On a Markov-Modulated Shock and Wear Process

Abstract

We present transient and asymptotic reliability indices for a single-unit system that is subject to Markov-modulated shocks and wear. The transient results are derived from the (transform) solution of an integro-differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time-scaled version of the cumulative degradation at time t. This asymptotic result leads to a simple normal approximation for a properly centered and space-scaled version of the system's lifetime distribution. Two numerical examples illustrate the quality of the normal approximation.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 2009
Accession Number
ADA536698

Entities

People

  • Dustin G. Mixon
  • Jeffrey P. Kharoufeh

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Degradation
  • Differential Equations
  • Distribution Functions
  • Equations
  • Logistics
  • Markov Chains
  • Markov Processes
  • Military Research
  • Operations Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Reliability
  • Standards
  • Stochastic Processes
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.
  • Statistical inference.

Technology Areas

  • Space