Failure rate is the frequency with which an engineered system or component fails, expressed for example in failures per hour. It is often denoted by the Greek letter λ (lambda) and is important in reliability engineering.In practice, the mean time between failures (MTBF, 1/λ) is often used instead of the failure rate. This is valid if the failure rate is constant (general agreement in some Reliability standards (Military and Aerospace) - part of the flat region of the Reliability bathtube curve , also called the "usefull life period". The MTBF is an important system parameter in systems where failure rate needs to be managed, in particular for safety systems. The MTBF appears frequently in the engineering design requirements, and governs frequency of required system maintenance and inspections. In special processes called renewal processes, where the time to recover from failure can be neglected and the likelihood of failure remains constant with respect to time, the failure rate is simply the multiplicative inverse of the MTBF (1/λ).
It is typical to model component reliability parameters by a single scalar value.
For example, a power transformer might be modeled with a failure rate of 0.03 per year. These scalar values, though useful, might not tell the entire story. Perhaps the most obvious example is the observation that the failure rates of certain components tend to vary with age.
It might seem reasonable to conclude that new equipment fails less than old equipment. When dealing with complex components, this is usually not the case.
In fact, newly installed electrical equipment has a relatively high failure rate due to the possibility that the equipment has manufacturing flaws, was damaged during shipping, was damaged during installation, or was installed incorrectly. This period of high failure rate is referred to as the infant mortality period or the equipment break-in period.
If a piece of equipment survives its break-in period, it is likely that there are no manufacturing defects, that the equipment is properly installed, and that the equipment is being used within its design specifications. It now enters a period referred to as its useful life, characterized by a nearly constant failure rate that can be accurately modeled by a single scalar number.
As the useful life of a piece of equipment comes to an end, the previously constant failure rate will start to increase as the component starts to wear out.
That is why this time is referred to as the wear out period of the equipment. During the wear out period, the failure rate of a component tends to increase exponentially until the component fails. Upon failure, the component should be replaced.
A graph that is commonly used to represent how a component’s failure rate changes with time is the bathtub curve. The bathtub curve begins with a high failure rate (infant mortality), lowers to a constant failure rate (useful life), and then increases again (wear out). Another name for the bathtub curve is the bathtub hazard function. The use of the term “hazard rate” is common in the field of reliability assessment and is equivalent to the failure rate of the component.
The example shown in Figure below is simplified in the sense that all transformers are initially the same age and all transformers have identical age-versus failure rate models. For actual systems, this is not the case and the initial system model will have a mix of equipment ages with a mix of failure rate models. For example, an initial system may have different failure rate models for transformers of different voltages, different sizes, different manufacturers, and so forth. Multiple types of equipment can also be considered such as transformers, cables, and poles. System models should not be more complicated than necessary, but should have sufficient detail so that the benefits viable aging infrastructure mitigation scenarios can be modeled and quantified.