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.     

One-person games of economic survival

This paper discusses the one-person economic survival game model with a discrete probability distribution for the contribution to surplus variable. The general game model and strategies in these games are examined, and necessary conditions which an undominated, stationary strategy must satisfy are obtained. For a special class of these games a mathematical formulation of the value of the game is given, and examples and theorems which relate to undominated strategies in this class are presented. This paper, in some sense, is a sequel to a portion of a paper by Shubik and Thompson [7] which appeared in this journal.     

The fixed charge problem

A fundamental unsolved problem in the programming area is one in which various activities have fixed charges (e.g., set-up time charges) if operating at a positive level. Properties of a general solution to this type problem are discussed in this paper. Under special circumstances it is shown that a fixed charge problem can be reduced to an ordinary linear programming problem.     

Finite statistical games and linear programming

The dual linear programs associated with finite statistical games are investigated and their optimal solutions are interpreted. The usual statistical game is generalized to a two-sided (inference) game and its possible application as a tactical model is discussed.     

Optimum sequential search with discrete locations and random acceptance errors

Much work has been done in search theory; however, very little effort has occurred where an object's presence at a location can be accepted when no object is present there. The case analyzed is of this type. The number of locations is finite, a single object is stationary at one location, and only one location is observed each step of the search. The object's location has a known prior probability distribution. Also known are the conditional probability of acceptance given the object's absence (small) and the conditional probability of rejection given the object's presence (not too large); these Probabilities remain fixed for all searching and locations. The class of sequential search policies which terminate the search at the first acceptance is assumed. A single two-part optimization criterion is considered. The search sequence is found which (i) minimizes the probability of obtaining n rejections in the first n steps for all n, and (ii) maximizes the probability that the first acceptance occurs within the first n steps and occurs at the object's location for all n. The optimum sequential search policy specifies that the next location observed is one with the largest posterior probability of the object's presence (evaluated after each step from Bayes Rule) and that the object is at the first location where acceptance occurs. Placement at the first acceptance seems appropriate when the conditional probability of acceptance given the object's absence is sufficiently small. Search always terminates (with probability one). Optimum truncated sequential policies are also considered. Methods are given for evaluating some pertinent properties and for investigating the possibility that no object occurs at any location.     

Optimizability of utility and value functions

For more than a decade, multiattribute utility/value theory and multiobjective mathematical programming have offered different approaches to similar problems. Unfortunately, the two areas have developed with little interaction in spite of their common aims. We consider the use of utility/value functions in a mathematical programming framework, and demonstrate that these functions often possess desirable properties from an optimization point of view. We conclude that a hybridization of approaches is more viable than is perhaps commonly assumed.