Computation of instant system availability and its applications
| Autor: | Patrick Kandege, Emmanuel Hagenimana, Song Li-xin |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematical optimization
Monotonicity Computation Value (computer science) Monotonic function 010103 numerical & computational mathematics Interval (mathematics) 01 natural sciences Upper and lower bounds 90B25 26A48 010104 statistics & probability Renewal equation Instant availability 0101 mathematics Repairable system Weibull distribution Mathematics Discrete mathematics Multidisciplinary Research Binary random variables Log-normal distribution 37A60 11KXX 60B12 Upper bound Instant |
| Zdroj: | SpringerPlus |
| ISSN: | 2193-1801 |
| Popis: | The instant system availability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_\tau (t)$$\end{document}Sτ(t) of a repairable system with the renewal equation was studied. The starting point monotonicity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_\tau (t)$$\end{document}Sτ(t) was proved and the upper bound of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_\tau (t)$$\end{document}Sτ(t) 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_\tau (t)$$\end{document}Sτ(t) 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. |
| Databáze: | OpenAIRE |
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