JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV RELIABILITY ENGINEERING Previous Question Paper (September - 2020 - R16)

The hazard rate, also known as the instantaneous failure rate, is defined as the probability that a component or system will fail in the next instant, given that it has survived up to the present time. Mathematically, if R(t) is the reliability function and f(t) is the probability density function of failures, the hazard rate λ(t) is expressed as:

For example, consider a light bulb with a constant failure rate of 0.001 failures per hour. This means that at any given hour, if the bulb is still functioning, there is a 0.1% probability that it will fail within the next hour. Unlike the failure rate over a long period, the hazard rate provides a dynamic measure of the likelihood of failure at a specific point in the component's life cycle.

The Bath Tub Curve is a graphical representation of the failure rate of a system or component over its entire operational life. It is divided into three distinct phases:

1. Infant Mortality Phase (Decreasing Failure Rate): Characterized by a high initial failure rate due to manufacturing defects, poor quality control, or installation errors. As these early failures are identified and removed, the failure rate drops rapidly.
2. Useful Life Phase (Constant Failure Rate): Also known as the 'steady-state' or 'intrinsic' failure period. During this time, the failure rate is low and relatively constant, typically caused by random, unpredictable events. This is the period where most systems are expected to operate reliably.
3. Wear-out Phase (Increasing Failure Rate): The final stage where the failure rate increases significantly as components degrade due to age, fatigue, corrosion, or environmental stress. Preventive maintenance or replacement is critical during this phase to avoid system failure.

The shape resembles a bathtub, with high rates at the start and end, and a flat, low-rate bottom section in the middle.