Confidence intervals for reliability and quantile functions with application to NASA space flight data

    Authors

    A. Heard;M. Pensky

    Comments

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    Abbreviated Journal Title

    IEEE Trans. Reliab.

    Keywords

    confidence intervals; generalized gamma distribution; Jeffreys; non-informative prior; GENERALIZED GAMMA-DISTRIBUTION; BINOMIAL PROPORTION; DISTRIBUTIONS; Computer Science, Hardware & Architecture; Computer Science, Software; Engineering; Engineering, Electrical & Electronic

    Abstract

    This paper considers the construction of confidence intervals for a cumulative distribution function F(z), and its inverse quantile function F-1(u), at some fixed points z, and u on the basis of an i.i.d. sample (X) under bar = {X-i}(i=1)(n), where n is relatively small. The sample is modeled as having a flexible, generalized gamma distribution with all three parameters being unknown. Hence, the technique can be considered as an alternative,to non-parametric confidence intervals, when X is a continuous random variable. The confidence intervals are constructed on the basis of Jeffreys noninformative prior. Performance of the resulting confidence intervals is studied via Monte Carlo simulations, and compared to the performance of nonparametric confidence intervals based on binomial proportion. It is demonstrated that the confidence intervals are robust; when data comes from Poisson or geometric distributions, confidence intervals based on a generalized gamma distribution outperform nonparametric confidence intervals. The theory is applied to the assessment of the reliability of the Pad Hypergol Servicing System of the Shuttle Orbiter.

    Journal Title

    Ieee Transactions on Reliability

    Volume

    55

    Issue/Number

    4

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    591

    Last Page

    601

    WOS Identifier

    WOS:000242547400004

    ISSN

    0018-9529

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