Chapter 4. Stochastic Models of Failure

  1. Nozer D. Singpurwalla

Published Online: 19 NOV 2007

DOI: 10.1002/9780470060346.ch4

Reliability and Risk: A Bayesian Perspective

Reliability and Risk: A Bayesian Perspective

How to Cite

Singpurwalla, N. D. (2006) Stochastic Models of Failure, in Reliability and Risk: A Bayesian Perspective, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470060346.ch4

Author Information

  1. The George Washington University, Washington DC, USA

Publication History

  1. Published Online: 19 NOV 2007
  2. Published Print: 4 AUG 2006

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470855027

Online ISBN: 9780470060346



  • stochastic models of failure;
  • Lebesgue decomposition formula;
  • mean residual life (MRL);
  • failure rate function or hazard rate function;
  • predictive failure rate function;
  • multivariate analogues of failure rate function;
  • hazard potential of items and individuals;
  • probability models for interdependent lifelengths;
  • causality and models in cascading failures


This chapter contains sections titled:

  • Introduction

  • Preliminaries: Univariate, Multivariate and Multi-indexed Distribution Functions

  • The Predictive Failure Rate Function of a Univariate Probability Distribution

  • Interpretation and Uses of the Failure Rate Function – the Model Failure Rate

  • Multivariate Analogues of the Failure Rate Function

  • The Hazard Potential of Items and Individuals

  • Probability Models for Interdependent Lifelengths

  • Causality and Models for Cascading Failures

  • Failure Distributions with Multiple Scales