The Bathtub Curve in Reliability

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The bathtub curve is widely used in modelling and predicting system failures. It consists of three sections:

  • Early Failures (Infant Mortality) Phase: This phase has a decreasing failure rate.
  • Random Failure (Useful Life) Phase: This phase has a constant failure rate.
  • Wear-out Phase: This phase has an increasing failure rate.

Early Failure Phase:

The early failure phase (also called the infant mortality phase) occurs when a product is used for the first time. It is an interval where the number of failures (or the probability of failure) is initially high but then decreases slowly until stabilizing at a low level.

Failure events during this time are usually caused by design flaws, material defects, production defects, or improper startup procedures.

A good example of this type of failure is the newly purchased house. During the first few years, it will have many problems such as cracks in walls, doors, windows, etc. These problems are primarily due to poor material, workmanship or bad design. As the house ages, these problems become less frequent because the contractor fixes them.

In the case of non-repairable products, the poor-quality products that fail during the early stage will be taken out of service, and the probability of failure of the remaining items will keep decreasing.

Some strategies to reduce the early phase failures include HALT, HASS, ESS and burn-in tests.

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  • Random Failure Phase:

    Once initial issues with the product have been resolved, the product enters the random failure phase. In this phase, the probability of failure remains constant over time.

    Much of the reliability analysis focuses on this product life cycle phase. This phase can last for several years. However, if the product is designed well, the probability of failure should remain stable after some time. This phase is also called the useful life phase.

    Wear-out Phase:

    As the product continues to operate, it gradually wears down. Eventually, the probability of failure increases dramatically. A typical example of this is the gradual deterioration of mechanical parts.

    The wear-out phase mainly happens because the component becomes worn out. When the part gets worn out, its performance deteriorates. The probability of failure increases rapidly as the part reaches the end of its lifetime.


    Reliability engineering is about predicting how long a product will perform satisfactorily. There are three phases in the product life cycle:

    • Infant mortality phase - This phase starts immediately after the product is sold. During this phase, many failures are mainly due to manufacturing defects, installation errors, or other human factors.

    • Random failure phase – After the product passes through the infant mortality phase, the probability of failures begins to decrease.

    • Wear-out phase – Once the product reaches the end of its lifespan, the probability of failure will increase significantly.


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