Michael J. Armstrong

A SURVEY OF THE MACHINE INTERFERENCE PROBLEM

Abstract This paper surveys the research published on the machine interference problem, also called the machine repairman problem, in which machines interfere with each other’s service. Our emphasis is on work that has appeared since the 1985 review by Stecke and Aronson. After describing the basic model and the scope of our study, we discuss the literature along several dimensions. We describe some of the more interesting papers, and offer some suggestions for topics holding particular promise for future studies. We conclude with comments about how the research has evolved over the past two decades.

Joint reliability-importance of components

Hong & Lie (1993) defined joint reliability importance (JRI) as a measure of how two components in a system interact in contributing to system reliability. Their definition and theorems regarding JRI were limited to statistically independent component states. This paper removes the statistical independence restriction by showing that similar results hold in the more general case where component failures can be statistically dependent; however, the calculation of actual values becomes more difficult, because covariance terms can appear in the JRI formula. Despite this, the essential determination and interpretation of the signs of the JRI remain unchanged. Thus analysts who wish to use JRI (e.g., as a design heuristic) can do so in working with real systems where statistical independence is not valid. It is further shown that JRI is always nonzero for some classes of systems. >

Joint optimization of maintenance and inventory policies for a simple system

We examine age replacement and ordering decisions for a system with only one component subject to random failure and with room for only one spare in stock. The system incurs costs for replacement, shortage, holding, and breakage; the lead time for receipt of an ordered spare is constant. We consider the solvability and desirability of jointly optimizing these two traditionally separate decisions. We show that the problem has some convexity properties that make it amenable to minimization. For our data set, we find that using separate optimization gives an average loss of 3% relative to the joint minimum; about a tenth of die time the difference was more than 10%, but in general this loss can vary from zero to arbitrarily large.

Students as Clients: A Professional Services Model for Business Education

The paper provides comments on an article about the limitations of the student-as-customer model for guiding the operations of a business school. The article proposed a student-as-junior-partner an...

Reliability-importance and dual failure-mode components

There are several measures of the importance of a component within a system in determining system reliability; these measures include structural importance, marginal reliability-importance. Some reliability-importance, and link importance. These measures are reviewed and then related to each other. Extensions are proposed to each importance measure to cover reliability models in which the components have two failure-modes rather than the conventional one failure-mode; these extensions have properties similar to those in the one failure-mode model.

Timing and quality decisions for entrepreneurial product development

Abstract An entrepreneur is developing a new product, and each period must decide whether to enter the market or to continue development. We formulate a model of this decision for ventures facing diminishing returns to product quality, and for which funding availability, product development success, and market competition growth are uncertain. We characterize the profit-maximizing time to stop product development and enter the market, and then show how this stopping time is affected by changes in the business environment. By further focussing our modeling assumptions, we are able to translate our time-based criteria into product quality terms; we propose that management set a target quality level that the product must meet in order for the venture to maximize profit. We also demonstrate that management should decrease this target (and hence the quality of the final product) over time, and adjust it to respond to changes in the business context.

Arbitration using the closest offer principle of arbitrator behavior

In this paper we introduce a model of arbitration decision making which generalizes several previous models of both conventional arbitration and final offer arbitration. We derive the equilibrium offers that risk neutral disputants would propose, and show how these offers would vary under different arbitration procedures. In particular, we show that optimal offers made under conventional arbitration will always be more extreme than those made under final offer arbitration.

A note on joint optimization of maintenance and inventory

Previous work by Armstrong and Atkins examined age replacement and spare ordering decisions for a system which contained one machine subject to random failure and with only one spare machine in stock or on order at any one time. In this technical note we consider several extensions to that work which generalize the cost terms and the order lead time while retaining the one-machine one-spare structure of the original paper.

A Stochastic Salvo Model for Naval Surface Combat

In this paper, we propose a stochastic version of the salvo model for modern naval surface combat. We derive expressions for the mean and variance of surviving force strengths and for the probabilities of the possible salvo outcomes in forms simple enough to be implemented in spreadsheet software. Numerical comparisons of the deterministic and stochastic models indicate that while the two models tend to provide similar estimates of the average number of ships surviving a salvo, this average by itself can be highly misleading with respect to the likely outcomes of the battle. Our results also suggest that a navys preferences for risk (variability) and armament (offensive versus defensive) will depend on not only its mission objectives but also on whether it expects to fight from a position of strength or of weakness.

The reset decision for segregated fund maturity guarantees

Abstract A segregated fund is a mutual fund whose value is protected by a maturity guarantee. An investor in such a fund may have the option of periodically resetting this guarantee to extend its life and increase the guaranteed amount. We model this guarantee reset decision using a discrete time Markov chain and analyse a decision strategy based upon a return threshold. We characterise the optimal value for this threshold and examine its properties. We show that the intuitive strategy of resetting the guarantee whenever the fund’s value has increased is not optimal but seems to provide good results.