The structure function for system reliability as predictive (imprecise) probability

Imprecise system reliability using the survival signature

The survival signature has been introduced to simplify quantification of reliability of systems which consist of components of different types, with multiple components of at least one of these types. The survival signature generalizes the system signature, which has attracted much interest in the theoretical reliability literature but has limited practical value as it can only be used for syst...

Predictive inference: From Bayesian inference to Imprecise Probability

INTRODUCTION 2 The " Bag of marbles " example " Bag of marbles " problems (Walley, 1996) • " I have. .. a closed bag of coloured marbles. I intend to shake the bag, to reach into it and to draw out one marble. What is the probability that I will draw a red marble? " • " Suppose that we draw a sequence of marbles whose colours are (in order): blue, green, blue, blue, green, red.

Imprecise Probability

Imprecise Probability

1 Overview Quantification of uncertainty is mostly done by the use of precise probabilities: for each event A, a single (classical, precise) probability P (A) is used, typically satisfying Kolmogorov's axioms [4]. Whilst this has been very successful in many applications, it has long been recognized to have severe limitations. Classical probability requires a very high level of precision and co...

Reducing Uncertainty by Imprecise Judgements on Probability Distributions: Application to System Reliability

In this paper the judgement consisting in choosing a function that is believed to dominate the true probability distribution of a continuous random variable is explored. This kind of judgement can significantly increase precision in constructed imprecise previsions of interest, which of great importance for applications. New formulae for computing system reliability are derived on the basis of ...