2 research outputs found
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Modeling the probability of failure on demand (pfd) of a 1-out-of-2 system in which one channel is “quasi-perfect”
Our earlier work proposed ways of overcoming some of the difficulties of lack of independence in reliability modeling of 1-out-of-2 software-based systems. Firstly, it is well known that aleatory independence between the failures of two channels A and B cannot be assumed, so system pfd is not a simple product of channel pfds. However, it has been shown that the probability of system failure can be bounded conservatively by a simple product of pfdA and pnpB (probability not perfect) in those special cases where channel B is sufficiently simple to be possibly perfect. Whilst this “solves” the problem of aleatory dependence, the issue of epistemic dependence remains: An assessor’s beliefs about unknown pfdA and pnpB will not have them independent. Recent work has partially overcome this problem by requiring only marginal beliefs – at the price of further conservatism. Here we generalize these results. Instead of “perfection” we introduce the notion of “quasi-perfection”: a small pfd practically equivalent to perfection (e.g. yielding very small chance of failure in the entire life of a fleet of systems). We present a conservative argument supporting claims about system pfd. We propose further work, e.g. to conduct “what if?” calculations to understand exactly how conservative our approach might be in practice, and suggest further simplifications
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Conservative Claims for the Probability of Perfection of a Software-based System Using Operational Experience of Previous Similar Systems
We begin by briefly discussing the reasons why claims of probability of non-perfection ( pnp ) may sometimes be useful in reasoning about the reliability of software-based systems for safety-critical applications. We identify two ways in which this approach may make the system assessment problem easier. The first concerns the need t o assess the chance of lifetime freedom from failure of a single system . The second concerns the need to assess the reliability of multi-channel software-diverse fault tolerant systems – in this paper, 1-out-of-2 systems. In earlier work (Littlewood and Rushby 2012, Littlewood and Povyakalo 2013) it was proposed that, in certain applications, claims for possible perfection of one of the channels in such a system may be feasible. It was shown that in such a case there is a particularly simple conservative expression for system pfd (probability of failure on demand) , involving the pfd of one channel , and the pnp of the other. In this paper we address the problem of how to assess such a pnp . In previous work (Zhao 2015) we have addressed this problem when the evidence available is only extensive failure - free working of the system in question. Here we consider the case in which there is, in addition , evidence of the previous success of the software development procedures used to build the system: specifically, several previous similar systems built using the same process have exhibited failure -free working during extensive operational exposure