Bayes sequential strategies for crossing a field containing absorption points

A sequential decision problem is considered in which N particles have to cross a given field. Two alternative crossing paths are available. An unknown number of absorption points J₁ and J₂ are planted at each of the crossing paths. The bivariate prior distribution of (J₁,J₂) is given. If a particle passes close to an absorption point it may survive with probability s, 0 < s < 1. If a particle is absorbed, both the particle and the absorption point are ruined. There is no replacement of ruined absorption points. All absorption points act independently. The particles crciss the field in a consecutive order, and a crossing path can be chosen for each particle. The objective is to maximize the expected number of survivors. The Bayes sequential procedure is characterized. The csmditions under which the Bayes strategy is determined by the maximal posterior survival probabilities are specified.     

A queuing process with bilevel hysteretic service-rate control

The purpose of this paper is to analyze the effect of a particular control doctrine applied to the service mechanism of a queuing process. A bilevel hysteretic control based on queue length control levels is employed in an M/M/1 queuing system. Expressions are obtained for queue length probabilities, the first two factorial moments of queue length and two figures of merit for describing control performance under the assumption of statistical equilibrium. Computational examples illustrate the effects on queuing processes subject to this type of control. Several cost formulae are considered for comparison of costs when the queue control doctrine is varied. Situations in which hysteretic control is useful are discussed.     

Solutions for a class of n-person games in partition function form

A unique polyhedral solution is given for most n-person games in partition function form when only partitions into coalitions with 1, n-1, and n players have large payoffs.     

Some pros and cons of MIL-STD-414

MIL-STD-414 has been in existence in its original form since 1957. Obviously, there are some things that are right about 414. But there are some changes to the standard that are long overdue. This article presents some pros and cons of 414 and a recommendation that it be replaced by a MIL-STD-414A. Two concerns regarding ANSI/ASQC Z1.9 are discussed.     

Application of renewal theory to continuous sampling plans

Renewal theory is used to study the effectiveness of a class of continuous sampling plans first introduced by Dodge. This approach provides a simple way of viewing and computing the long-run Average Outgoing Quality (AOQ) and its maximum AOQL. More importantly, it is used to study the average outgoing quality in a short production run through an approximation formula AOQ^*(t). Formulas for AOQ and AOQ^*(t) are provided. By simulation, it is found that AOQ^*(t) is sufficiently accurate in situations corresponding to actual practice.