Multivariate Phase-Type Distributions

Article Abstract:

If a random variable can be represented as the time until absorption in a finite state absorbing Markov chain then it is of the phase type (PH). Various applications of PH distributions can be found in reliability theory. They can be written in a closed form which makes it easier to evaluate several probabilistic quantities. Extensions of the univariate case to the multivariate case are developed. They have many properties of the univariate phase. Examples are given.

Multivariate analysis, Statistics (Data), Stochastic Model, Statistics, Markov Process, Theory

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Extensions of the Freund Distribution with Applications in Reliability Theory

Article Abstract:

The Freund distribution is a model where the exponential residual lifetime of one component depends on another component. It is shown that there is one functional representation that can define several extensions of the Freund distribution. It also yields properties of the distribution that apply to reliability theory.

Hardware, Scientific Research

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Continuous Multistate Structure Functions

Article Abstract:

Usually systems and components are on or off. Thus the structure function is a binary function with binary variables. However components may be partially failed. They may be multistate systems. These systems are analyzed and decomposed into elementary components.

Applications, Models, Sets, Systems, Function Analysis, Minimization

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• Abstracts: On the Use of Replacements to Extend System Life. Some Reliability Applications of the Variability Ordering. Inspection Policies for Fault Location

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