The bathtub curve is a particular shape of a

failure rate Failure is the social concept of not meeting a desirable or intended objective, and is usually viewed as the opposite of success. The criteria for failure depends on context, and may be relative to a particular observer or belief system. On ...

graph. This graph is used in

reliability engineering Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended functi ...

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 ...

. The 'bathtub' refers to the shape of a line that curves up at both ends, similar in shape to a

bathtub A bathtub, also known simply as a bath or tub, is a container for holding water in which a person or another animal may Bathing, bathe. Most modern bathtubs are made of thermoformed Acrylic resin, acrylic, porcelain enamel, porcelain-enameled s ...

. The bathtub curve has 3 regions: #The first region has a decreasing

due to early

failure Failure is the social concept of not meeting a desirable or intended objective, and is usually viewed as the opposite of success. The criteria for failure depends on context, and may be relative to a particular observer or belief system. On ...

s. #The middle region is a constant failure rate due to

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

failures. #The last region is an increasing failure rate due to wear-out failures. Not all products exhibit a bathtub curve failure rate. 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. Many electronic consumer product life cycles follow the bathtub curve. 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 amounts of products in use and associated failure rate data. 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. 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. Ever ...

corresponding to a bathtub curve may be analysed using a Weibull chart or in a reliability contour map.

See also

References

Further reading