Articles

Introducing the “Bath Tub” curve concept

In the Reliability and Maintenance world, we often refer to what is known as the “bathtub” curve and ask the question: “What is the bathtub curve for this equipment?” The name “bathtub” comes from the equipment failure rate curve resembling a sanitary bathtub’s longitudinal section. In reality, it is rarely symmetrical and looks more like a distorted “u” or “v” shaped figure. The bathtub curve can be useful in various circumstances and help an operator better manage their assets over time. However, it is important to understand where it comes from and what it means so we can avoid misusing or misinterpreting it.

Definition of Reliability

Reliability, in its academic root, is defined as the probability that a system will perform its intended function in a specified mission time and within specific process conditions. Reliability (R) is related to the Probability of Success as opposed to the Probability of Failure (F), and the relation between R and F is:

$$ \displaystyle \large R = 1 – F (t) \ \:\:\:\: \:\:\:\: (for \:mission\: time\: t) $$

In the above context, a reliability example would be: What is the probability that a centrifugal pump in a sheltered enclosure will push 3,000m3/day of sweet crude oil without unplanned failures for a period of 8,760 running hours?