate is high but quickly decreasing as defective products are identified and discarded, and early sources of potential failure such as handling and installation error are surmounted. In the mid-life of a product - generally, once it reaches consumers - the failure rate is low and constant. In the late life of the product, the failure rate increases, as age and wear take their toll on the product. Many consumer products strongly reflect the bathtub curve, such as computer processors.

The bathtub curve is often modeled by a piecewise set of three hazard functions,



While the bathtub curve is useful, not every product or system follows a bathtub curve hazard function.

The term "Military Specification" is often used to describe systems in which the infant mortality section of the bathtub curve has been burned outBurn in

Burn in is that process by which components of a system are exercised prior to being placed in service....
 or removed. This is done mainly for life critical or system critical applications as it greatly reduces the possibility of the system failing early in its life. Manufacturers will do this at some cost generally by means similar to accelerated stress testing.

In reliability engineering, the cumulative distribution functionCumulative distribution function

In probability theory, the cumulative distribution function completely describes the probability distribution of a real-val...
 corresponding to a bathtub curve may be analysed using a Weibull chart.

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