Abstract
In the present paper we consider a multistate monotone system of multistate components. Following a Bayesian approach, the ambition is to arrive at the posterior distributions of the system availabilities and unavailabilities to the various levels in a fixed time interval based on both prior information and data on both the components and the system. We argue that a realistic approach is to start out by describing our uncertainty on the component availabilities and unavailabilities to the various levels in a fixed time interval, based on both prior information and data on the components, by the moments up till order m of their marginal distributions. From these moments analytic bounds on the corresponding moments of the system availabilities and unavailabilities to the various levels in a fixed time interval are arrived at. Applying these bounds and prior system information we may then fit prior distributions of the system availabilities and unavailabilities to the various levels in a fixed time interval. These can in turn be updated by relevant data on the system. This generalizes results given in Natvig and Eide (Scand J Statist 14:319–327, 1987) considering a binary monotone system of binary components at a fixed point of time. Furthermore, considering a simple network system, we show that the analytic bounds can be slightly improved by straightforward simulation techniques.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Natvig, B., Gåsemyr, J.I. & Reitan, T. Bayesian Assessment of Availabilities and Unavailabilities of Multistate Monotone Systems. Methodol Comput Appl Probab 14, 1075–1095 (2012). https://doi.org/10.1007/s11009-011-9221-3
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DOI: https://doi.org/10.1007/s11009-011-9221-3