Pattern Time Distributions and Their Applications

9610046罗斯这项研究调查了随机过程的某些性质，这些性质适用于生产系统中的操作问题。特别地，对于具有任意分布的独立的、同分布的随机变量序列，调查者研究特定(固定)模式出现的第一时间的分布。这样的序列可以表示各种实用量中的任何一个；例如，质量特征的观测值的移动平均，或者多组件的、容易发生故障的系统的连续状态。解决这个问题的传统方法试图研究嵌入马尔可夫链的结构，并被证明在计算上是困难的。研究人员提出了一种基于更新理论论证的新方法，以获得边界和近似，从而提供分析工具和高效的模拟过程。一个相关的问题，也在这个项目中研究，涉及到改进基于中心极限定理的卷积逼近。虽然这项工作的主要目的是理论上的，但研究人员也将研究这些问题的计算方面。这项工作与可靠性和质量控制方面的基本问题直接相关，特别是在多变量控制图领域。因此，这项研究可望在多变量质量监测领域既取得可应用于广泛问题的理论进展，又能产生实用的新工具。后者是运筹学中一个活跃且极其重要的领域，基于随机过程的技术有望在这一领域做出重大贡献。

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.