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Type-I hybrid censoring of multiple samples. (English) Zbl 1432.62329
Summary: We consider inference based on multiple samples subject to type-I hybrid censoring. The original data is supposed to be obtained as failure times from \(k \geq 2\) independent type-I censored sequential \(r\)-out-of-\(n\) systems. For the mean \(\vartheta\) of exponentially distributed lifetimes, we derive the distribution of the maximum likelihood estimator \(\hat{\vartheta}\) given the condition that at least one failure has been observed in the \(k\) samples. As special cases, we get results for particular multi-sample hybrid censoring models, that is, for multi-sample type-I hybrid censoring and multi-sample type-I progressive hybrid censoring, respectively. As a tool, we need expressions for the convolutions of B-splines in terms of iterative divided differences. The resulting expressions are used to determine the exact density functions efficiently as well as to construct exact confidence intervals for \(\vartheta\). Furthermore, we propose two approximated two-sided confidence intervals as an alternative for larger sample sizes. The results are illustrated by data as well as by simulations.

MSC:
62N01 Censored data models
90C90 Applications of mathematical programming
Software:
StInt
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