title: Computation of instant system availability and its applications.
abstract: The instant system availability [Formula: see text] of a repairable system with the renewal equation was studied. The starting point monotonicity of [Formula: see text] was proved and the upper bound of [Formula: see text] is also derived. It was found that the interval of instant system availability monotonically decreases. In addition, we provide examples that validate the analytically derived properties of [Formula: see text] based on the Lognormal, Gamma and Weibull distributions and the results show that the value of T is slightly smaller than its value defined in Theorem 2. The procedure of using a bathtub as application for this article is also discussed.
authors.affiliation: School of Mathematical Sciences, Dalian University of Technology, China, Dalian, 116023 China.
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Hagenimana
authors.affiliation: School of Mathematical Sciences, Dalian University of Technology, China, Dalian, 116023 China.
authors.forename: Song
authors.initials: S
authors.lastname: Lixin
authors.affiliation: School of Mathematical Sciences, Dalian University of Technology, China, Dalian, 116023 China.
authors.forename: Patrick
authors.initials: P
authors.lastname: Kandege
keywords: Binary random variables; Instant availability; Monotonicity; Renewal equation; Repairable system; Upper bound