Some estimates of reliability using interference theory

According to “interference theory” of reliability, a component fails if the maximum stress exceeds the component's strength. Assuming that both these quantities are random and their distributions are normal, we obtain in this paper some point and interval estimates of reliability when the stress distribution is known and a few observations exist on component strengths.     

The next decade of logistics research

Pathbreaking logistics research over the next 10 years will focus on systems problems. Whereas past research generally has taken a “bottom-up” approach, future investigations are likely to pursue a “top-down” philosophy. Specifically, attention will concentrate on diagnosis of systems' improvement potentials; easy-to-use analytic approaches, inherently approximative, will be devised for quickly ascertaining whether a complex operating system can be substantially and effectively improved. Theories to assist in overall systems design, particularly the setting of boundaries and buffers among systems components, will be developed. At the same time, techniques for accurately forecasting future systems performance will be investigated. Underlying such research will be efforts to gain better understanding of management information requirements, including approaches for monitoring systems performance and providing early warning detection of systems degradation Improved management information systems will have to be coupled with appropriate design of managerial organizations and assignment of decision making responsibilities. Important avenues of research will he development of robust approaches, that is, both mathematical techniques and organizational approaches that are not too adversely affected by limited data, a changing environment, and human frailly. Finally, critical research will be directed at the implementation process, especially the interaction among initiation, design, testing and ultimate adoption This prognosis will explore the above themes in the context of large-scale, complex systems. The decision areas will encompass inventory replenishment, multiechelon hierarchies for stockage and maintenance, procurement, transportation, scheduling, facilities planning, budgeting, reliability and personnel management.     

Renewal processes of phase type

This paper discusses a class of analytically and numerically tractable renewal processes, which generalize the Poisson process. When used to describe interarrival or service times in queues, these renewal processes lead to computationally explicit solutions which involve only real arithmetic. Previous modifications of the Poisson process, based on the Erlang or the hyperexponential distributions, appear as particular cases.     

Evaluation of force structures under uncertainty

A model, for assessing the effectiveness of alternative force structures in an uncertain future conflict, is presented and exemplified. The methodology is appropriate to forces (e.g., the attack submarine force) where alternative unit types may be employed, albeit at differing effectiveness, in the same set of missions. Procurement trade-offs, and in particular the desirability of special purpose units in place of some (presumably more expensive) general purpose units, can be addressed by this model. Example calculations indicate an increase in the effectiveness of a force composed of general purpose units, relative to various mixed forces, with increase in the uncertainty regarding future conflicts.     

A dual criteria sequencing problem with earliness and tardiness penalties

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)‐time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we show that the problems are NP‐hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than . © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 422–431, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10020