Causative matrix technique for deriving interim period transition probabilities in nonstationary markov process

The Markov assumption that transition probabilities are assumed to be constant over entire periods has been applied in economic and social structures, for example, in the analysis of income and wage distributions. In many cases, however, nonstationary transition probabilities exist over different periods. Based on causative matrix technique, this study shows a binomial approximation for obtaining nonstationary interim transition probabilities under undisturbance when the first and the last transition matrices are known.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

On the aggregation of preferences

The article attempts to show how network theory may be applied to gain new and better insights into basic economic problems. Starting with a precise definition of what is meant by acting and, in particular, by economic acting, we direct the line of argumentation toward solving the problem of how to aggregate economic decisions. Results indicate that network theory might well prove itself to be a powerful instrument in developing a theory of human behavior much more comprehensive than currently used models.     

A targeting model that minimizes collateral damage

This paper considers the problem of allocating weapons to achieve targeting objectives while simultaneously minimizing aggregate damage to surrounding nonmilitary facilities, each of which has an upper limit to the damage it is permitted to incur. A model is formulated which assumes only that damage to individual targets or associated facilities does not decrease as the number of allocated weapons increases. An implicit enumeration algorithm, based on that of Lawler and Bell is described that yields optimal integer solutions. An example is presented.     

A characterization of the value of zero-sum two-person games

For the family D, consisting of those zero-sum two-person games which have a value, the value-function on D is characterized by four properties called objectivity, monotony, symmetry and sufficiency.     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

Efficient multinomial selection in simulation

Consider a simulation experiment consisting of v independent vector replications across k systems, where in any given replication one system is selected as the best performer (i.e., it wins). Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (Procedure BEM) prescribes a minimum number of replications, denoted as v*, so that the probability of correctly selecting the true best system (PCS) meets or exceeds a prespecified probability. Assuming that larger is better, Procedure BEM selects as best the system having the largest value of the performance measure in more replications than any other system. We use these same v* replications across k systems to form (v*)^k pseudoreplications that contain one observation from each system, and develop Procedure AVC (All Vector Comparisons) to achieve a higher PCS than with Procedure BEM. For specific small-sample cases and via a large-sample approximation we show that the PCS with Procedure AVC exceeds the PCS with Procedure BEM. We also show that with Procedure AVC we achieve a given PCS with a smaller v than the v* required with Procedure BEM. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 459–482, 1998     

Estimating reliability of components with increasing failure rate using series system data

The maximum likelihood estimator (MLE) for a distribution function with increasing failure rate is derived, based on a collection of series system data. Applications can arise in industries where operating environments make available only such system-level data, due to system configuration or type-II censoring. The estimator can be solved using isotonic regression. For the special case in which systems contain one component, the estimator is equivalent to the restricted maximum likelihood estimator of Marshall and Proschan [9]. The MLE is illustrated using emergency diesel generator failure data from the nuclear industry. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 115–123, 1998