Diversity, dependence and independence

We propose a very general, unifying framework for the concepts of dependence and independence. For this purpose, we introduce the notion of diversity rank. By means of this diversity rank we identify total determination with the inability to create more diversity, and independence with the presence of maximum diversity. We show that our theory of dependence and independence covers a variety of dependence concepts, for example the seemingly unrelated concepts of linear dependence in algebra and dependence of variables in logic.Peer reviewe

A note on reliability estimation of functionally diverse systems

It has been argued that functional diversity might be a plausible means of claiming independence of failures between two versions of a system. We present a model of functional diversity, in the spirit of earlier models of diversity such as those of Eckhardt and Lee, and Hughes. In terms of the model, we show that the claims for independence between functionally diverse systems seem rather unrealistic. Instead, it seems likely that functionally diverse systems will exhibit positively correlated failures, and thus will be less reliable than an assumption of independence would suggest. The result does not, of course, suggest that functional diversity is not worthwhile; instead, it places upon the evaluator of such a system the onus to estimate the degree of dependence so as to evaluate the reliability of the system

Modeling the effects of combining diverse software fault detection techniques

The software engineering literature contains many studies of the efficacy of fault finding techniques. Few of these, however, consider what happens when several different techniques are used together. We show that the effectiveness of such multitechnique approaches depends upon quite subtle interplay between their individual efficacies and dependence between them. The modelling tool we use to study this problem is closely related to earlier work on software design diversity. The earliest of these results showed that, under quite plausible assumptions, it would be unreasonable even to expect software versions that were developed ‘truly independently’ to fail independently of one another. The key idea here was a ‘difficulty function’ over the input space. Later work extended these ideas to introduce a notion of ‘forced’ diversity, in which it became possible to obtain system failure behaviour better even than could be expected if the versions failed independently. In this paper we show that many of these results for design diversity have counterparts in diverse fault detection in a single software version. We define measures of fault finding effectiveness, and of diversity, and show how these might be used to give guidance for the optimal application of different fault finding procedures to a particular program. We show that the effects upon reliability of repeated applications of a particular fault finding procedure are not statistically independent - in fact such an incorrect assumption of independence will always give results that are too optimistic. For diverse fault finding procedures, on the other hand, things are different: here it is possible for effectiveness to be even greater than it would be under an assumption of statistical independence. We show that diversity of fault finding procedures is, in a precisely defined way, ‘a good thing’, and should be applied as widely as possible. The new model and its results are illustrated using some data from an experimental investigation into diverse fault finding on a railway signalling application

Modeling software design diversity

Design diversity has been used for many years now as a means of achieving a degree of fault tolerance in software-based systems. Whilst there is clear evidence that the approach can be expected to deliver some increase in reliability compared with a single version, there is not agreement about the extent of this. More importantly, it remains difficult to evaluate exactly how reliable a particular diverse fault-tolerant system is. This difficulty arises because assumptions of independence of failures between different versions have been shown not to be tenable: assessment of the actual level of dependence present is therefore needed, and this is hard. In this tutorial we survey the modelling issues here, with an emphasis upon the impact these have upon the problem of assessing the reliability of fault tolerant systems. The intended audience is one of designers, assessors and project managers with only a basic knowledge of probabilities, as well as reliability experts without detailed knowledge of software, who seek an introduction to the probabilistic issues in decisions about design diversity

Assessing the reliability of diverse fault-tolerant software-based systems

We discuss a problem in the safety assessment of automatic control and protection systems. There is an increasing dependence on software for performing safety-critical functions, like the safety shut-down of dangerous plants. Software brings increased risk of design defects and thus systematic failures; redundancy with diversity between redundant channels is a possible defence. While diversity techniques can improve the dependability of software-based systems, they do not alleviate the difficulties of assessing whether such a system is safe enough for operation. We study this problem for a simple safety protection system consisting of two diverse channels performing the same function. The problem is evaluating its probability of failure in demand. Assuming failure independence between dangerous failures of the channels is unrealistic. One can instead use evidence from the observation of the whole system's behaviour under realistic test conditions. Standard inference procedures can then estimate system reliability, but they take no advantage of a system’s fault-tolerant structure. We show how to extend these techniques to take account of fault tolerance by a conceptually straightforward application of Bayesian inference. Unfortunately, the method is computationally complex and requires the conceptually difficult step of specifying 'prior' distributions for the parameters of interest. This paper presents the correct inference procedure, exemplifies possible pitfalls in its application and clarifies some non-intuitive issues about reliability assessment for fault-tolerant software

The use of proofs in diversity arguments

The limits to the reliability that can be claimed for a design-diverse fault-tolerant system are mainly determined by the dependence that must be expected in the failure behaviours of the different versions: claims for independence between version failure processes are not believable. In this note we examine a different approach, in which a simple secondary system is used as a back-up to a more complex primary. The secondary system is sufficiently simple that claims for its perfection (with respect to design faults) are possible, but there is not complete certainty about such perfection. It is shown that assessment of the reliability of the overall fault-tolerant system in this case may take advantage of claims for independence that are more plausible than those involved in design diversity

The impact of diversity upon common mode failures

Recent models for the failure behaviour of systems involving redundancy and diversity have shown that common mode failures can be accounted for in terms of the variability of the failure probability of components over operational environments. Whenever such variability is present, we can expect that the overall system reliability will be less than we could have expected if the components could have been assumed to fail independently. We generalise a model of hardware redundancy due to Hughes [Hughes 1987], and show that with forced diversity, this unwelcome result no longer applies: in fact it becomes theoretically possible to do better than would be the case under independence of failures

The Determinants and Effects of Board Nomination Committees*

This article assesses the corporate governance-related antecedents of nomination committee adoption, and the impact of nomination committees' existence and their composition on board independence and board demographic diversity. We conducted a longitudinal study of board composition amongst 210 Swiss public companies from January 2001 through December 2003, a period during which the Swiss (Stock) Exchange (SWX) introduced new corporate governance-related disclosure guidelines. We find firms with nomination committees are more likely to have a higher number of independent and foreign directors, but not more likely to have a higher number of female board members. Further, the existence of nomination committees is associated with a higher degree of nationality diversity but is not related to board educational diversity. We also find that nomination committee composition matters in the nomination of independent and foreign, but not of female directors. Our results suggest that understanding different board roles and composition require a multi-theoretical approach, and that agency theory, resource-dependence theory and group effectiveness theory help to explain different aspects of board composition and effectiveness. Finally, the article discusses the concept of diversity and appropriate ways to study diversity in a boardroom contex