Pattern Time Distributions and Their Applications

小行星9610046 本研究探讨了随机过程的某些性质，这些性质在生产系统的操作问题中具有应用。 特别是，对于具有任意分布的独立同分布随机变量序列，研究者研究特定（固定）模式出现的第一次分布。 这样的序列可以表示各种实际量中的任何一个;例如，质量特性观测值的移动平均值，或多部件、易故障系统的连续状态。 传统的方法来解决这个问题，试图研究嵌入马尔可夫链的结构，并证明是计算困难的。 研究人员提出了一种新的方法，基于更新理论的参数，以获得边界和近似，可以导致分析工具和有效的仿真程序。 一个相关的问题，也在这个项目中研究，涉及改进的中心极限定理为基础的卷积近似。 虽然这项工作的主要重点是理论上的，调查人员也将研究这些问题的计算方面。 这项工作直接关系到可靠性和质量控制的基本问题，特别是在多元控制图领域。 因此，这项研究预计将导致理论上的进步，可以应用到广泛的问题，以及在多元质量监测领域的实用新工具。 后者是运筹学的一个活跃且极其重要的领域，其中基于随机过程的技术有望做出重大贡献。

9610046 Ross This research investigates certain properties of stochastic processes that have applications to operational problems in production systems. In particular, for an independent, identically distributed sequence of random variables with arbitrary distribution, the investigator studies the distribution of the first time at which a particular (fixed) pattern appears. Such a sequence may represent any of a variety of practical quantities; e.g., a moving average of observations of quality characteristics, or the successive states of a multi-component, failure-prone system. Traditional approaches to this problem have attempted to study the structure of imbedded Markov chains and prove to be computationally intractable. The investigator proposes a new approach based on renewal-theoretic arguments to obtain bounds and approximations that can lead to analysis tools and efficient simulation procedures. A related problem, also studied in this project, involves improving on central limit theorem-based approximations of convolutions. While the primary thrust of the work is theoretical, the investigator will study the computational aspects of these problems as well. This work has direct relevance to fundamental problems in reliability and quality control, particularly in the area of multivariate control charts. Thus this research is expected to result in both theoretical advances that can be applied to a wide range of problems as well as in practical new tools in the area of multivariate quality monitoring. The latter is an active and extremely important area of operations research, and one in which stochastic process-based techniques can be expected to make significant contributions.