Bayesian Assessment of Availabilities and Unavailabilities of Multistate Monotone Systems

Bent Natvig (), Jørund Inge Gåsemyr () and Trond Reitan ()
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Bent Natvig: University of Oslo
Jørund Inge Gåsemyr: University of Oslo
Trond Reitan: University of Oslo

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 4, 1075-1095

Abstract: 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.

Keywords: Availabilities; Bayesian assessment; Multistate monotone systems; Unavailabilities; 62NO5; 90B25 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11009-011-9221-3

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