On excess-, current-, and total-life distributions of phase-type renewal processes

Consider a renewal process whose interrenewal-time distribution is phase type with representation (α, T). We show that the (time-dependent) excess-life distribution is phase type with representation (α′, T), where α′ is an appropriately modified initial probability vector. Using this result, we derive the (time-dependent) distributions for the current life and the total life of the phase-type renewal process. They in turn enable us to obtain the equilibrium distributions for the three random variables. These results simplify the computation of the respective distribution functions and consequently enhance the potential use of renewal theory in stochastic modeling—particularly in inventory, queueing, and reliability applications. © 1992 John Wiley & Sons, Inc.     

Gas and the North‐West Frontier

John Terraine, Business in Great Waters: The U Boat Wars 1916 ‐1945. London: Leo Cooper, 1989. Pp.xx + 841; £19.50.

Peter Simkins, Kitchener's Armies: The Raising of the New Armies, 1914–16. Manchester: Manchester University Press, 1988. Pp.xvi + 359; index; illustrations. £37.50 (hardback).

Keith Grieves, Sir Eric Geddes: Business and Government in War and Peace. Manchester and New York: Manchester University Press, 1989. Pp.xiv + 188; £35.

Jeffrey Grey, The Commonwealth Armies and the Korean War: An Alliance Study. Manchester: Manchester University Press, 1988. Pp.xii + 244; £12.95.

Rajan Menon and Daniel N. Nelson (eds.), Limits to Soviet Power. Lexington, MA/Toronto: Lexington Books, 1989. Pp.vii + 231; $35.

Michael Leifer, ASEAN and the Security of South‐East Asia. London and New York: Routledge, 1989. Pp.x + 198; £30.

Grant Wardlaw, Political Terrorism: Theory, Tactics and Counter‐measures. Cambridge: Cambridge University Press, second edn. 1989. Pp.xv + 248; £27.50 (hardback); £10.95 (paperback).

John F. Murphy, Punishing International Terrorists: The Legal Framework for Policy Initiatives. Totowa, NJ: Rowman &; Allanheld 1985. Pp.x + 142; $25.95.

Hanns Maull and Otto Pick (eds.), The Gulf War. London: Pinter Publishers, 1989. Pp.193; £30.

Royal United Services Institute for Defence Studies and Brassey's Defence Yearbook 1989. London: Brassey's Defence Publishers, 1989. Pp.xxviii + 361; £35.

Virginia Gamba‐Stonehouse, Strategy in the Southern Oceans: A South American View. London: Pinter Publishers, 1989. Pp.xiii + 155; £30.

Ola Tunander, Cold Water Politics: The Maritime Strategy and Geopolitics of the Northern Front. London: Sage Publications for the International Peace Research Institute, Oslo, 1989. Pp.194; £25.

Richard Fieldhouse and Shunji Taoka, Superpowers at Sea: An Assessment of the Naval Arms Race. Oxford: Oxford University Press for SIPRI, 1989. Pp.183; £19.50.

Kenneth E. Boulding, Conflict and Defense: A General Theory. University Press of America, 1988. Pp.xiv + 347; $16.75 (paperback). (First Published, 1962).     

Ho Chi Minh and the origins of the Vietnamese doctrine of guerrilla tactics

In a very important sense, the Vietnamese military history of the communist era began in 1941, when Ho Chi Minh prepared ‘Guerrilla Tactics’ (Cach Danh Du Kich).1 ?1. Ministry of Defense Center for the Military Encyclopedia Ministry of Defense Center for the Military Encyclopedia. 1996. Tu Dien Bach Hoa Quan Su Vietnam, Hanoi: People's Army Publishing Company.  [Google Scholar], Tu Dien Bach Hoa Quan Su Vietnam, 69. The publication of this essay, which was a manual on the tactics, techniques, and procedures of guerrilla warfare, preceded the founding of the first armed propaganda unit (Tuyen Truyen Doi Vo Trang) on 22 December 1944, which later became the People's Army of Vietnam (PAVN, Quan Doi Nhan Dan); as well as the revolutionary writings of Truong Chinh (1946–1947) and Vo Nguyen Giap (1959). The fact that ‘Tactics’ was published by the Viet Minh reinforces the claim made by the PAVN that it was the first authoritative Vietnamese writing on this important subject.     

