Bathtub curve

{{Short description|Curve for failure rates over time}} [[File:Bathtub curve.svg|thumb|right|350px|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).]]

In [[reliability engineering]] and [[deterioration modeling]], a '''bathtub curve''' is a [[failure rate]] graph that curves up at both ends, similar in shape to a [[bathtub]].{{cite book |last1=Smith |first1=David J. |date=2022 |title=Reliability, Maintainability and Risk |edition=10 |publisher=Elsevier |chapter=Chapter 2 - Understanding Terms and Jargon |doi=10.1016/B978-0-323-91261-7.00007-1 |isbn=978-0-323-91261-7 |pages=22-23}} The term can also apply to any graph with this shape.{{cite web |title=Bathtub-Shaped Distribution |url=https://www.statisticshowto.com/bathtub-shaped-distribution/ |website=Statistics How To |archive-url=https://web.archive.org/web/20250318104402/https://www.statisticshowto.com/bathtub-shaped-distribution/ |archive-date=18 March 2025 |access-date=28 November 2025}}

Many but not all electronic consumer product life cycles follow the bathtub curve.{{Cite book|author=J. Lienig, H. Bruemmer|title=Fundamentals of Electronic Systems Design|pages=54|publisher=Springer International Publishing|date=2017|isbn=978-3-319-55839-4|doi=10.1007/978-3-319-55840-0}} It is difficult to know where a product is along the bathtub curve, or even if the bathtub curve is applicable to a certain product without large numbers of products in use and associated failure rate data.

In reliability engineering, the [[cumulative distribution function]] corresponding to a bathtub curve may be analysed using a [[Weibull chart]] or in a reliability contour map.

==Description== The bathtub curve has 3 regions: #The first region has a decreasing [[failure rate]] due to early [[failure|failures]] (a.k.a. the "Infant Mortality Phase"). #The middle region is a constant failure rate due to [[random]] failures (a.k.a. the "Useful Life Phase"). #The last region is an increasing failure rate due to [[wear-out]] failures (a.k.a. the "Wear-Out Phase").

A product is said to follow the bathtub curve if in the early life of a product, the failure rate decreases as defective products are identified and discarded, and early sources of potential failure such as manufacturing defects or damage during transit are detected. In the mid-life of a product the failure rate is constant. In the later life of the product, the failure rate increases due to wearout.

If products are retired early or have decreased usage near their end of life, the product may show fewer failures per unit calendar time (but not per unit use time) than the bathtub curve predicts.

Some manufacturers [[burn in]] or [[product testing|test]] their products in an attempt to reduce early failures.{{cite web |last1=Klein |first1=Andy |title=Drive Failure Over Time: The Bathtub Curve Is Leaking |url=https://www.backblaze.com/blog/drive-failure-over-time-the-bathtub-curve-is-leaking/ |date=26 October 2021 |publisher=Backblaze |archive-url=https://web.archive.org/web/20211027123712/https://www.backblaze.com/blog/drive-failure-over-time-the-bathtub-curve-is-leaking/ |archive-date=27 October 2021 |access-date=28 November 2025}}

==See also== *[[Gompertz–Makeham law of mortality]]

==References== {{Reflist}}

==Further reading== *{{cite journal |last1=Klutke |first1=G. |last2=Kiessler |first2=P.C. |last3=Wortman |first3=M. A. |title=A critical look at the bathtub curve |journal=IEEE Transactions on Reliability |issn=0018-9529 |doi=10.1109/TR.2002.804492 |volume=52 |issue=1 |pages=125–129 |date=March 2003 }}

{{DEFAULTSORT:Bathtub Curve}} [[Category:Reliability engineering]] [[Category:Engineering failures]] [[Category:Curves]]