Reasoning about the Reliability Of Diverse Two-Channel Systems In which One Channel is "Possibly Perfect"

Bev Littlewood (City University, UK) and John Rushby

IEEE Transactions on Software Engineering, Vol. 38, No. 5, September/October 2012, Pages~1178--1194.

Selected as the Spotlight Paper for the issue and available to the public for free for 30 days.


This paper refines and extends an earlier paper by the first author. It considers the problem of reasoning about the reliability of fault-tolerant systems with two "channels" (i.e., components) of which one, A, because it is conventionally engineered and presumed to contain faults, supports only a claim of reliability, while the other, B, by virtue of extreme simplicity and extensive analysis, supports a plausible claim of "perfection."

We begin with the case where either channel can bring the system to a safe state. The reasoning about system probability of failure on demand (pfd) is divided into two steps. The first concerns aleatory uncertainty about (i) whether channel A will fail on a randomly selected demand and (ii) whether channel B is imperfect. It is shown that, conditional upon knowing p_A (the probability that A fails on a randomly selected demand) and p_B (the probability that channel B is imperfect), a conservative bound on the probability that the system fails on a randomly selected demand is simply p_A x p_B. That is, there is conditional independence between the events "A fails" and "B is imperfect." The second step of the reasoning involves epistemic uncertainty represented by an assessor's beliefs about the distribution of (p_A, p_B) and it is here that dependence may arise. However, we show that under quite plausible assumptions, a conservative bound on system pfd can be constructed from point estimates for just three parameters. We discuss the feasibility of establishing credible estimates for these parameters.

We extend our analysis from faults of omission to those of commission, and then combine these to yield an analysis for monitored architectures of a kind proposed for aircraft.


BibTeX Entry

	AUTHOR = {Bev Littlewood and John Rushby},
	TITLE = {Reasoning About The Reliability Of Diverse Two-Channel
		Systems In Which One Channel Is ``Possibly Perfect''},
	JOURNAL = {IEEE Transactions on Software Engineering},
	VOLUME = 38,
	NUMBER = 5,
	PAGES = {1178--1194},
	MONTH = sep # {/} # oct,
	YEAR = 2012

Having trouble reading our papers?
Return to John Rushby's bibliography page
Return to the Formal Methods Program home page
Return to the Computer Science Laboratory home page