Warranty analysis and renewal function estimation

Estimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, say t, of the renewal function. However, in warranty analusis, typically t is small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.     

Relationships among potential sorties,ground support,and aircraft reliability

A methodology is developed for assessing tactical airfield/aircraft system effectiveness, and for evaluating effectiveness changes resulting from incremental investments in ground support resources and/or aircraft reliability. Two categories of ground support functions–turnaround and maintenance–are distinguished. The measure of effectiveness is the maximum potential sortie rate achievable by the system. The methodology enables empirical derivation of the general equation of the tactical airfield/aircraft system. It also enables graphical presentation of the system tradeoffs in the form of a System Analysis Chart.     

A mathematical programming approach to the scheduling of sorting operations

In this paper we describe an approach to the scheduling and/or real-time control of sorting operations in the presence of deadlines. The problem arises in the postal service where mail has to be sorted by zip codes, and in the banking system where checks have to be sorted according to the bank on which they are drawn. In both applications losses are incurred if items miss their clearing deadlines. For example, in check-sorting an extremely important objective of the control system is to reduce the “float” i.e., the total dollar value of the checks which miss their deadlines. The proposed real-time control system utilizes a linear program which chooses between alternative sort-patterns and assigns the various processing steps to the time periods between deadlines.     

The single period procurement problem where dedicated supplier capacity can be reserved

In this article we consider the single period procurement strategy for an item with uncertainty in its demand and uncertainty in the capacity of the supplier. Dedicated capacity can be ensured by paying a premium charge to the supplier. The other decision variable is the replenishment quantity to request. It turns out to be very easy to select the best value of this latter quantity. On the other hand, we are only able to characterize the general behavior of the expected profit as a function of the level of dedicated capacity. In general, there can be multiple local maxima as a function of the dedicated capacity. However, for the special, but important, case of normally distributed demand, normally distributed capacity and a linear cost for reserving capacity, an algorithm is developed for finding the best level of dedicated capacity. Some preliminary insights regarding the extension to multiple periods are presented. © 1995 John Wiley & Sons, Inc.     

The determination of optimal base-stock inventory policy when the costs of under- and oversupply are uncertain

This article considers the determination of the optimal base-stock inventory policy for the newsboy inventory model when there is uncertainty about either or both of its basic cost inputs: either C_u, the marginal cost of an undersupply mistake, or C_o, the marginal cost of an oversupply mistake. Such uncertainties often arise in implementing the newsboy model, especially with respect to C_u, whose value depends mostly on the often-imponderable economic consequences of a lost sale or backorder. Given this uncertainty, we use decision theory to propose and analyze two measures of policy “goodness” and two base-stock selection criteria, which in combination provide four alternative “optimal” base-stock policies. Formulas and/or conditions defining each alternative policy are provided. Our empirical study indicates that the recommended policy can be quite sensitive to the measure/criterion chosen, and that the consequences of the wrong choice can be quite considerable.     

EU armed forces and social media: convergence or divergence?

This article explores how armed forces in EU member states work with and view social media in national and international settings, and what the patterns of convergence/divergence are on these issues. To that end, a questionnaire targeted at EU armed forces was constructed. An index of qualitative variation was calculated to explore the relative convergence among respondents (n = 25) on issues of risks and opportunities with using social media nationally and internationally. Consistent with previous research on European armed forces, we found higher levels of divergence than convergence. Contrary to our expectations that similar challenges, joint international standards, and membership in international organizations would foster convergence with regard to social media use in areas of deployment, we found that convergence appeared foremost pertaining to the domestic level. Policy divergence was strongest in areas of deployment.