Statistical consistency with Dempster's rule on diagnostic trees having uncertain performance parameters

Citations of this article
Mendeley users who have this article in their library.


This paper defines statistical consistency, a property that we propose as a necessary characteristic of any calculus for evidence combination. Statistical consistency holds when the combination of repeated observations of a system in a given state leads to the indication that the system is in that state of nature. We show that, for a suitable choice of parameters, Dempster's rule has this desirable property, both for simple systems and for systems composed of a hierarchy of subsystems and described by diagnostic or fault trees, but for other parameter values the rule leads to the wrong conclusion. A necessary and sufficient condition for the existence of simple bpa's being statistically consistent is that p0 + 11 > 1, where p0 and q1 are the reliability (or specificity) and sensitivity of individual sensors detecting malfunctions in components and (sub)systems. A sufficient condition for statistical consistency is that the reliability and sensitivity of each sensor be greater than 0.5. We show that statistical consistency is preserved under diagnostic tree formation. © 1992.




Durham, S. D., Smolka, J. S., & Valtorta, M. (1992). Statistical consistency with Dempster’s rule on diagnostic trees having uncertain performance parameters. International Journal of Approximate Reasoning, 6(1), 67–81.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free