The bathtub curve is widely used in

reliability engineering Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specifie ...

and

deterioration modeling Deterioration modeling is the process of modeling and predicting the physical conditions of equipment, structures, infrastructure or any other physical assets. The condition of infrastructure is represented either using a deterministic index or ...

. It describes a particular form of the

hazard function Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering. The failure rate of a ...

which comprises three parts: *The first part is a decreasing

failure rate Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering. The failure rate of a ...

, known as early

failure Failure is the state or condition of not meeting a desirable or intended objective (goal), objective, and may be viewed as the opposite of Success (concept), success. The criteria for failure depends on context, and may be relative to a parti ...

s. *The second part is a constant failure rate, known as

random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. Ind ...

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 A bathtub, also known simply as a bath or tub, is a container for holding water in which a person or animal may bathe. Most modern bathtubs are made of thermoformed acrylic, porcelain-enameled steel or cast iron, or fiberglass-reinforced poly ...

: 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 speaking for consumer products—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 electronic 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. In reliability engineering, the

cumulative distribution function In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Ev ...

corresponding to a bathtub curve may be analysed using a

Weibull chart Weibull is a Swedish locational surname. The Weibull family share the same roots as the Danish / Norwegian noble family of Falsenbr>They originated from and were named after the village of Weiböl in Widstedts parish, Jutland, but settled in Skån ...

. Hang Zhou, Ajith Kumar Parlikad, and Andrew Harrison from the

University of Glasgow , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

, and

Rolls-Royce Rolls-Royce (always hyphenated) may refer to: * Rolls-Royce Limited, a British manufacturer of cars and later aero engines, founded in 1906, now defunct Automobiles * Rolls-Royce Motor Cars, the current car manufacturing company incorporated in ...

have demonstrated and mathematically proved that the wear-out stage of the 'bathtub curve' can be further brought to a higher dimension, and is developed into the concept of reliability surface, with its dimensionality reduction projection as the reliability contour map.

See also

References

Further reading