On the application and extension of system signatures in engineering reliability

Following a review of the basic ideas in structural reliability, including signature‐based representation and preservation theorems for systems whose components have independent and identically distributed (i.i.d.) lifetimes, extensions that apply to the comparison of coherent systems of different sizes, and stochastic mixtures of them, are obtained. It is then shown that these results may be extended to vectors of exchangeable random lifetimes. In particular, for arbitrary systems of sizes m < n with exchangeable component lifetimes, it is shown that the distribution of an m‐component system's lifetime can be written as a mixture of the distributions of k‐out‐of‐n systems. When the system has n components, the vector of coefficients in this mixture representation is precisely the signature of the system defined in Samaniego, IEEE Trans Reliabil R–34 (1985) 69–72. These mixture representations are then used to obtain new stochastic ordering properties for coherent or mixed systems of different sizes. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

De-Constructing the French Wars: Napoleon as Anti-Strategist

The Emperor Napoleon I is regarded as one of the greatest generals of all time and, as such, he has attracted an immense bibliography. In spite of this, there have been few studies of him as a strategist: instead, it is simply assumed that it was enough for the Emperor to have conducted an operation for it to have had a logical strategic goal. In this article, however, Napoleon is shown to have been primarily an opportunist, who was frequently guided by the needs of the moment and swayed from his course by circumstance, while it is further suggested that, even considered on their own merits, many of his decisions were faulty in the extreme.     

Traitor or patriot? Andrey Vlasov and the Russian liberation movement 1942–45

Catherine Andreyev, Vlasov and the Russian Liberation Movement: Soviet Reality and Emigre Theories. Cambridge: Cambridge University Press, 1987. Pp.251; $34.50.

Sergej Froehlich, General Wlassow: Russen und Deutsche zwischen Hitler und Stalin (revised and edited by Edel von Freier). Koeln: Markus Verlag, 1987. Pp.403; DM.39.80.

Joachim Hoffmann, Die Geschichte der Wlassow‐Armes. Freiburg: Verlag Rombach, 1986. Pp.468; DM32.     

The economic effects of inspector error on attribute sampling plans

In this paper the effects of inspector error on a cost-based quality control system are investigated. The system examined is of a single sampling plan design involving several cost components. Both type I and type II inspector errors are considered. The model employs a process distribution, thus assuming that a stochastic process of some kind governs the quality of incoming lots. Optimal plan design is investigated under both error-free and error-prone inspection procedures and some comparisons are made.     

On maximum internally stable sets of a graph

The paper makes some remarks on the paper of Hakimi and Frank and shows a simplified way of applying the concept of alternating forest. An algorithm for finding a maximum internally stable set of an undirected graph is constructed and some examples are given.     

Nonstationary stochastic gold-mining: A time-sequential tactical-allocation problem

This paper presents an extension of gold-mining problems formulated in earlier work by R. Bellman and J. Kadane. Bellman assumes there are two gold mines labeled A and B, respectively, each with a known initial amount of gold. There is one delicate gold-mining machine which can be used to excavate one mine per day. Associated with mine A is a known constant return rate and a known constant probability of breakdown. There is also a return rate and probability of breakdown for mine B. Bellman solves the problem of finding a sequential decision procedure to maximize the expected amount of gold obtained before breakdown of the machine. Kadane extends the problem by assuming that there are several mines and that there are sequences of constants such that the jth constant for each mine represents the return rate for the jth excavation of that mine. He also assumes that the probability of breakdown during the jth excavation of a mine depends on j. We extend these results by assuming that the return rates are random variables with known joint distribution and by allowing the probability of breakdown to be a function of previous observations on the return rates. We show that under certain regularity conditions on the joint distributions of the random variables, the optimal policy is: at each stage always select a mine which has maximal conditional expected return per unit risk. This gold-mining problem is also a formulation of the problem of time-sequential tactical allocation of bombers to targets. Several examples illustrating these results are presented.