Nonparametric Estimation for a General Repair Model.

Abstract

The construction and analysis of repair models is an important area in reliability. A commonly used model is the minimal repair model. Under this model, repair restores the state of the system to its level prior to failure. Kijima introduced repair models that could be classified as "better-than-minimal". Under Kijima's models, the system, upon repair, is functionally the same as a working system of lesser age which has never experienced failure. In this paper, we present a new approach to the modelling of better-than-minimal repair models. Using this approach, we construct a general repair model that contains Kijima's models as special cases. We also study the problem of estimating the distribution of the time to first failure of a system maintained by general repair. We make use of counting processes to show strong consistency of the estimator and prove results on weak convergence. Finally, we derive a Hall-Wellner type asymptotic confidence band for the estimator.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1995
Accession Number
ADA300996

Entities

People

  • Crisanto Dorado
  • Jayaram Sethuraman
  • Myles Hollander

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Availability
  • Consistency
  • Convergence
  • Distribution Functions
  • Estimators
  • Gaussian Processes
  • Integral Equations
  • Military Research
  • Probability
  • Random Variables
  • Simulations
  • Statistical Algorithms
  • Stochastic Processes
  • Theorems
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Facility/Structural Engineering.
  • Statistical inference.