Confidence intervals for reliability growth models with small sample sizes

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Abstract

Fully Bayesian approaches to analysis can be overly ambitious where there exist realistic limitations on the ability of experts to provide prior distributions for all relevant parameters. This research was motivated by situations where expert judgement exists to support the development of prior distributions describing the number of faults potentially inherent within a design but could not support useful descriptions of the rate at which they would be detected during a reliability-growth test. This paper develops inference properties for a reliability-growth model. The approach assumes a prior distribution for the ultimate number of faults that would be exposed if testing were to continue ad infinitum, but estimates the parameters of the intensity function empirically. A fixed-point iteration procedure to obtain the maximum likelihood estimate is investigated for bias and conditions of existence. The main purpose of this model is to support inference in situations where failure data are few. A procedure for providing statistical confidence intervals is investigated and shown to be suitable for small sample sizes. An application of these techniques is illustrated by an example.
Original languageEnglish
Pages (from-to)257-262
Number of pages6
JournalIEEE Transactions on Reliability
Volume52
Issue number2
DOIs
Publication statusPublished - Jun 2003

Keywords

  • reliability
  • reliability management
  • management theory
  • statistics

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  • Impacts

    International standards and working practices of UK Aerospace & Defence industry changed by reliability growth modelling

    Lesley Walls (Participant) & John Quigley (Participant)

    Impact: Impact - for External PortalEconomic and commerce, Professional practice, training and standards

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