A sequential bayes procedure for reliability demonstration

A common problem in life testing is to demonstrate that the mean time to failure, θ, exceeds some minimum acceptable value, say θ₁, with a given confidence coefficient γ. When this is true, it is said that “θ₁ has been demonstrated with a confidence γ”. In this paper a Sequential Bayes Procedure (SBP) for demonstrating (by means of. a probability statement) that θ exceeds θ₁ is presented. The SBP differs from the classical procedure in the sense that a prior distribution is assumed on the parameter θ, calling for a Bayesian approach. The procedure is based on the sequence of statistics.     

A comparative study of demand forecasting techniques for military helicopter spare parts

This paper deals with techniques applicable to predicting spare parts demand for military helicopters. The military helicopter is a distinct weapons system, whose unique configuration may preclude the direct application of forecasting techniques which have proved successful for other weapon systems. Furthermore, although the military helicopter has become extremely important tactically in modern warfare, it has received scant attention in terms of research concerning its supply support. Specifically, this paper summarizes research done to measure and compare the forecasting accuracy of six mathematical models, as they were applied to three prominent military helicopters. In addition, the paper describes attempts that were made to define, where possible, the conditions under which a specific forecasting technique might be applicable. In general, it is shown that the most accurate set of helicopter spare parts demand forecasts are produced by a second order polynomial exponential smoothing model. This model is observed to have most accurately described the highly volatile, and upward-trended demand time series which were the subject of the study.     

A solution for queues with instantaneous jockeying and other customer selection rules

This paper presents a general solution for the M/M/r queue with instantaneous jockeying and r > 1 servers. The solution is obtained in matrices in closed form without recourse to the generating function arguments usually used. The solution requires the inversion of two (Z^r?1) × (2^r?1) matrices. The method proposed is extended to allow different queue selection preferences of arriving customers, balking of arrivals, jockeying preference rules, and queue dependent selection along with jockeying. To illustrate the results, a problem previously published is studied to show how known results are obtained from the proposed general solution.     

The value statement

Frequently there exists an insufficient amount of actual data upon which to base a decision. In this paper a method is presented whereby the subjective opinions of a group of qualified persons are utilized to quantify the relative importance of a finite number of parameters or objectives. A means of testing the consistency among the judges is given which allows the decision maker to determine the validity of the opinions gathered. The application presented here is in the area of Multiple Incentive Contracting. Namely, a method is proposed to facilitate the answering of the question, “What is the value to the purchaser of an incremental change in the performance of a system?” Such a vehicle is not essential to the methodology proposed.     

A methodology for estimating expected usage of repair parts with application to parts with no usage history

In this paper a model is presented which focuses on the difficult problem of predicting demands for items with extremely low usage rates. These form the bulk of repair parts in military systems. The basic notion underlying the model is the pooling of usage data for common design items with movement for the purpose of estimating usage rates for similar items which have shown no movement. A unique feature of the model is that it also makes possible the estimation of usage rates for items newly introduced into a system for which no previous usage history is available.     

Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs

Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs.     

A proof for the longest-job-first policy in one-machine scheduling

We consider a one-machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due-date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.     

Hyperbolic integer programming

The hyperbolic integer program is treated as a special case of a hyperbolic program with a finite number of feasible points. The continuous hyperbolic program also belongs to this class since its solution can be obtained by considering only the extreme points of the feasible set. A general algorithm for solving the hyperbolic integer program which reduces to solving a sequence of linear integer problems is proposed. When the integer restriction is removed, this algorithm is similar to the Isbell-Marlow procedure. The geometrical aspects of the hyperbolic problem are also discussed and several cutting plane algorithms are given.