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Concept# Bathtub curve

Summary

The bathtub curve is a particular shape of a failure rate graph. This graph is used in reliability engineering and deterioration modeling. The 'bathtub' refers to the shape of a line that curves up at both ends, similar in shape to a bathtub. The bathtub curve has 3 regions:
The first region has a decreasing failure rate due to early failures.
The middle region is a constant failure rate due to random 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 corresponding to a bathtub curve may be analysed using a Weibull chart or in a reliability contour map.

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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 specified period of time. Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time. The reliability function is theoretically defined as the probability of success at time t, which is denoted R(t).

Survival analysis

Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology.

Exponential distribution

In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.

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