Estimating Component Characteristics from System Failure-Time Data

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 <(<(F)over bar>)over cap>F(N)(t) of the component survival function (F) over bar (t) is identified and shown to be accessible numerically in any application of interest. The asymptotic distribution of <(<(F)over bar>)over cap>(N)(t) is also identified, facilitating the construction of approximate confidence intervals for F(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. (C) 2010 Wiley Periodicals, Inc. Naval Research Logistics 57: 380-389, 2010