Estimating component characteristics from system failure‐time data |
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Authors: | Debasis Bhattacharya Francisco J Samaniego |
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Institution: | 1. Visva‐Bharati University, West Bengal, India;2. University of California, Davis, California 95616 |
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Abstract: | Suppose that failure times are available from a random sample of N systems of a given, fixed design with components which have i.i.d. lifetimes distributed according to a common distribution F. The inverse problem of estimating F from data on observed system lifetimes is considered. Using the known relationship between the system and component lifetime distributions via signature and domination theory, the nonparametric maximum likelihood estimator N(t) of the component survival function (t) is identified and shown to be accessible numerically in any application of interest. The asymptotic distribution of N(t) is also identified, facilitating the construction of approximate confidence intervals for (t) for N sufficiently large. Simulation results for samples of size N = 50 and N = 100 for a collection of five parametric lifetime models demonstrate the utility of the recommended estimator. Possible extensions beyond the i.i.d. framework are discussed in the concluding section. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010 |
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Keywords: | Nonparametric maximum likelihood estimation component lifetime distribution inverse problems reliability system signatures dominations asymptotic distribution approximate confidence intervals identifiability |
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