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.     

The National resistance army (NRA) as a guerrilla force

Africa has had no shortage of guerrilla movements since 1975. However, very few have been successful that have not fought against European colonial rule or white minority regimes. Fundamentally, without external support, these movements have been almost universally failures. One major exception to this rule was the National Resistance Army of Uganda, which overthrew the regime led by General Tito Okello in 1986. What made the National Resistance Army a success and distinct from other guerrilla armies were its sound leadership, its superior organization and its creative strategy.     

Reviews

Douglas S. Derrer, We Are All the Target: A Handbook of Terrorism Avoidance and Hostage Survival. Annapolis, MD: US Naval Institute Press, 1992. Pp. x+135, notes, index. $14.95. ISBN 01–55750–150–5

Ian Knight, Zulu: Isandlwana and Rorke's Drift, 22–23 January 1879. London: Windrow & Greene, 1992. Pp.136, 150 illus., incl 8 colour plates, maps, biblio. £35. ISBN 1–872004–23–7

Ian Knight, By the Orders of the Great White Queen: Campaigning in Zululand through the Eyes of the British Soldiers, 1879. London: Greenhill Books and Novato: Presidio Press, 1992. Pp. 272, 17 illus., 1 map. £18.95. ISBN 1–85367–122–3

Manfried Rauchensteiner and Erwin A. Schmidl (eds.), Formen des Krieges: vom Mittelalter zum ‘Low‐intensity’ Conflict’. Graz : Verlag Styria, 1991. Pp.208. DM35. ISBN 3–22–12139–7

Harold J. Kearsley, Maritime Power and the Twenty‐First Century. Dartmouth: Dartmouth Publishing Company, Limited, 1992. Pp.xv + 203, 13 diagrams, index. £32.50. ISBN 1–85521–288–9     

Expeditionary police advising: some causes of failure

ABSTRACT

The practice of dispatching teams of police advisors to other states to build or train foreign security forces began at the end of the nineteenth century, yet there exists no definitive history of the practice, or any definitive theoretical approach underpinning why such missions succeed or fail. Drawing upon their recent edited book on expeditionary police advising, and by examining the donor or sending states, the host nations, and the use of police in counterinsurgency situations, the authors present some key reasons why such missions fail, and lay some groundwork for additional study of this important subject.     

A stochastic assignment problem

There are n boxes with box i having a quota value Balls arrive sequentially, with each ball having a binary vector attached to it, with the interpretation being that if X_i = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015     

India's Evolving Nuclear Posture

This article analyzes India's nuclear doctrine, finding it to be critically flawed and inimical to strategic stability in South Asia. In pursuing an ambitious triad of nuclear forces, India is straying from the sensible course it charted after going overtly nuclear in 1998. In doing so, it is exacerbating the triangular nuclear dilemma stemming from India's simultaneous rivalries with China and Pakistan. Strategic instability is compounded by India's pursuit of conventional “proactive strategy options,” which have the potential to lead to uncontrollable nuclear escalation on the subcontinent. New Delhi should reaffirm and redefine its doctrine of minimum credible nuclear deterrence, based on small nuclear forces with sufficient redundancy and diversity to deter a first strike by either China or Pakistan. It should also reinvigorate its nuclear diplomacy and assume a leadership role in the evolving global nuclear weapon regime.