Bathtub curve

The 'bathtub curve' hazard function (blue, upper solid line) is a combination of a decreasing hazard of early failure (red dotted line) and an increasing hazard of wear-out failure (yellow dotted line), plus some constant hazard of random failure (green, lower solid line).

The bathtub curve is widely used in reliability engineering. It describes a particular form of the hazard function which comprises three parts:

• The first part is a decreasing failure rate, known as early failures.
• 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 a bathtub: steep sides and a flat bottom.

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 rapidly 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 product life cycles strongly exhibit the bathtub curve.

While the bathtub curve is useful, not every product or system follows a bathtub curve hazard function, for example if units are retired or have decreased use during or before the onset of the wear-out period, they will show fewer failures per unit calendar time (not per unit use time) than the bathtub curve.

The term "Military Specification" is often used to describe systems in which the infant mortality section of the bathtub curve has been burned out 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 environmental stress screening.

In reliability engineering, the cumulative distribution function corresponding to a bathtub curve may be analysed using a Weibull chart.

See also

• Gompertz–Makeham law of mortality

References

Klutke, G.; Kiessler, P.C.; Wortman, M.A. "A critical look at the bathtub curve". IEEE Transactions on Reliability 52 (1): 125–129. doi:10.1109/TR.2002.804492. ISSN 0018-9529. Retrieved 2015-06-16.