Faculty Publications

Predictability Of Operational Processes Over Finite Horizon

Document Type

Article

Keywords

Bayesian predictive distribution, entropy, maintenance, minimal repair, mixed Poisson processes, nonhomogeneous Poisson processes, reliability, renewal processes, stochastic orderings

Journal/Book/Conference Title

Naval Research Logistics

Volume

58

Issue

6

First Page

531

Last Page

545

Abstract

Operational processes are usually studied in terms of stochastic processes. The main information measure used for predictability of stochastic processes is the entropy rate, which is asymptotic conditional entropy, thus not suitable for application over a finite horizon. We use the conditional entropy to study the predictability of stochastic processes over the finite horizon. It is well-known that the conditional entropies of stationary processes decrease as the processes evolve, implying that, on average, their pasts become more informative about prediction of their future outcomes. Some important operational processes such as martingale, models for maintenance policies, nonhomogeneous Poisson, and mixed Poisson processes are nonstationary. We show that as a nonstationary process evolves, it may provide more information or less information about the future state of the system. We develop results for comparing the predictability of stochastic processes. © 2011 Wiley Periodicals, Inc.

Department

Department of Mathematics

Original Publication Date

1-1-2011

DOI of published version

10.1002/nav.20465

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