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Many large organizations have developed ambitious programs to build reliability databases by collecting field failure data from a large variety of components. To make the database concise, the component lifetime data are recorded in an aggregate way in these databases. The data format is different from traditional lifetime data and the statistical inference is challenging. In this talk, we propose a general parametric estimation framework for the aggregate data. We first address the failure-censored aggregate data, where each data point is a summation of a series of collective failures representing the cumulative operating time of one component position from system commencement to the last component replacement. Then, we consider the time-censored aggregate data, where only the number of component replacements in a component position during an operation time interval is reported. An approximate Bayesian computation algorithm that does not require evaluating the likelihood function is proposed, and a model selection procedure is proposed to identify an appropriate model for the time-censored aggregate data.
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