Confidence intervals for ranked means

Suppose that observations from populations π₁, …, π_k (k ≥ 1) are normally distributed with unknown means μ₁., μ_k, respectively, and a common known variance σ². Let μ_[1] μ … ≤ μ_[k] denote the ranked means. We take n independent observations from each population, denote the sample mean of the n observation from π₁ by X _i (i = 1, …, k), and define the ranked sample means X _[1] ≤ … ≤ X _[k]. The problem of confidence interval estimation of μ₍₁₎, …,μ_[k] is stated and related to previous work (Section 1). The following results are obtained (Section 2). For i = 1, …, k and any γ(0 < γ < 1) an upper confidence interval for μ_[i] with minimal probability of coverage γ is (? ∞, X _[i]+ h) with h = (σ/n^1/2) Φ^?1(γ^1/k-i+1), where Φ(·) is the standard normal cdf. A lower confidence interval for μ_[i] with minimal probability of coverage γ is (X _i[i] – g, + ∞) with g = (σ/n^1/2) Φ^?1(γ^1/i). For the upper confidence interval on μ_[i] the maximal probability of coverage is 1– [1 – γ^1/k-i+1]ⁱ, while for the lower confidence interval on μ_[i] the maximal probability of coverage is 1–[1– γ^1/i] ^k-i+¹. Thus the maximal overprotection can always be calculated. The overprotection is tabled for k = 2, 3. These results extend to certain translation parameter families. It is proven that, under a bounded completeness condition, a monotone upper confidence interval h(X ₁, …, X _k) for μ_[i] with probability of coverage γ(0 < γ < 1) for all μ = (μ_[1], …,μ_[k]), does not exist.     

MAD: Mathematical analysis of downtime

The MAD model presents a mathematic treatment of the relationship between aircraft reliability and maintainability, system manning and inspection policies, scheduling and sortie length, and aircraft downtime. Log normal distributions are postulated for subsystem repair times and simultaneous repair of malfunctions is assumed. The aircraft downtime for maintenance is computed with the distribution of the largest of k log normal distributions. Waiting time for maintenance men is calculated either by using a multiple-channel queuing model or by generating the distribution of the number of maintenance men required and comparing this to the number of men available to determine the probability of waiting at each inspection.     

Scheduling to minimize release-time resource consumption and tardiness penalties

We consider the problem of scheduling a set of jobs with a common due-date on a single-machine where the release time of a job is related to the amount of resource consumed. The objective is to minimize the total resource consumption and the total tardiness. While the problem is strongly NP-hard in general, we discuss two different special cases for which special properties are identified and used to develop efficient pseudo-polynomial time algorithms. © 1995 John Wiley & Sons, Inc.     

Strategic and Budgetary Necessity,or Decision-making ‘Along the Grain’? The Royal Navy and the 1981 Defence Review

The 1981 Defence Review undertaken by John Nott as Secretary of State for Defence controversially and dramatically cut the capabilities of the Royal Navy’s surface fleet. Many of those involved in these decisions have emphasised the budgetary and politico-strategic drivers for these reductions in capability, and the first generation of academic analysis has broadly followed this position. However, recently released government and private archival sources demonstrate that Nott’s review was initially much more severe than thought, and that this was due as much to the presumptions and assumptions of the key decision makers as to any strategic or budgetary factors.     

The Demand for Military Expenditure in Europe: The Role of Fiscal Space in the Context of a Resurgent Russia

A variant of established work on the demand for military expenditure is developed based on a practical concept of fiscal space from the perspective of short-term government choices concerning public expenditures. A new indicator, referred to as fiscal capacity, is defined and used as a candidate explanatory variable in an empirical model of European defence spending over the 2007–2016 period. Fiscal capacity is found to outperform simpler measurements of economic conditions, notably GDP growth forecasts, in explaining changes in defence spending efforts as a share of GDP. Regarding security environment variables, the results suggest that Russia has recently come to be seen as a potential military threat by European nations, leading to defence spending increases, the more so the shorter the distance to stationed or deployed Russian forces, and particularly so by those European nations that have a land border with Russia. A prospective exercise is then carried out in order to assess the capacity of EU member states that are also members of NATO to reach NATO’s 2% goal for defence spending over a mid-term horizon.