Availability of a Renewable, Checked System

A recursive framework for time-dependent characteristics of tested and maintained standby units with arbitrary distributions for failures and repairs

“…With instantaneous repairs (τ¼ 0) and equal test intervals the above equations for u k (x) reduce to those of [15] and also boil down to Eq. (9) of [17].…”

“…Models for category [T old ,F new ] have been developed in [2,[13][14][15][16][17], Refs. [15][16][17] focusing on the unavailability function and Refs.…”

“…[15][16][17] focusing on the unavailability function and Refs. [2,13,14] more on maintenance, cost functions and optimisation.…”

“…Concerning earlier works on the unavailability of a unit in category [T old ,F new ], Ole Platz [15] analysed this process with a general time-to-failure distribution and periodic tests while assuming instantaneous tests and repairs (i.e., zero durations), and no periodic renewals. Hilsmeier et al [17] developed explicit results and numerous examples under the same conditions as Platz.…”

“…Section 2 of the current paper develops an explicit unavailability function for a unit in [T old ,F new ] category by extending the recursive approach of Platz-formalism [15]. As extensions to earlier approaches the current method allows arbitrary testing times (intervals), arbitrary distributions to failure times and repair durations as well as additional failure modes caused by tests, human errors and true demands.…”