Bathtub curve as a Markovian process to describe the reliability of repairable components

Reliability‐based smart‐maintenance model for power system generators

“…Regarding the generators' failure rate, it is common to use the bathtub curve to describe it. Bathtub curve is divided into four stages [33]. The first stage is the infant mortality, which is defined by the policy of the manufacturer and it corresponds to the period of guarantee.…”

“…Then, by using Weibull distribution in combination with Gumbel distribution [35], the bathtub curve mathematical model can incorporate maintenance action as given in the following equation [33]:…”

“…When the component reaches the end lifetime stage, the component cannot be repaired, and the repair rate goes to zero. Thus, the repair rate can be mathematically written as follows [33]:…”

“…Then, the degradation of the component is quantified using the degradation rate and lifetime of the component. The expression that described the degradation is given by [33]…”

Smart Maintenance Model for Operational Planning of Static Synchronous Compensators

“…This is described as the state in which once it is reached, there is no possibility to go to any other state. The particularity of this state is that it presents a mean time to absorption defined as [15]:…”